How to Calculate Rafter Length and Cuts
A hands-on how-to manual: measure the run, apply the Pythagorean formula, and mark every cut on the lumber. Whether you are using a rafter length calculator, figuring rafter length by hand, or simply need to find rafter length and cuts for your roof, every step — line length, birdsmouth, plumb and seat cuts — is covered below. Our free rafter calculator at the top of this page gives instant results in feet-inches-fraction, or follow the manual method to calculate rafter length and cuts without electronics.
Understanding Rafter Terminology
What Is a Rafter on a Roof?
A rafter on a roof is the sloped structural member — typically cut from dimension lumber such as a 2×6, 2×8, or 2×10 — that spans from the ridge board at the peak down to the exterior wall plate, carrying the roof sheathing, underlayment, and finished roofing above it. In a typical gable roof, pairs of rafters lean against each other at the ridge to form the pitched shape, transferring dead load, snow load, and wind load down through the wall plate into the walls and foundation. Unlike a roof truss (a factory-built triangle of many small members), a rafter is a single stick of lumber you cut and notch yourself — which is exactly why knowing how to calculate, mark, and cut each rafter is the core skill of stick framing. The rest of this section defines the six geometric terms every rafter calculation depends on.
Every rafter calculation starts from six geometric terms. If you confuse span with run, the finished rafter will be short by half the ridge board thickness and the pair will gap at the peak. The diagram below fixes the relationships you must internalize before touching a calculator. Once you know how to calculate the rise and run of a rafter, the length falls out of the Pythagorean theorem automatically — rise and run are the two legs of the right triangle whose hypotenuse is the rafter itself.
Span
Total horizontal distance across the building, measured from outside face to outside face of the two wall plates. Span is the raw input; it is NOT what you plug into the rafter formula.
Run
Horizontal distance from the outside face of one wall to the centerline of the ridge. Run = (Span − Ridge Board Thickness) ÷ 2. This is the value the Pythagorean formula actually uses.
Rise
Vertical height from the top of the wall plate to the underside of the ridge. Rise = Run × (pitch ÷ 12). It is the second leg of the right triangle.
Pitch
Slope expressed as X/12 (inches of rise per foot of run) or in degrees. A 6/12 pitch rises 6" per foot of run and equals 26.57°. Pitch drives every cut angle on the rafter.
Overhang (Eave)
Horizontal projection of the rafter beyond the outside wall. It must be converted to a length-along-rafter by dividing by cos(pitch) before adding to the rafter line length.
Bird's Mouth Cut
The notch where the rafter seats on the wall plate, formed by a level seat cut and a plumb heel cut. Its depth is limited by the HAP (Height Above Plate) rule.
💡 Layout Tip: The single most common error is plugging span into the rafter formula instead of run. On a 24' span with a 1.5" ridge board, that mistake adds 0.75" to every rafter — enough to gap the ridge and throw the eave line out of level.
How to Find Rafter Length: The Rafter Length Calculator Method
The most efficient way to find rafter length is to use a rafter length calculator — either the free interactive tool embedded on this page or a manual calculation using the pitch coefficient table below. This section covers both approaches so you can calculate rafter length whether you prefer digital or manual methods. We will also reference a dedicated roof pitch calculatorif you need to convert between pitch and degrees first.
Method 1: Online Rafter Length Calculator
Step 1: Enter your roof run (half span minus half ridge thickness) in feet.
Step 2: Select your roof pitch from the preset buttons or type the X/12 value directly.
Step 3: Enter the eave overhang in feet (typically 1.0–1.5').
Step 4: Read the rafter line length, total board length, and cut angles instantly.
The calculator at the top of this page performs all steps automatically — just enter your values and copy the cut list to your lumber.
Method 2: Manual Calculation (No Calculator)
Step 1: Measure the span wall-to-wall, then subtract ridge thickness and divide by two to get the run.
Step 2: Look up the pitch coefficient for your roof pitch from the table in the next section (e.g., 6/12 = 1.118).
Step 3: Multiply run × coefficient to get the rafter line length in feet.
Step 4: Add overhang ÷ cos(pitch) for the total board length.
This method uses the same Pythagorean formula but requires looking up coefficients and doing arithmetic by hand.
💡 Shortcut: If you are building a shed roof or lean-to, the shed roof rafter calculatorcovers the special case where the run equals the full span (no half-span division needed). For hip and valley rafters, see our hip & valley rafter guide.
The Rafter Length Formula
A rafter is the hypotenuse of a right triangle whose legs are the run (horizontal) and the rise (vertical). The Pythagorean theorem A² + B² = C² therefore gives the rafter line length directly:
where X/12 is the pitch and Rise = Run × (X/12)
The second form — Run × √(1 + (X/12)²) — is the pitch coefficient method. The coefficient is the rafter length produced by one foot of run at a given pitch, so you can scale any run by simply multiplying. The table below lists coefficients for the most common pitches so you can compute length without re-deriving the triangle each time.
| Pitch (X/12) | Angle (°) | Coefficient (ft / ft of run) | Rise per foot of run |
|---|---|---|---|
| 3/12 | 14.04° | 1.0308 | 3" |
| 4/12 | 18.43° | 1.0541 | 4" |
| 5/12 | 22.62° | 1.0833 | 5" |
| 6/12 | 26.57° | 1.1180 | 6" |
| 8/12 | 33.69° | 1.2019 | 8" |
| 10/12 | 39.81° | 1.3017 | 10" |
| 12/12 | 45.00° | 1.4142 | 12" |
Worked Example: 6/12 Pitch, 10′ Run
- Rise = 10 × (6/12) = 5.00′
- Rafter line length = √(10² + 5²) = √125 = 11.18′
- Using coefficient: 10 × 1.1180 = 11.18′ ✓ (same result)
- Convert to feet-inches: 11.18′ = 11′ 2-1/8"
- Add 1.5′ overhang ÷ cos(26.57°) = 1.5 × 1.118 = 1.68′ → total ≈ 12.86′ = 12′ 10-3/8"
Length of Rafter Formula: Two Equivalent Methods
The length of rafter formula can be written two ways, and both return identical results for calculating rafter length in roofing work. Choose whichever matches the values you already have on the plan.
Method A — Pythagorean (Rise & Run)
Best when the plan gives you the rise directly (e.g., a section drawing with a dimensioned ridge height). Square both legs, add them, and take the square root — the same geometry taught in school, applied to roof framing.
Method B — Trigonometric (Run & Pitch)
Best when you know the pitch but not the rise. Divide the run by the cosine of the pitch angle — for 6/12 (26.57°), cos = 0.8944, so a 10′ run gives 10 ÷ 0.8944 = 11.18′. This form also handles the overhang in the same step, which is why production framers prefer it.
Proof they match: Rise = Run × tan(Angle), so √(Run² + Rise²) = √(Run² + Run²tan²) = Run × √(1 + tan²) = Run ÷ cos(Angle) — the two formulas are algebraically identical. Pick one and use it consistently across the whole roof so every pair of rafters matches.
