Rafter Length Calculator
Rafter length = (run + overhang) × slope factor, where run = half the span minus half the ridge and the slope factor = √(pitch² + 144) ÷ 12. A 24 ft span at 6/12 with a 12 in overhang and 1.5 in ridge gives about 14.47 ft, so buy 16 ft stock. Pitch: Roof Pitch Calculator.
How it's calculated: Run = span ÷ 2 − ridge thickness ÷ 2; slope factor = √(pitch² + 12²) ÷ 12; total length = (run + overhang) × slope factor.
Result appears here
Fill in the fields and press Calculate.
Formula, calculation, assumptions and sources
Run = span ÷ 2 − (ridge thickness ÷ 2)
Slope factor = √(pitch² + 12²) ÷ 12
Body length = run × slope factor; overhang length = overhang × slope factor
Total rafter length = (run + overhang) × slope factor
Run the calculation to see each step with your own numbers.
24 ft span, 6-in-12 pitch, 12 in overhang, 1.5 in ridge.
Run = 12 − 0.0625 = 11.94 ft
Slope factor = √180 ÷ 12 = 1.1180
Body length = 11.94 × 1.118 = 13.35 ft; overhang = 1 × 1.118 = 1.12 ft
Total rafter length ≈ 14.47 ft → buy 16 ft stock; plumb cut 26.6° from vertical
- Common rafter on a symmetrical gable roof; the run is measured from the outside of the wall plate to the centre of the ridge.
- Measured along the top edge of the rafter (the 'line length'); the birdsmouth and plumb cuts are laid out from this — see the Birdsmouth Cut Calculator.
- Hip, valley and jack rafters are longer/shorter and cut at compound angles — not covered here.
- Does not size the rafter (depth/species/grade) — see the Wood Beam Span and Floor Joist calculators and the IRC rafter tables.
- Why subtract half the ridge board?
- The rafter run is measured to the centreline of the roof, but the rafter actually stops against the face of the ridge board. Subtracting half the ridge thickness gives the true run to the rafter's plumb cut.
- Does this include the overhang?
- It gives you both: the body length (heel to ridge) and the overhang length separately, plus the total. Cut the tail after the rafter is up so the fascia line is straight.
- How long is a rafter for a 24 ft span?
- About 14.47 ft at a 6-in-12 pitch with a 12 in overhang and a 1.5 in ridge board: 13.35 ft from heel to ridge plus 1.12 ft of tail. Buy 16 ft stock.
- How do I find rafter length from the roof pitch?
- Work out the slope factor, √(pitch² + 144) ÷ 12, and multiply it by the horizontal run. A 6-in-12 roof has a factor of 1.118, so each foot of run needs 1.118 ft of rafter.
- Which lumber length should I buy for the rafters?
- The next stock length above the total rafter length, because the plumb and tail cuts are laid out from it. A 14.47 ft rafter is cut from 16 ft stock.
Rafter geometry
Right-triangle roof-framing geometry (line length = run × √(pitch² + 12²) ÷ 12). Standard framing references — e.g. 'Roof Framing' (Marshall Gross); IRC R802. No empirical constant.
Unit conversion
About the Rafter Length Calculator
The Rafter Length Calculator gives the cut length of a common rafter — the body from the wall to the ridge, the overhang, and the total — plus the plumb-cut angle, from the building span, roof pitch and overhang. It works along the top edge of the rafter (the line length); the birdsmouth notch is laid out from that with the Birdsmouth Cut Calculator. It does not size the rafter — depth, species and grade come from a span table or an engineer.
What you enter
- Building span (outside to outside of walls)
- Roof pitch (rise-in-12) — Rise per 12 units of run. A low slope is 3–4; a steep roof is 9–12.
- Overhang (horizontal, at the eave) — Horizontal projection of the eave. Common: 12–24 in.
- Ridge board thickness — 1.5 in for a 2x ridge, 1.75+ for LVL. The rafter run stops half this short of the span centre.
What you get back
- Rafter run (per rafter) — the exact result of the calculation.
- Total rise — the exact result of the calculation.
- Rafter body length (heel to ridge) — the exact result of the calculation.
- Overhang length (along the rafter) — the exact result of the calculation.
- Total rafter length — Heel to rafter tail, before the plumb cuts. Buy the next stock length up.
- Plumb-cut angle from vertical — the exact result of the calculation.
The formula, a worked example, the assumptions behind it and the sources are shown in full below the calculator.
Related calculators
- Roof Pitch Calculator — Roof angle, slope factor and rise-in-12 pitch from a rise and run.
- Birdsmouth Cut Calculator — Birdsmouth (seat) cut dimensions for a rafter at a given pitch.
- Roof Area Calculator — Sloped surface area of a simple gable or hip roof from its footprint and pitch.
- Framing Calculator — Stud count and lineal feet for a wall at a given stud spacing.
Related articles
- What Is a Birdsmouth Cut on a Rafter? — A birdsmouth cut is a notch cut into the underside of a rafter so it seats flush and level on the top of the wall plate below it.
- Understanding Roof Pitch: 4/12, 6/12 and Other Ratios — Roof pitch notation like 6/12 tells you the rise over a 12-unit run — here's how to read it and what different ratios mean for a roof in practice.
Part of the Roofing calculators.