Rafter Length Calculator: Pitch, Run and Common Rafters

Quick Answer: The length of a common rafter is found with Pythagoras: rafter length = √(run² + rise²), where the run is the horizontal distance from the wall plate to the ridge centre (half the building span, less half the ridge thickness) and the rise is the vertical height gained over that run. The pitch angle relates the two: rise = run × tan(pitch), so rafter length per metre of run = 1 ÷ cos(pitch) = sec(pitch). For example, a 3 m run at 30° pitch gives a rise of 1.732 m and a rafter length of √(3² + 1.732²) = 3.46 m before adding the eaves overhang.

Summary

Getting rafter lengths right is the difference between a roof that lands cleanly on the wall plate and a day spent re-cutting timber. The maths is simple — it is just a right-angled triangle — but the practical pitfalls are in the setting-out: where you measure the run from, whether you have allowed for the ridge board thickness, the plumb and seat cuts, and the eaves overhang. This article gives the formulas, a ready-reference table you can keep on the van, and worked examples with real numbers.

For a tradesperson, the rafter calculation underpins everything from ordering timber lengths to pricing a cut roof versus trussed rafters. A cut roof (rafters cut and assembled on site) gives flexibility for awkward shapes; trussed rafters are factory-made to a design and arrive ready to fix. Either way, knowing the true rafter length lets you order the right stock length, allow for waste, and check the structural span against the timber section.

A common misconception is that "rafter length" is a single number. It is not: there is the line length (centre of wall plate to centre of ridge), the true cutting length once you account for the ridge board and any birdsmouth, and the overall length including the eaves overhang. Always be clear which one you are quoting. The structural span — the clear distance the rafter bridges unsupported — is a separate figure again, and it is the span (not the sloping length) you check against the span tables in Approved Document A.

Key Facts

• Run — the horizontal distance from the outside of the wall plate to the centre of the ridge; for a symmetrical roof this is half the building span minus half the ridge board thickness.
• Rise — the vertical height the roof gains over the run; rise = run × tan(pitch angle).
• Pitch — the slope of the roof, given as an angle (degrees) or sometimes as a ratio of rise:run.
• Common rafter length — the sloping length from wall plate to ridge: √(run² + rise²), or equivalently run × sec(pitch).
• Rafter length per metre of run — equals sec(pitch) = 1 ÷ cos(pitch); multiply by the run in metres to get the line length.
• Eaves overhang — add the sloping overhang separately; overhang sloping length = horizontal overhang × sec(pitch).
• Birdsmouth (seat cut) — the notch where the rafter sits on the wall plate; depth should not exceed one third of the rafter depth.
• Plumb cut — the vertical cut at the ridge end, cut to the pitch angle.
• Common UK domestic pitches — tiled roofs commonly 30-45°; many concrete interlocking tiles allow down to ~17.5-22.5°; natural slate typically 20-40°; check the manufacturer's minimum.
• Minimum pitch is product-driven — each tile/slate has a minimum pitch below which it is not weathertight; going below it voids cover.
• Span tables apply to the horizontal span, not the sloping length — see [timber spans](/knowledge/carpentry/timber-spans) for C16/C24 rafter spans per Approved Document A.
• Ridge board thickness — typically deduct half the ridge board (e.g. 12.5 mm for a 25 mm ridge) from the run for an accurate cut.

Quick Reference Table

Rafter length and rise per 1 metre of run at common pitches (multiply by your actual run):

Common pitch ratios: 4:12 ≈ 18.4°, 6:12 ≈ 26.6°, 7:12 ≈ 30.3°, 12:12 = 45° (rise:run).

Detailed Guidance

The formulas

Two relationships do all the work:

1. Rise from pitch: rise = run × tan(pitch)
2. Rafter length: rafter = √(run² + rise²) = run × sec(pitch), where sec(pitch) = 1 ÷ cos(pitch)

To get the pitch angle from a known rise and run, use pitch = arctan(rise ÷ run). All three forms describe the same right-angled triangle: the run is the base, the rise is the height, and the rafter is the hypotenuse.

Worked example 1 — pitch known

A symmetrical gable roof on a building 6 m wide, pitched at 30°, with a 25 mm ridge board.