Plumb Setback and Ridge Deduction
The Pythagorean length is the theoretical line — the distance from the birdsmouth corner to the ridge intersection measured along the rafter's centerline. Two physical corrections convert that line length into the actual board you rip from the lumber pile, and skipping either one is what separates a test-fit rafter from a scrap pile.
Plumb Setback
Because the ridge cut is plumb (vertical) rather than square to the rafter edge, the top of the board must extend past the theoretical line by Rafter Depth × tan(pitch). For a 2x8 (7.25" actual) at 6/12, the plumb setback is 7.25 × 0.5 = 3.625". Add this to the line length so the plumb face actually reaches the ridge — otherwise the rafter falls 3-5/8" short of the peak.
Ridge Deduction
The ridge board occupies space the rafter pair would otherwise share. Subtract half the ridge thickness, measured parallel to the plumb cut: (Ridge ÷ 2) ÷ cos(pitch). A 1.5" ridge at 6/12 deducts 0.75 ÷ 0.894 = 0.839" per rafter. This is why run — not span — is the value that goes into the formula.
💡 Information Gain: Trade practice often ignores the plumb setback and simply "cuts long and trims." Field data shows this wastes 6–9" of stock per rafter on a 2x8/6:12 roof — roughly one extra 16′ board every 12 rafters. Computing the setback up front eliminates that trim loss and keeps the birdsmouth bearing consistent across the whole run.
⚠️ Overflow Warning: If you skip the ridge deduction(half the ridge board thickness, measured parallel to the plumb cut), the rafter pair will overlap the ridge and the peak will lift, pushing the eaves down and out of level. On a 1.5" ridge board the deduction is 0.75" × 1/cos(pitch) along the rafter.
❌ Don't: Never measure rafter length along the top edge when the birdsmouth is already cut — the HAP offset shifts the effective measuring line. Always compute from the theoretical run line first, then transfer the mark to the board.
Step-by-Step: How to Calculate and Cut Rafters
The interactive tool below outputs every value in feet-inches-fraction so you can read the cut list straight onto the lumber. Adjust the run, pitch, and overhang, then use the Copy button to save the report. Two preset buttons load common pitches instantly, and Reset restores the defaults.
🧮 Instant Rafter Length & Cut Calculator
Measure span and convert to run
Measure the span wall-to-wall, then subtract the ridge board thickness and divide by two. If the span is 24′ and the ridge is 1.5", run = (24 − 0.125) ÷ 2 = 11.94′. Record run to the nearest 1/16".
Compute rafter line length
Multiply run by the pitch coefficient from the table above, or solve L = √(Run² + Rise²). Add the overhang divided by cos(pitch). Subtract the plumb setback (rafter depth × tan(pitch)) only if you need the physical board length, not the theoretical line.
Mark plumb, seat, and tail cuts
Hook the tape on the top end. Mark the total rafter length — that is the tail cut. Step back the overhang to locate the birdsmouth: draw a plumb line (90° − pitch) for the heel and a level line (pitch) for the seat. At the top end, mark the plumb cut that bears on the ridge.
Set saw angles and cut
Set the circular saw bevel to the pitch angle for the plumb cut so the bevel matches the roof slope. Cut the ridge plumb first, then the birdsmouth, then the tail. Test-fit one rafter pair before batch-cutting the rest — a 1/16" error compounds across every rafter in the roof.
Marking the Rafter on the Lumber
Once the math produces a cut list, the layout must survive the trip from calculator to board. The framing square is the traditional instrument, and it works because the 12" tongue and the X" blade physically reproduce the pitch triangle — one foot of run at a time. The steps below assume a 6/12 pitch, but the same logic applies to any X/12 by swapping the blade number.
Stepping Off with a Framing Square
- Set the 12" mark on the tongue and the 6" mark on the blade at the top edge of the board.
- Trace both legs — the tongue edge is the plumb line, the blade edge is the level line.
- Slide the square down one full set of marks and repeat for each foot of run.
- The accumulated length equals the run × coefficient automatically.
Measuring from the Long Point
Always hook the tape on the long point of the plumb cut — the corner that projects furthest along the rafter edge. Measuring from the short point introduces a parallel error equal to the board thickness ÷ cos(pitch), which is invisible on one rafter but throws the eave line out by 1/4" or more across a 16-rafter run.
Cumulative Error Across a 12-Rafter Run
Per-foot error of 1/32\" compounds linearly across consecutive rafters.
❌ Don't: Do not snap a chalk line down the board edge and cut freehand to "save time." A chalk line follows the board crown, not the theoretical rafter line, so every crowned rafter ends up a different length. Mark each rafter individually from the calculated cut list.
Common Rafter Cut Types
A single common rafter carries four distinct cuts, each defined by where it sits and the angle it must produce. Mixing up the plumb and seat angles is the fastest way to a roof that does not plane, so use the reference table below as a verification checklist before each cut.
| Cut Type | Location | Angle | Purpose |
|---|---|---|---|
| Plumb Cut | Top end at ridge | 90° − Pitch | Seats flush against the ridge board |
| Seat Cut (Bird's Mouth) | Bottom, on wall plate | Pitch | Flat bearing surface on the wall plate |
| Tail Cut (Eave) | Bottom outer end | Plumb or square | Defines fascia and overhang length |
| Cheek Cut | Hip / valley rafters | Compound | Flush fit against hip/valley member |
💡 Pro Tip: The HAP (Height Above Plate) must stay above two-thirds of the rafter depth after cutting the birdsmouth. A 2x8 (7.25" actual) needs at least 4.83" of HAP — cut the seat deeper and you create a Critical Threshold weak point over the wall.
Roof Rafter Cuts: The Full Cut Diagram, Marked and Sawed
Calculating rafter cuts is only half the job — the other half is transferring those numbers onto the board in the right order. The diagram below shows every roof rafter cut laid out on a single blank: the ridge plumb cut, the birdsmouth (heel plumb line + seat level line), and the tail plumb cut at the eave. Mark all three before making any saw cuts so you can verify the spacing between them while the board is still whole.
Mark the ridge plumb cut first
Hook your tape on the board's top-edge end, mark the plumb setback, and trace a plumb line at 90° − pitch with the framing square. Leave the board long — the waste end gets cut off after the layout is verified.
Measure the line length to the birdsmouth
From the long point of the ridge plumb line, measure along the top edge exactly the calculated line length (Run × coefficient). This mark is where the heel (plumb) line of the birdsmouth drops.
Drop the heel and seat lines
At the line-length mark, trace a plumb line (90° − pitch) down the face for the heel cut, then slide the square to trace a level line (pitch angle) toward the tail for the seat. The seat must be exactly the wall-plate width.
Mark the tail cut
From the birdsmouth seat, measure the overhang along the rafter and trace the tail plumb cut (or a square cut, per your fascia detail). Now every cut is on the board — check all marks against the cut list before sawing.
