Roof pitch calculator
A roof's pitch in degrees from its span and rise, or the rise from its pitch, with the rafter length.
Span, run and rise
The span is the horizontal distance the roof covers, from wall plate to wall plate. The run is how much of that one rafter covers: half the span on an ordinary roof with a ridge down the middle, all of it on a lean-to. The rise is the height from the wall plate up to the ridge. The pitch is the angle at the eaves, and it comes from the run and the rise alone: tan⁻¹ of rise divided by run.
That is why the roof type matters so much. The same 6,000 mm span with a 2,000 mm rise is a 33.7° roof with a ridge in the middle, and an 18.4° lean-to.
Degrees here, inches in 12 in America
British tile and slate data sheets give pitch in degrees. American calculators and forums give it as inches of rise per 12 inches of run, so "6 in 12" means 26.6°. The two cannot be compared without converting, and a figure copied from the wrong source looks nothing like the minimum on a data sheet. This page leads with degrees and shows the figure in 12 underneath.
The rafter is longer than the plan says
An overhang measured on the plan, straight out from the wall, is shorter than the timber that covers it, because the timber runs along the slope. A 300 mm overhang at 35° is 366 mm of rafter. The page does that sum for you.
The rafter length here runs to the ridge line, the centre of the ridge. Where rafters meet a ridge board, each stops at its face instead, so take off half the board's thickness, measured along the slope, which is slightly more than half.
The pitch the covering needs
Every tile and slate has a minimum pitch set by its manufacturer, and below it wind-driven rain gets under the laps. Check the product against the pitch before ordering, not after. For the stairs underneath, the stair calculator checks a flight against the building regulations guidance, and the triangle calculator does the same trigonometry for any other right angle.
Common questions
- How do I measure the pitch of a roof I already have?
- From the loft. Hold a spirit level level against the underside of a rafter, mark 1,000 mm along it, and measure straight up from that mark to the rafter. Choose mono pitch here, enter 1,000 as the span and your measurement as the rise, and the pitch is the answer. No ladder, and no guessing from the street.
- What is 6 in 12 in degrees?
- 26.6°. The American way of stating pitch is inches of rise per 12 inches of run, so 4 in 12 is 18.4°, 6 in 12 is 26.6°, 9 in 12 is 36.9° and 12 in 12 is 45°. British data sheets, and this page, give degrees; the figure in 12 is shown underneath for anyone reading an American source.
- Dual pitch or mono pitch?
- A dual-pitched roof has a ridge with a slope either side, so each rafter covers half the span. A mono pitch, or lean-to, has one slope covering all of it. For the same span and rise, a lean-to is therefore at a much lower pitch, which is the commonest mix-up in these sums.
- Is the rafter length the length of timber to buy?
- It is the length along the slope from the wall plate to the ridge line, plus the overhang if you entered one. Allow for the cuts at each end and a margin for trimming, then round up to the next length your merchant stocks.
- What pitch do tiles or slates need?
- Every tile and slate has a minimum pitch set by its manufacturer and printed on its data sheet, and some need a bigger overlap below a certain pitch. Below the minimum, wind-driven rain gets under the laps. Check the product you intend to use against the pitch this page gives you.