# Roof Pitch Converter Degrees, percent and ratio in one place, plus roof factor and slope length. - Page: https://jianzhujisuan.com/en/roof-pitch-convert - Category: Area and Volume (https://jianzhujisuan.com/en/c/area-volume) - Chinese version: https://jianzhujisuan.com/zh/roof-pitch-convert.md - Data checked: 2026-10-25 ## Quick result With the default inputs (Known as Degrees, Value 30, Horizontal run 10 m): **Pitch (degrees) 30.00 °** ## Inputs | Parameter | Type | Default | Unit | Note | |---|---|---|---|---| | Known as | select | Degrees | — | | | Value | number | 30 | — | | | Horizontal run | number | 10 | m | | ## Formula - **Degrees → percent**: p = tan(θ) × 100 - **Degrees → ratio**: 1 : cot(θ) - **Percent → degrees**: θ = arctan(p/100) - **Roof factor**: k = 1 / cos(θ) - **Rise**: h = run × tan(θ) - **Slope length**: l = run / cos(θ) ## Worked example 30 degrees over a 10 m run: 57.7% and 1:1.73, roof factor 1.1547, rise 5.77 m, slope length 11.55 m, rise 0.577 m per metre. ### The other notation: X/12 roof pitch, the way every English-speaking drawing writes it (the 1:X ratio on this page does not cover it) | Pitch notation | Degrees | Percent | Roof factor | 100 m² plan → sloped (m²) | In squares (100 ft²) | |---|---|---|---|---|---| | 1/12 | 4.76 | 8.3 | 1.0035 | 100.3 | 10.80 | | 2/12 | 9.46 | 16.7 | 1.0138 | 101.4 | 10.91 | | 3/12 | 14.04 | 25.0 | 1.0308 | 103.1 | 11.10 | | 4/12 | 18.43 | 33.3 | 1.0541 | 105.4 | 11.35 | | 5/12 | 22.62 | 41.7 | 1.0833 | 108.3 | 11.66 | | 6/12 | 26.57 | 50.0 | 1.1180 | 111.8 | 12.03 | | 7/12 | 30.26 | 58.3 | 1.1577 | 115.8 | 12.46 | | 8/12 | 33.69 | 66.7 | 1.2019 | 120.2 | 12.94 | | 9/12 | 36.87 | 75.0 | 1.2500 | 125.0 | 13.45 | | 10/12 | 39.81 | 83.3 | 1.3017 | 130.2 | 14.01 | | 11/12 | 42.51 | 91.7 | 1.3566 | 135.7 | 14.60 | | 12/12 | 45.00 | 100.0 | 1.4142 | 141.4 | 15.22 | **X/12 and 1:X are not the same thing.** X/12 reads as X units of rise per 12 units of run — X on top, 12 underneath — so 6/12 is 26.57 degrees while 1:6 is only 9.46. Copy 6/12 into a metric drawing as 1:6 and the roof flattens by more than half. To use the factor: plan area × factor = sloped area. It is 1.0541 at 4/12, 1.1180 at 6/12 and 1.4142 at 12/12, so 100 m² of plan on a 12/12 roof is really 141.4 m². The last column is the English pricing unit: 1 square = 100 ft² = 9.2903 m², and asphalt shingles come 3 bundles to the square. ## Questions ### Is there a quick conversion between percent and degrees? Below about 10 degrees, percent is roughly degrees × 1.75 with little error; above that you need tan. The pairs worth memorising: 5°≈8.7%, 10°≈17.6%, 15°≈26.8%, 20°≈36.4%, 25°≈46.6%, 30°≈57.7%, 35°≈70.0%, 40°≈83.9% and 45°=100%. Note that 45 degrees is exactly 100%, not 50% - this is where percent pitch most often goes wrong. ### Which is steeper, 1:2 or 1:5? 1:2 is steeper. In 1:X the 1 is the vertical rise and X the horizontal run, so a smaller X is steeper: 1:2 is about 26.6° (50%) and 1:5 about 11.3° (20%). The one that catches people out is 2:1, which reads rise:run and equals 63.4°. Always check whether a drawing says 1:X or X:1 - getting the direction wrong changes the pitch two- or three-fold. ### How does pitch affect roof area and material quantities? Sloped area = plan area × roof factor (1/cosθ). The steeper the roof, the more material the same footprint needs: ×1.155 at 30 degrees, i.e. 15.5% extra; ×1.414 at 45 degrees, 41.4% extra; only ×1.015 at 10 degrees, which is negligible. Membranes are taken off the sloped area plus laps, battens and purlins are set out along the slope length, and ridge and eave trims follow the slope length plus details. The classic estimating error is quoting plan area as roof area - on a steep roof that loses double-digit percentages of material, so read the roof factor and slope length here together, never the angle alone. ### The drawing says 4/12 — what is that in degrees? 18.43 degrees, which is 33.3%. Read it as 4 units of rise per 12 of run, so it is a 1:3 slope, not 1:4, and the roof factor is 1.0541. US residential work sits mostly between 4/12 and 8/12, with 6/12 (26.57 degrees, 50%) the most common; below 2/12 ordinary asphalt shingles generally cannot be used. ### Is a 2% drainage fall the same as a roof pitch? Both are slopes, but not at the same scale. 2% is 1.15 degrees, a flat-roof drainage fall meant only to stop ponding; the 20% (11.31 degrees) minimum for tiled roofs is about letting tiles lap and shed water. The US 2/12 happens to be 16.7%, in between. Do not treat a 2% drainage fall as a usable tiled-roof pitch — tiles laid at 2% let water creep back under the laps. ### How is the roof factor used in a quote? Three steps: measure the horizontal plan area, not the distance up the slope; multiply by the roof factor to get the sloped area; then order on the sloped area, and say which area a square-metre rate refers to. For example 120 m² of plan at 6/12, factor 1.1180, is 134.2 m² of sloped roof — 14.2 m² of extra tile and labour hides in that factor, and the steeper the roof the more hides there (41.4% at 12/12). Scaffolding, safety netting and cradle access, on the other hand, are often priced on plan area or on eaves length, so agree which measure applies before signing: the same roof can be quoted three different ways. ## Related tools - [Room Area Calculator](https://jianzhujisuan.com/en/room-area): Floor, ceiling, walls, skirting and volume, all at once. - [Wall Area and Paint Calculator](https://jianzhujisuan.com/en/wall-area): Net wall area with openings deducted, plus paint and filler. - [Roof Area Calculator](https://jianzhujisuan.com/en/roof-area): True sloped roof area, rafter length and ridge rise from pitch. - [Circle and Sector Calculator](https://jianzhujisuan.com/en/circle-calc): Circle area and circumference plus sector, arc, chord and segment. - [Triangle Area Calculator](https://jianzhujisuan.com/en/triangle-area): Area from three sides, with angles, inradius and circumradius. - [Battered Pit Volume Calculator](https://jianzhujisuan.com/en/pit-volume): Top dimensions and frustum volume from base size, depth and batter. --- Generated by BuildCalc. All calculations run in your browser; no data is uploaded. Formulas follow national standards and common trade practice; local codes govern.