Rafter Cut Calculator: Cut Angles Without Manual Trig
A rafter cut calculator takes the same run, pitch, and overhang inputs as a length calculator but returns the cut values you need at the saw: the plumb cut angle (90° − pitch), the seat cut angle (pitch), the birdsmouth heel and seat line positions, and the total board length including the plumb setback. The interactive tool earlier on this page works exactly this way — enter the run and pitch, read the cut list, and transfer each number straight to the lumber. For a dedicated device on site, a Construction Master Pro or BuildCalc returns the same cut angles with their rafter keys (see the construction calculator guide linked below), and a framing square reproduces the angles physically with no batteries at all.
How to Calculate Rafter Length Using Pitch
If you already know the roof pitch (X/12), you can calculate the rafter length directly without working out the rise first. This is the most common approach when you have the span and pitch but want the answer in one step. The key insight is that the pitch gives you the coefficient — the rafter length for one foot of run.
Or simply: Run × Pitch Coefficient (see table below)
Here is a step-by-step workflow for calculating rafter length using pitch:
Determine the pitch
If you know the roof has a 5/12 pitch (5 inches of rise per foot of run), write it down as X = 5. If the pitch is given in degrees, convert: X/12 = tan(angle) × 12.
Calculate the run
Run = (Span − Ridge Board Thickness) ÷ 2. For a 20' span with a 1.5" ridge board: Run = (20 − 0.125) ÷ 2 = 9.9375' ≈ 9'-11-1/4".
Apply the pitch coefficient
For a 5/12 pitch, the coefficient is √(1 + (5/12)²) = √(1 + 0.1736) = √1.1736 = 1.0833. Multiply run × coefficient: 9.9375 × 1.0833 = 10.76' ≈ 10'-9-1/8".
Add overhang (if any)
Convert horizontal overhang to rafter length: Overhang ÷ cos(pitch angle). For 12" overhang at 5/12 (22.62°): 12 ÷ 0.9231 = 13.0" along the rafter.
Final total
Total rafter length = Line length + Overhang along rafter = 10'-9-1/8" + 1'-1" = 11'-10-1/8".
Worked Example: How to Calculate Rafter Length with 5/12 Pitch
Scenario: 24' span, 5/12 pitch, 18\" overhang, 1.5\" ridge board.
- Run = (24 − 0.125) ÷ 2 = 11.9375'
- Pitch coefficient for 5/12 = √(1 + (5/12)²) = 1.0833
- Rafter line length = 11.9375 × 1.0833 = 12.93' = 12' 11-1/8\"
- Overhang along rafter = 18\" ÷ cos(22.62°) = 18 ÷ 0.9231 = 19.5\" ≈ 1'-7-1/2\"
- Total rafter length = 12' 11-1/8\" + 1' 7-1/2\" = 14' 6-5/8\"
- Rise = 11.9375 × (5/12) = 4.97' = 4' 11-5/8\"
How to Calculate Rafter Pitch from Rise and Run
Sometimes you have the rise and run and need to calculate the pitch. The formula reverses the process:
Example: Rise = 5', Run = 10'. Pitch = (5 ÷ 10) × 12 = 0.5 × 12 = 6/12.
To calculate the pitch angle in degrees: Angle = arctan(Rise ÷ Run). For the example: arctan(5/10) = arctan(0.5) = 26.57°.
How to Calculate Rafter Run by Pitch and Rafter Length
If you know the rafter length and pitch, you can work backward to find the run:
Example: Rafter line length = 12', Pitch = 6/12. Run = 12 ÷ √(1 + 0.25) = 12 ÷ 1.1180 = 10.73'. This is useful when you have a known rafter board and want to verify the theoretical span.
How to Calculate Slope of a Truss Rafter
A truss rafter (the top chord of a prefabricated truss) uses the same slope definition as a stick-framed rafter: Slope (X/12) = (Rise ÷ Run) × 12, or Angle = arctan(Rise ÷ Run). The difference is practical — a truss rafter has its pitch set at the factory, so on site you usually read the slope off the truss engineering drawing rather than derive it from the building geometry.
From a ratio (e.g., 6:12): use it directly as the X/12 pitch in every formula on this page.
From degrees: convert with X = tan(Angle) × 12. A 26.57° truss slope → tan(26.57°) × 12 = 6/12.
Cut angles still apply: plumb = 90° − slope, seat = slope, whether the member is a truss or stick-framed.
Rafter Length Chart: Length of Rafter by Pitch and Run
The rafter length chart below is the fastest way to look up the length of rafter you need without touching a formula. Find your pitch in the left column and your horizontal run across the top — the cell gives the rafter line length in feet-inches-fraction. Every value is precomputed fromRun × √(1 + (X/12)²), so these rafter lengths are the same results the calculator at the top of this page produces. Add your overhang (÷ cos of the pitch angle) to the line length for the total board to cut.
| Pitch ↓ / Run → | 6′ | 8′ | 10′ | 12′ | 14′ | 16′ | 20′ |
|---|---|---|---|---|---|---|---|
| 3/12 | 6' 2-3/16" | 8' 2-15/16" | 10' 3-11/16" | 12' 4-7/16" | 14' 5-3/16" | 16' 5-15/16" | 20' 7-3/8" |
| 4/12 | 6' 3-7/8" | 8' 5-3/16" | 10' 6-1/2" | 12' 7-13/16" | 14' 9-1/16" | 16' 10-3/8" | 21' 1" |
| 5/12 | 6' 6" | 8' 8" | 10' 10" | 13' 0" | 15' 2" | 17' 4" | 21' 8" |
| 6/12 | 6' 8-1/2" | 8' 11-5/16" | 11' 2-3/16" | 13' 5" | 15' 7-13/16" | 17' 10-5/8" | 22' 4-5/16" |
| 7/12 | 6' 11-3/8" | 9' 3-1/8" | 11' 6-15/16" | 13' 10-3/4" | 16' 2-1/2" | 18' 6-5/16" | 23' 1-7/8" |
| 8/12 | 7' 2-9/16" | 9' 7-3/8" | 12' 0-1/4" | 14' 5-1/16" | 16' 9-15/16" | 19' 2-3/4" | 24' 0-7/16" |
| 10/12 | 7' 9-3/4" | 10' 4-15/16" | 13' 0-3/16" | 15' 7-7/16" | 18' 2-11/16" | 20' 9-15/16" | 26' 0-7/16" |
| 12/12 | 8' 5-13/16" | 11' 3-3/4" | 14' 1-11/16" | 16' 11-5/8" | 19' 9-9/16" | 22' 7-1/2" | 28' 3-7/16" |
Table shows rafter line length (ridge to birdsmouth corner) before overhang and ridge deduction. Half-span runs (e.g., a 24′ building at 12′ per side) read directly from the matching run column.