• Half span = 3.0 m. Deduct half the ridge (12.5 mm) → run = 2.9875 m (for a quick estimate, use 3.0 m).
• Rise = run × tan(30°) = 3.0 × 0.5774 = 1.732 m.
• Rafter line length = √(3.0² + 1.732²) = √(9 + 3.0) = √12 = 3.464 m, or 3.0 × sec(30°) = 3.0 × 1.1547 = 3.464 m. Both methods agree.
• Add eaves overhang: for a 300 mm horizontal overhang, sloping overhang = 0.3 × sec(30°) = 0.3 × 1.1547 = 0.346 m, so overall rafter ≈ 3.81 m. Order a 4.2 m length to allow for cuts and waste.

Worked example 2 — rise and run known (no protractor)

A lean-to where you can measure directly: run = 4.0 m, rise = 1.5 m.

• Rafter = √(4.0² + 1.5²) = √(16 + 2.25) = √18.25 = 4.272 m.
• Pitch = arctan(1.5 ÷ 4.0) = arctan(0.375) = 20.6° — useful for checking the chosen tile's minimum pitch.

Worked example 3 — sizing from total span

A roof spanning 8 m at 35° pitch.

• Run = half span = 4.0 m (ignoring ridge thickness for the estimate).
• Rise = 4.0 × tan(35°) = 4.0 × 0.7002 = 2.80 m.
• Rafter = 4.0 × sec(35°) = 4.0 × 1.2208 = 4.88 m line length.
• This rafter would typically need an intermediate support (purlin) for many timber sections — check the clear span against the rafter span tables before specifying.

Setting out the cuts

Mark the plumb cut at the ridge to the pitch angle, then measure the line length down the rafter and mark the birdsmouth (seat cut) at the wall plate. The birdsmouth seat sits on the plate; its depth must not exceed one third of the rafter depth to preserve strength. From the birdsmouth, continue the line for the overhang and mark the foot/plumb cut at the fascia. A roofing/framing square or a digital angle finder makes repeat cuts consistent across all common rafters.

Cut roof vs trussed rafters

A cut roof gives you these calculations to do on site and suits irregular plans, dormers and hips. Trussed rafters arrive engineered and cut to a design — you don't calculate rafter lengths, but you must know the span and pitch to order them. See [roof truss types](/knowledge/carpentry/roof-truss-types) for truss options and [pitched roof structure](/knowledge/roofing/pitched-roof-structure) for how the components fit together.

Frequently Asked Questions

How do I calculate rafter length from pitch and span?

Take half the span as the run, find the rise with rise = run × tan(pitch), then rafter length = √(run² + rise²). Or skip the rise: rafter = run × (1 ÷ cos(pitch)). Add the sloping overhang separately.

What's the difference between run and span?

The span is the full width the roof covers (wall plate to wall plate). The run is the horizontal distance from one wall plate to the ridge centre — for a symmetrical roof, half the span (minus half the ridge thickness).

Do I use the rafter length or the run for span tables?

Span tables in Approved Document A are based on the horizontal span the rafter bridges, not its sloping length. Use the clear horizontal distance between supports.

How much overhang should I add?

Eaves overhang is a design choice, commonly 200-450 mm horizontally. Convert it to sloping length by multiplying the horizontal overhang by sec(pitch), then add it to the rafter length and allow extra for the foot cut.

What's the minimum pitch for my tiles?

It depends on the product. Many concrete interlocking tiles go down to around 17.5-22.5°, plain tiles and natural slate usually need more (often 25-40°). Always check the manufacturer's stated minimum pitch — below it the roof is not weathertight.

Regulations & Standards

• Approved Document A (Structure) — basis for rafter, joist and beam span tables; the horizontal span governs timber section selection.

• BS 5534 — Code of practice for slating and tiling, including minimum pitch and fixing requirements.

• BS 5268 / BS EN 1995 (Eurocode 5) — structural use of timber and timber design.

• BS 8103 — structural design of low-rise buildings, including roof design guidance.

• Building Regulations 2010 — overarching requirement that roof structures be adequately designed and constructed.

• Approved Document A: Structure (GOV.UK) — span tables and structural guidance

• TRADA: Timber roof construction guidance — industry technical guidance on cut and trussed roofs

• BS 5534 (BSI) — slating and tiling code of practice

• GOV.UK: Building regulations approval — when roof structural work needs sign-off

• timber spans — rafter, joist and beam span tables for C16/C24 timber

• roof truss types — trussed rafter options and when to use them

• pitched roof structure — how rafters, purlins and ridge fit together

• pitched roof principles — pitched roof design fundamentals