Rafter Length Calculator
The length of a common rafter from the span and roof pitch — with the overhang, plumb cut angle and total timber.
How long to cut the rafters.
How the rafter length calculator works
A rafter is the hypotenuse of the roof triangle. From the run (half the span) and the pitch, the rafter length is run ÷ cos(pitch), and the rize is run × tan(pitch).
The plumb cut at the ridge is the pitch angle itself; the seat cut at the wall is its complement. The overhang adds along the same slope, so it too is multiplied by 1/cos(pitch).
Formula: rafter = run / cos θ; rise = run × tan θ
Worked examples
| Inputs | Rafter length | Note |
|---|---|---|
| 8 m span at 22.5° | 4.33 | 4.33 m rafter |
| A 5-in-12 pitch | 4.333 | 22.6° — almost the same |
| A steep roof | 5.657 | rafter 5.66 m, rize 4 m |
FAQFrequently asked questions
How do I find rafter length?
Divide the run — half the span — by the cosine of the pitch angle.
What is a 5-in-12 pitch?
Five units of rize for every twelve of run, which is 22.6°. It is the standard American way of quoting pitch.
What angle do I cut?
The plumb cut at the ridge is the pitch angle; the seat cut at the wall plate is 90° minus it.
Does the overhang change the angle?
No, only the length. It continues along the same slope, so it is also divided by cos(pitch).
Should I add for the birdsmouth?
The seat cut removes material but not length. What this gives is the theoretical length along the top edge — add a little for trimming.
Where these figures come from
- The Engineering ToolBox — material densities, coverage and unit data — bulk densities, concrete at 2,400 kg/m³, board and sheet sizes
- Gypsum Association — gypsum board sizes — 4 × 8 and 4 × 12 ft sheets
- ADA Standards for Accessible Design — ramps (§405) — maximum running slope 1:12
- International Code Council — the International Residential Code
Last checked: September 2026. Coverage rates and material sizes are typical manufacturer figures — check the product you buy.