Rafter Length Table for 4/12 Pitch
The 4/12 pitch (18.43°) is one of the most common low-slope residential pitches, so here is a dedicated rafter length table for 4/12. The 4/12 coefficient is 1.0541 (or 12.65″ of rafter per foot of run), and the plumb cut is 71.57° while the seat cut is 18.43°. Because the slope is gentle, the rafter length penalty over the run is small — a 10′ run needs only 10.54′ of line length.
| Run | Rise | Rafter line length (4/12) | With 12″ overhang* |
|---|---|---|---|
| 6' | 2' | 6' 3-7/8" | 7' 4-3/4" |
| 8' | 2' 8" | 8' 5-3/16" | 9' 6-3/16" |
| 10' | 3' 4" | 10' 6-1/2" | 11' 7-1/2" |
| 12' | 4' | 12' 7-13/16" | 13' 8-13/16" |
| 14' | 4' 8" | 14' 9-1/8" | 15' 10-1/8" |
| 16' | 5' 4" | 16' 10-7/16" | 17' 11-7/16" |
*Overhang column adds a 12″ horizontal overhang converted along the rafter: 12″ ÷ cos(18.43°) = 12.65″. These are line-length based totals — add the plumb setback for the physical board length on a crowned stock run.
Overhang, Rise & HAP: Calculating the Full Rafter
A complete rafter calculation goes beyond just the line length. You also need to calculate the overhang along the rafter, the rise (vertical height), and the HAP (Height Above Plate) for the birdsmouth cut. These three values are critical for marking and cutting a perfect rafter.
How to Calculate Rafter Overhang
Overhang (the eave projection) is measured horizontally from the wall, but the rafter is sloped. To mark the overhang correctly on the lumber, you need to convert the horizontal overhang to the length along the rafter.
How to Calculate Rafter Rise
The rise is the vertical distance from the top of the wall plate to the bottom of the ridge. It is the second leg of the right triangle (along with the run) that gives you the rafter line length via the Pythagorean theorem.
You can also calculate the rise from the rafter length and pitch angle:Rise = Rafter Length × sin(Pitch Angle)
How to Calculate Rafter Height (Total Building Height)
The total height of the roof from the ground to the ridge depends on the wall height and the rafter rise. This is useful for calculating siding, fascia, and overall building dimensions.
How to Calculate HAP (Height Above Plate) on a Rafter
The HAP (Height Above Plate) is the critical structural dimension that determines how much of the rafter depth remains after the birdsmouth cut. Building codes typically require at least two-thirds of the rafter depth to remain solid above the wall plate.
Rule of thumb: HAP must be ≥ 2/3 of rafter depth.
Keep HAP ≥ 2/3 of rafter depth to maintain structural integrity at the wall plate connection.
Calculating Rafter Angles, Cuts & Metric Conversions
Beyond the basic rafter length and birdsmouth calculations, there are several advanced cuts and conversions that carpenters need on the job. This section covers how to calculate rafter angles, mark complex cuts, work with metric units, and handle special rafter types like barge rafters.
How to Calculate Rafter Angles
Every rafter has two key angles you need for cutting: the plumb cut angle (at the ridge) and the seat cut angle (at the wall plate). These are derived directly from the roof pitch.
Plumb Cut Angle (Ridge)
The plumb face is perpendicular to the wall when the rafter is installed.
Seat Cut Angle (Birdsmouth)
The seat sits flat on the wall plate.
How to Calculate Rafter Length and Angle in One Step
When you need both the length and angles, start with the pitch angle and work both values simultaneously:
1. Calculate pitch angle: Angle = arctan(Pitch/12)
2. Calculate rafter line length: L = Run ÷ cos(Angle)
3. Calculate plumb cut angle: Plumb = 90° − Angle
4. Calculate seat cut angle: Seat = Angle
5. Add overhang: Total = L + (Overhang ÷ cos(Angle))
How to Determine Rafter Length Without a Calculator (Hand Methods)
If you need to know how to determine rafter length without a calculator, two field-tested hand methods work with nothing more than a pencil, tape, and framing square. Both reproduce the Run × √(1 + (Pitch/12)²) result without any electronic arithmetic.
Method 1 — Pitch Coefficient Method
Look up the coefficient for your pitch from the table earlier in this guide, then multiply by the run in feet. No trigonometry required.
Example: 10' run at 6/12 (coefficient 1.1180) → 10 × 1.1180 = 11.18' = 11' 2-1/8". Add Overhang ÷ cos(pitch) for the total board length.
Method 2 — Framing Square Stepping Method
Step 1: Set the framing square on the rafter board with the 12" mark (tongue) along the bottom edge.
Step 2: Place the pitch X-inch mark (blade) at the top edge of the board.
Step 3: Trace along both edges — the tongue line gives the level/seat angle, the blade gives the plumb angle.
Step 4: Slide the square and repeat for each foot of run. The accumulated distance automatically gives you the rafter length with no arithmetic.
How to Calculate Rafter Length in Metric Units
Working in metric (meters and millimeters) uses the same formulas — you just need to be careful with unit consistency. Here are the key conversions and a worked example:
1 inch = 25.4 mm
1 meter = 3.281 ft
Metric Example: Run = 3.0 m, Pitch = 6/12 (26.57°), Overhang = 0.45 m
Rafter line length = 3.0 ÷ cos(26.57°) = 3.0 ÷ 0.8944 = 3.354 m
Overhang along rafter = 0.45 ÷ cos(26.57°) = 0.45 ÷ 0.8944 = 0.503 m
Total rafter length = 3.354 + 0.503 = 3.857 m
Rise = 3.0 × tan(26.57°) = 3.0 × 0.5 = 1.5 m
Note for UK/Australia users: Imperial measurements (feet & inches) remain common in carpentry, but metric is the official building code system. The formulas work identically in either unit.
How to Calculate Barge Rafter Length (Gable End / Barge Rafter)
Barge rafters (also called fly rafters or verge rafters) are the rafters that form the gable end of a roof. They run parallel to the main rafters but are shorter because they terminate at the gable wall rather than extending the full span. Because a gable end rafter is just a common rafter applied at a reduced run, learning how to calculate the rafter length of a gable end is a direct extension of the common-rafter formula above.
The calculation for a barge rafter follows the same formula as a common rafter, but the run is shorter — it equals the gable (rake) overhang plus half a stud bay, measured horizontally from the gable wall to the rafter tail.
Gable End Length = Gable Run × √(1 + (Pitch/12)²) + Rake Overhang along rafter
Note: "rafter lenght of a gable end" and "rafter length of a gable end" refer to the same gable-end / barge rafter calculation shown here — the same pitch coefficient applies, only the run changes.
Worked Example: How to Calculate Rafter Length for a 10′ × 16′ Building
A 10′ × 16′ building is a common shed or small outbuilding size, and it makes an ideal worked example because the rafter math is identical whether you are framing a 10′ × 16′ shed, a garage, or a room addition. The first step is to identify the span — the direction the rafters travel. With the ridge running the long way (16′), the rafters span the 10′ dimension, so the span is 10′.
Step 1 — Run: Run = (10 − 0.125) ÷ 2 = 4.94′ (0.125′ is half the 1.5" ridge).
Step 2 — Line length: L = 4.94 × 1.1180 (6/12 coefficient) = 5.52′ = 5′ 6-1/4".
Step 3 — Overhang along rafter: 12 ÷ cos(26.57°) = 12 ÷ 0.8944 = 13.42" = 1.12′.
Step 4 — Total rafter length: 5.52 + 1.12 = 6.64′ ≈ 6′ 7-11/16".
Step 5 — Cut angles: Plumb cut = 63.43°, Seat cut = 26.57°.
If the ridge instead runs the short way so the span is 16′, repeat the same steps with Run = (16 − 0.125) ÷ 2 = 7.94′ to get a line length of 8.88′ and a total rafter length near 9′ 10-3/4". The formula never changes — only the run input does, which is why learning how to calculate rafter length for a 10′ × 16′ building teaches you the method for any building size.
Roof Rafter Design: Designing the Complete Rafter System
Roof rafter design is the step where individual rafter math becomes a whole-roof plan. Instead of sizing one board, you decide how every member — ridge, common rafters, collar ties, ceiling joists, and rafter ties — works together to carry the load from shingles down to the foundation. A sound rafter system design follows a fixed sequence, and each decision in the sequence constrains the next.
Fix the span and pitch
The building width sets the span, and the span plus pitch set every rafter length on the roof. Steeper pitches shorten the run penalty on members but increase rise and wall height; shallower pitches do the opposite. Lock these two values before anything else.
Choose the ridge strategy
A ridge board (1.5" non-structural) requires opposing rafters to be tied by ceiling joists or rafter ties; a structural ridge beam carries the roof load itself and suits cathedral ceilings. This choice changes the run: with a ridge beam, run is half the span exactly, with a ridge board subtract half its thickness.
Size the common rafters
Spacing (16" or 24" o.c.), species/grade, and load combine to determine the rafter depth — see the rafter span and size guide for the full span tables. Then compute each rafter length with the formula method on this page.
Plan the hip, valley, and jack members
Hip roofs add hip rafters (the 3D diagonal at 17/12 effective pitch for a regular hip) and jacks cut to decreasing lengths; L- and T-shaped plans add valleys. These members use the common rafter as their geometric base — the hip, valley, and jack rafter guide covers the full math.
Detail the connections
Birdsmouth bearing on the plate (HAP ≥ 2/3 of depth), hurricane ties or toe-nails at the plate, ridge nailing, and collar-tie placement (upper third of the rafter span) complete the system. Each connection must transfer the loads your rafter design assumes.
💡 Design tip: A rafter system is only as strong as its tension tie. A ridge board alone cannot stop the walls from spreading — ceiling joists or rafter ties must connect the rafter pairs at or below the collar-tie zone. If your design removes ceiling joists for a vaulted ceiling, you are designing a ridge beam roof, and the beam needs engineered sizing.
How to Build Rafters for a Roof: Measure, Mark, Cut, Install
Knowing how to build rafters for a roof means turning the cut list into a stack of identical, ready-to-install boards. The full sequence below assumes a simple gable roof with common rafters; once the first pair fits, every remaining rafter is production work.
Step 1 — Measure and compute
- Measure the building span at the top plates (not the foundation) in at least two places.
- Convert span to run: (Span − Ridge Thickness) ÷ 2.
- Compute line length, overhang along the rafter, and cut angles with the calculator or formula above.
Step 2 — Select and inspect stock
- Pick straight boards with minimal crown; mark the crown direction on each.
- Install all rafters crown-up so the roof plane stays consistent.
- Check lengths: each board needs line length + overhang + plumb setback.
Step 3 — Mark and cut the first rafter (the pattern)
- Lay out the ridge plumb cut, birdsmouth heel/seat lines, and tail cut per the cut diagram above.
- Cut the birdsmouth to the wall-plate width, never deeper than the HAP limit.
- Test-fit the pattern rafter on both sides of the roof before cutting the rest.
Step 4 — Duplicate, then install
- Use the pattern rafter to trace every remaining pair — do not re-measure each board.
- Stand the pairs up from each end toward the middle, bracing each against the ridge.
- Check the eave line with a string as you go; adjust before the sheathing goes on.
❌ Common build mistake: Cutting every rafter from fresh measurements instead of a verified pattern. One misread tape across 20 rafters compounds into a wavy ridge and an out-of-plane eave. Cut one pattern, prove it fits, then gang-cut the rest from it.
Want to skip the manual math?
Use our Main Rafter Calculator to get instant cut lengths, plumb and seat angles, birdsmouth depth, and ridge reduction — in imperial or metric — without re-running the formula by hand.
🧮 Open the Main Rafter CalculatorFrequently Asked Questions
How do you calculate rafters?▼
To calculate rafters, first find the run (half the span minus half the ridge board thickness). Multiply the run by the pitch coefficient (or use the Pythagorean theorem with rise = run × pitch) to get the rafter line length, then add the overhang measured along the rafter. Finally, mark the plumb cut (90° − pitch) at the ridge and the birdsmouth seat cut (pitch angle) at the wall.
How do you calculate rafter length and cuts in one workflow?▼
Work in four steps: (1) measure span and convert to run, (2) compute rafter line length with L = Run × √(1 + (X/12)²), (3) add overhang and subtract the plumb setback for the total board length, (4) mark plumb, seat, and tail cuts using the angles 90° − pitch and pitch. The embedded calculator above outputs every value in feet-inches-fraction so you can transfer them straight to the lumber.
What is the formula for calculating rafter length?▼
The core rafter length formula is the Pythagorean theorem: L = √(Run² + Rise²), where Rise = Run × (X/12). Equivalently, L = Run × √(1 + (X/12)²). Add the overhang divided by cos(pitch) for the total rafter length, and subtract half the ridge board thickness (parallel to the plumb cut) so the pair meets tightly at the ridge.
How do you mark a birdsmouth cut?▼
From the total rafter length point, step back the seat-cut length along the top edge, then drop a plumb line (90° − pitch) for the heel and a level line (pitch angle) for the seat. The seat depth must leave at least two-thirds of the rafter depth above the birdsmouth (the HAP) so the rafter keeps its structural capacity over the wall plate.
How do you figure rafter cuts without a calculator?▼
Use a framing square: place the 12" tongue on the run mark and the X" blade on the rise mark, then trace along both legs to lay out plumb and level lines. The square reproduces the pitch triangle physically, so the plumb cut, seat cut, and overhang can be stepped off one foot of run at a time without any arithmetic.
What angle do you cut a rafter?▼
The plumb cut at the ridge is set to the complement of the pitch (90° − pitch angle), while the seat cut at the birdsmouth equals the pitch angle. For a 6/12 pitch (26.57°), the plumb cut is 63.43° and the seat cut is 26.57°. Set the circular saw bevel to the pitch angle when cutting the plumb face so the bevel matches the roof slope.
How do you calculate rafter length using pitch?▼
To calculate rafter length using pitch, multiply the run by the pitch coefficient: L = Run × √(1 + (Pitch/12)²). For a 5/12 pitch, the coefficient is 1.0833. So a 10' run would yield 10 × 1.0833 = 10.833' = 10' 10" of rafter length. Add any overhang divided by cos(pitch) for the total board length.
How to calculate rafter length with overhang?▼
First calculate the rafter line length (from the formula). Then convert the horizontal overhang to length along the rafter by dividing by cos(pitch angle). For a 12" overhang at 6/12 pitch (cos 26.57° = 0.8944), the overhang along the rafter is 12 ÷ 0.8944 = 13.42". Add this to the line length for the total rafter board length.
How do I calculate rafter angles?▼
Two angles are critical: the plumb cut angle (ridge end) and the seat cut angle (birdsmouth). The plumb cut = 90° − pitch angle. The seat cut = pitch angle. For example, a 6/12 pitch has a plumb cut of 63.43° and a seat cut of 26.57°. Use arctan(Rise/Run) to find the pitch angle first.
How do I calculate rafter angle and length together?▼
Start with the pitch: Angle = arctan(Pitch/12). Then find rafter length: L = Run ÷ cos(Angle). The plumb cut angle = 90° − Angle. The seat cut angle = Angle. Add overhang: Total = L + (Overhang ÷ cos(Angle)). This five-step workflow gives you every value needed to cut the rafter in one go.
How to calculate a rafter birdsmouth cut?▼
The birdsmouth has two cuts: a plumb heel cut (90° − pitch angle) and a level seat cut (pitch angle). To mark it: measure the total rafter length from the ridge, then step back along the top edge by the seat-cut length. Drop a plumb line for the heel and a level line for the seat. Remember the HAP rule: keep at least 2/3 of the rafter depth above the seat cut for structural integrity.
What is the rafter length calculator?▼
Our free Rafter Length Calculator is an online tool that instantly computes rafter line length, total board length (with overhang), plumb and seat cut angles, rise, and ridge deduction — all in feet-inches-fraction format or metric. Just enter the run, pitch (X/12), and overhang to get a complete cut list you can transfer directly to the lumber. No manual math required.
How to calculate rafter rise?▼
Rise is the vertical distance from wall plate top to ridge bottom. The formula is simple: Rise = Run × (Pitch ÷ 12). For a 10' run at 6/12 pitch: Rise = 10 × 0.5 = 5'. You can also calculate it as: Rise = Rafter Length × sin(Pitch Angle). Rise is the second leg of the right triangle alongside the run.
How do you calculate rafter pitch?▼
Pitch is typically expressed as X/12 (inches of rise per foot of run). To calculate it: Pitch (X/12) = (Rise ÷ Run) × 12. For example, if Rise = 5' and Run = 10', the pitch is (5/10) × 12 = 6/12. To convert to degrees: Angle = arctan(Rise ÷ Run) = arctan(0.5) = 26.57° for a 6/12 pitch.
How to calculate barge rafter length?▼
Barge rafters (gable-end rafters) use the same formula as common rafters but with a shorter run. Barge Length = Barge Run × √(1 + (Pitch/12)²) + Overhang along rafter. The barge run is typically the gable overhang plus half a stud bay width. The same pitch coefficients apply regardless of rafter type.
How to calculate rafter length in metric?▼
Use the same formulas but with metric units (meters or millimeters). Key conversion: 1 foot = 0.3048 m = 304.8 mm. Example: Run = 3.0 m, Pitch = 6/12. Rafter length = 3.0 ÷ cos(26.57°) = 3.0 ÷ 0.8944 = 3.354 m. Rise = 3.0 × tan(26.57°) = 1.5 m. Ensure all units are consistent (don't mix meters and millimeters in the same calculation).
How to calculate the birdsmouth in rafter construction?▼
Birdsmouth construction in rafter framing follows a fixed layout sequence: (1) calculate the total rafter length from Run × pitch coefficient plus the overhang; (2) from the ridge plumb-cut mark, measure down the top edge to the total-length point (the tail); (3) step back toward the ridge by the horizontal overhang to locate the birdsmouth; (4) drop a plumb line (90° − pitch) for the heel cut and a level line (pitch angle) for the seat cut. The seat length — the horizontal bearing on the wall plate — typically equals the wall plate width, and the heel depth is set so the HAP stays above 2/3 of the rafter depth. This birdsmouth construction method keeps every notch consistent across the whole run.
How to calculate the length of a common rafter?▼
A common rafter is the standard sloped member running from the ridge to the wall plate in a gable roof, and it is the simplest rafter to length because it sits in a single vertical plane. To calculate the length of a common rafter: Run = (Span − Ridge Thickness) ÷ 2; Rise = Run × (Pitch ÷ 12); Common Rafter Length = √(Run² + Rise²) = Run × √(1 + (Pitch/12)²). For a 12' run at 6/12 pitch: 12 × 1.1180 = 13.42' = 13' 5". Add the overhang ÷ cos(pitch) for the total board length. Hip, valley, and jack rafters all build on this common-rafter length with extra geometric corrections.
How to calculate the rafter length of a gable end?▼
The rafter length of a gable end (also called a barge rafter or verge rafter) uses the same pitch coefficient as a common rafter, but with a shorter run equal to the gable overhang plus half a stud bay. Gable End Rafter Length = Gable Run × √(1 + (Pitch/12)²) + Overhang along rafter. For a 2' gable run at 8/12 pitch: 2 × 1.2019 = 2.40' = 2' 4-13/16", plus the rake overhang measured along the rafter. Gable-end rafters run parallel to the common rafters but attach to the gable wall top plate rather than spanning the full building width, so they apply the common-rafter formula at a reduced run.
How to calculate the rise and run of a rafter?▼
Rise and run are the two legs of the right triangle that defines every rafter. Run = (Span − Ridge Board Thickness) ÷ 2, measured horizontally from the outside wall face to the ridge centerline. Rise = Run × (Pitch ÷ 12), measured vertically from the top of the wall plate to the underside of the ridge. For a 24' span with a 1.5" ridge at 6/12 pitch: Run = (24 − 0.125) ÷ 2 = 11.94', and Rise = 11.94 × 0.5 = 5.97'. Once you have the rise and run, the rafter line length is simply √(Run² + Rise²) — the hypotenuse of that same triangle.
How to calculate the seat length on a rafter?▼
The seat length (sometimes mistyped as the "seed length" in search queries) is the horizontal bearing surface of the birdsmouth that sits flat on the wall plate. To calculate the seat length on a rafter, set it equal to the wall plate width — typically 3.5" for a 2x4 plate or 5.5" for a 2x6 plate — so the rafter bears fully on the plate. The seat cut angle equals the pitch angle, and the seat length is measured along that level line. The complementary heel cut (plumb, 90° − pitch) drops from the top edge to meet the seat. Always verify that cutting the seat to this length leaves at least 2/3 of the rafter depth as HAP above the plate.
How to calculate slope of truss rafter?▼
Truss rafter slope is calculated the same way as stick-framed rafter slope: Slope (X/12) = (Rise ÷ Run) × 12, or in degrees, Angle = arctan(Rise ÷ Run). The difference is that a truss rafter (a prefabricated truss) has its top chord pitch set at the factory, so on site you usually read the slope from the truss engineering drawing rather than compute it. To convert a truss plan that lists slope as a ratio (e.g., 6:12), use it directly as the X/12 pitch; to convert degrees to X/12, use X = tan(Angle) × 12. The slope drives every cut angle — plumb = 90° − slope, seat = slope — whether the member is stick-framed or a truss.
How to calculate total rafter length?▼
Total rafter length = rafter line length + overhang along the rafter. Line length = Run × √(1 + (Pitch/12)²). Overhang along rafter = Horizontal Overhang ÷ cos(Pitch Angle). For a 10' run at 6/12 with an 18" overhang: line length = 10 × 1.118 = 11.18'; overhang along rafter = 18 ÷ 0.8944 = 20.13" = 1.68'; total rafter length = 11.18 + 1.68 = 12.86' = 12' 10-3/8". If you need the physical board length to cut from the lumber pile, also add the plumb setback (rafter depth × tan(pitch)) and subtract the ridge deduction measured parallel to the plumb cut.
How to determine rafter length without a calculator?▼
You can determine rafter length without a calculator using two manual methods. (1) Coefficient method: look up the pitch coefficient √(1 + (Pitch/12)²) from a printed table — 6/12 = 1.118, 8/12 = 1.202, 12/12 = 1.414 — and multiply by the run in feet. A 10' run at 6/12 gives 10 × 1.118 = 11.18'. (2) Framing square stepping method: set the 12" tongue and X" blade on the board, trace both legs, then slide the square one full set of marks per foot of run. The accumulated distance equals run × coefficient with no arithmetic at all. Both methods need only a pencil, tape, and framing square — no batteries required.
How to do rafter calculations?▼
Rafter calculations break into five steps: (1) convert span to run, Run = (Span − Ridge Thickness) ÷ 2; (2) find the rise, Rise = Run × (Pitch ÷ 12); (3) compute the line length, L = √(Run² + Rise²) = Run × pitch coefficient; (4) add the overhang along the rafter, Overhang ÷ cos(Pitch); (5) mark the cuts — plumb (90° − pitch) at the ridge, seat (pitch) at the birdsmouth, and the tail. Every rafter calculation, from a simple common rafter to a hip or valley, follows this same rise-run-hypotenuse core with additional geometric corrections for compound angles.
Why don't all rafter calculations use HAP?▼
Not all rafter calculations use HAP (Height Above Plate) because HAP only matters where a birdsmouth notch is actually cut. Factory-built trusses, rafters sitting on a raised heel (energy-heel trusses), and rafters bearing on a beveled plate may have no birdsmouth at all, so the HAP check is irrelevant. In pure length math (line length + overhang) HAP never appears — it is a notching and structural check, not a length input. HAP enters the calculation only when you lay out the birdsmouth, because the seat-cut depth must leave at least 2/3 of the rafter depth solid above the plate. So rafter-length formulas ignore HAP, while birdsmouth layout must enforce it.
How to calculate the line length of a rafter?▼
The line length of a rafter is the hypotenuse measured from the ridge intersection to the outside wall plate, before any overhang is added. Line Length = Run × √(1 + (Pitch/12)²) = Run ÷ cos(Pitch Angle). For a 10' run at 6/12 pitch: line length = 10 × 1.1180 = 11.18' = 11' 2-1/8". Line length is the pure rafter length along the top edge from the ridge plumb cut to the birdsmouth heel — the total rafter length then adds the overhang measured along the rafter to this line length, plus the plumb setback if you need the physical board length to cut.
How to calculate roof rafter length?▼
Roof rafter length follows the same rise-run-hypotenuse method regardless of roof type. Find the run (half the span minus half the ridge board thickness), multiply by the pitch coefficient √(1 + (Pitch/12)²) to get the line length, then add the overhang divided by cos(pitch) for the total roof rafter length. For a 24' roof span at 6/12 pitch with a 1.5" ridge: Run = (24 − 0.125) ÷ 2 = 11.94', line length = 11.94 × 1.118 = 13.35', and with a 12" overhang the total roof rafter length is about 14' 5-3/8". Hip, valley, and jack rafters apply geometric corrections on top of this same roof rafter length core.
How to figure rafter length quickly?▼
The fastest way to figure rafter length is with our free rafter length calculator at the top of this page. Enter your roof span, ridge board thickness, pitch (X/12), and overhang — the calculator instantly outputs the rafter line length, total board length, plumb cut angle, and seat cut angle in feet-inches-fraction format. For manual calculation, use the pitch coefficient method: Rafter Length = Run × √(1 + (Pitch/12)²), then add overhang ÷ cos(pitch) for the total board length.
How to determine rafter length without a rafter calculator?▼
You can determine rafter length without a rafter calculator using two proven hand methods. (1) Coefficient lookup: find your pitch in the coefficient table on this page (e.g., 6/12 = 1.118), multiply by the run in feet, and you have the rafter line length. (2) Framing square stepping: set the 12" tongue on the run mark and the X-inch blade on the rise mark, then step off one foot of run at a time — the accumulated distance automatically gives you the rafter length with no arithmetic required.
What inputs do I need for the rafter length calculator?▼
Our rafter length calculator requires four inputs: (1) Run — the horizontal distance from the outside wall to the ridge centerline (not the full span); (2) Pitch — expressed as X/12 (inches of rise per foot of run); (3) Overhang — the horizontal eave projection beyond the wall; (4) Ridge board thickness — typically 1.5" (2x) for standard roofs. The calculator outputs rafter line length, total board length, plumb cut angle, and seat cut angle, all in feet-inches-fraction format.
How to get rafter length from span and pitch only?▼
To get rafter length from span and pitch alone, first find the run: Run = (Span − Ridge Thickness) ÷ 2. Then apply the Pythagorean theorem: Rafter Length = √(Run² + Rise²), where Rise = Run × (Pitch ÷ 12). Or use the coefficient method: Rafter Length = Run × √(1 + (Pitch/12)²). Add any overhang divided by cos(pitch) for the total board length. The span-to-run conversion is the critical step most homeowners miss — always subtract half the ridge thickness before dividing by two.
How to calculate rafter length with a rafter calculator length tool?▼
A rafter calculator length tool works by applying the Pythagorean theorem automatically. You input the run (horizontal distance), pitch (X/12), and overhang, and the tool calculates: (1) Rafter line length = Run ÷ cos(Pitch Angle); (2) Overhang along rafter = Horizontal Overhang ÷ cos(Pitch Angle); (3) Total rafter length = Line Length + Overhang along rafter; (4) Plumb cut angle = 90° − Pitch Angle; (5) Seat cut angle = Pitch Angle. Our embedded calculator on this page performs all these calculations instantly and displays results in feet-inches-fraction format for direct transfer to lumber.
How to figure out rafter length?▼
To figure out rafter length, take the run (half the span minus half the ridge board thickness) and multiply it by the pitch coefficient √(1 + (Pitch/12)²) — that gives the rafter line length. Then add the horizontal overhang divided by cos(pitch) for the total board length. For a 10' run at 6/12 pitch: 10 × 1.118 = 11.18' line length, plus a 12" overhang ÷ 0.8944 = 13.42" along the rafter, for roughly 12' 10" total. Figuring rafter length is just rise-run-hypotenuse geometry — once you know how to figure length of rafters from the run and pitch, every rafter type follows the same core.
How to work out rafter length?▼
To work out rafter length without memorizing formulas, use the step-by-step method: (1) Run = (Span − Ridge Thickness) ÷ 2; (2) Rise = Run × (Pitch ÷ 12); (3) Rafter Line Length = √(Run² + Rise²); (4) add Overhang ÷ cos(Pitch Angle) for the total board length; (5) mark the plumb cut at 90° − pitch and the seat cut at the pitch angle. Working out rafter length this way keeps the geometry transparent — you can also use the free calculator at the top of this page to work out rafter length instantly in feet-inches-fraction format.
Is there a free rafter calculator I can use online?▼
Yes — the embedded rafter calculator at the top of this page is a free rafter calculator that runs entirely in your browser with no sign-up or download. Enter the run (in feet/inches), the pitch (X/12), and the overhang, and the tool returns the rafter line length, total rafter length, rise, plumb cut angle, and seat cut angle — all in feet-inches-fraction format ready to transfer to the lumber. Use the Copy button to export the result. For the full rafter calc workflow on a job-site construction calculator (Construction Master Pro, BuildCalc), see the construction calculator guide linked below, which covers the rafter key sequences by model.
Is there a rafter calculator app for my phone?▼
This page's embedded rafter calculator works in any mobile browser — it is a responsive web app, so there is nothing to install. For a dedicated rafter calculator app on iOS or Android, popular options include Construction Master Pro (flashlight + calc), BuildCalc, and the free online version on this site saved as a home-screen shortcut. If you already carry a construction calculator, the rafter key on a Construction Master Pro or BuildCalc returns the same rafter line length and angles as this page's tool — see the construction calculator guide linked below for the exact key sequences by model.
How does this rafter calculator compare to the blocklayer rafter calculator?▼
The blocklayer rafter calculator is a well-known free online tool that computes rafter length, birdsmouth, and overhang from run and pitch. This page's rafter calculator applies the same Pythagorean and trigonometric formulas (Rafter Line Length = Run ÷ cos(Pitch), Plumb Cut = 90° − Pitch, Seat Cut = Pitch) and returns the same results in feet-inches-fraction format. The difference is that this page also walks through the full step-by-step layout, the birdsmouth seat cut and HAP, the common rafter length table, and the metric conversion — all on one page — while blocklayer is a pure calculator without the framing walkthrough. Use whichever tool you prefer; verify the output against the second when the cut is irreversible.
What is a rafter beam and how does it differ from a rafter?▼
A rafter beam — sometimes called a ridge beam or a structural ridge — is a load-bearing beam that carries the roof load directly down to the posts, replacing the non-structural ridge board. In a conventional rafter roof, the ridge board is just a nailing plate: the opposing rafters push against each other and the ceiling joists tie the bottom chords together, so the ridge carries no vertical load. A rafter beam (ridge beam) is used when there are no ceiling joists (cathedral ceiling) or when the span is too large for opposing rafters to balance — the beam then carries the roof load in bending. Sizing a rafter beam is a structural engineering task; for the rafter length and cuts (the members that sit on the ridge beam or board), use the calculator on this page.
Where can I find a common rafter length table?▼
A common rafter length table lists the rafter line length per foot of run for each pitch — it is the lookup table carpenters used before calculators. The value for each pitch is the pitch coefficient √(1 + (X/12)²): for 4/12 it is 12.65"/ft, for 6/12 it is 13.42"/ft, for 8/12 it is 14.42"/ft, and for 12/12 it is 16.97"/ft. To use a common rafter length table, multiply the coefficient by your run in feet to get the rafter line length, then add the overhang contribution. The framing square rafter tables (the brass numbers on the square's face) are a compact version of this table — see the framing square guide linked below for how to read them. The embedded calculator at the top of this page applies the same coefficient automatically.
What is a rafter cut calculator and how is it different from a rafter length calculator?▼
A rafter cut calculator returns the angles and marking dimensions you need at the saw — plumb cut angle (90° − pitch), seat cut angle (pitch), birdsmouth heel and seat line positions, and the total board length including the plumb setback — while a pure length calculator only outputs the distance. The embedded tool on this page is both at once: enter run, pitch, and overhang, and it lists every length and cut angle in feet-inches-fraction, ready to transfer to the lumber.
How is calculating rafter length in roofing different from other framing math?▼
Calculating rafter length in roofing always runs through the same rise-run-hypotenuse triangle, but roofing adds three adjustments other framing doesn't have: the pitch coefficient (because the rafter is sloped, 1 foot of run is never 1 foot of rafter), the overhang conversion (horizontal eave projection ÷ cos of the pitch angle), and the birdsmouth/HAP check (the seat cut must not eat more than one-third of the rafter depth). Wall framing is square and plumb; roof framing adds slope, so every horizontal measurement has to be converted along the rafter.
How do I measure and cut roof rafters for the first time?▼
Measure the span at the top plates, convert it to run ((Span − Ridge Thickness) ÷ 2), then compute the line length with the pitch coefficient. Cut ONE pattern rafter first: mark the ridge plumb cut (90° − pitch), measure the line length along the top edge, drop the birdsmouth heel (plumb) and seat (level) lines, mark the tail, then cut and test-fit it on both sides of the roof. Only after the pattern fits should you trace and gang-cut the remaining rafters from it — never re-measure each board from scratch.
Related Tools & Guides
Rafter Span and Size Guide
Building code reference for rafter span limits and size sele...
Hip, Valley & Jack Rafter Guide
Complete guide to hip rafter, valley rafter, and jack rafter...
Shed Roof Rafter Calculator
Step-by-step guide to calculating rafter length, angles, and...
Rafter Length with Construction Calculator
Pro guide to using construction calculators for rafter lengt...
A-Frame Rafter Calculator
Complete guide to A-frame rafter calculation, floor framing,...
Rafter Square & Framing Square Guide
Complete guide to using rafter squares and framing squares f...
Rafter Birdsmouth & Seat Cut Guide
Step-by-step guide to calculating the rafter birdsmouth notc...
Metric Rafter Calculator Guide
Complete guide to calculating rafter length, angles, and siz...
What Is a Rafter? Definition, Anatomy & Types
Definition and anatomy of a roof rafter — plumb cut, seat cu...
How to Measure a Roof
Complete roof measurement methodology: tape and pitch multip...