Roof Pitch Calculator
Convert roof pitch to angle and slope
🔒 Runs locally · Method · · Disclaimer · Roof Pitch Calculator
Working out how to convert roof pitch to angle and slope is easier with Roof Pitch Calculator, which answers as you type. Enter Rise (cm per 100cm run) and Run (cm) in any order — Roof Pitch recalculates on every edit. Roof Pitch ties each output to its formula. Use Roof Pitch for a reliable number, fast. You can disconnect once Roof Pitch has loaded; the arithmetic runs locally. Roof Pitch is part of the Construction collection on CalcProMaster, alongside roof pitch calculator with slope, free calculators and more. Roof Pitch goes from question to answer fast. Start with Roof Pitch; the first number takes seconds.
What the defaults give
30 rise over 100 run is an angle of 16.7°, a slope of 30% and a pitch of 3.6/12.
All three describe one roof. Builders quote the 12-based pitch, engineers quote degrees, and drainage is often quoted as a percentage.
The formula
Angle θ = arctan(rise ÷ run)
Slope % = rise ÷ run × 100
Pitch per 12 = rise ÷ run × 12
The pitch-per-12 form exists because a framing square is 12 inches on its tongue; the rise over 12 inches of run is what a carpenter can mark directly on a rafter. Degrees need a calculator, percentages are for drainage and ramps, and the 12-based figure is what roofing materials are specified against.
Worked examples
30 over 100 → 16.7°, 30%, 3.6/12
15 over 100 → 8.5°, 15%, 1.8/12
60 over 100 → 31.0°, 60%, 7.2/12
30 over 50 → 31.0°, 60%, 7.2/12
30 over 200 → 8.5°, 15%, 1.8/12
Doubling the rise and halving the run give the same roof, which is the useful property of a ratio. A 3.6/12 roof is on the shallow side of normal for asphalt shingles: many manufacturers require at least 4/12 for a standard installation, with a double underlayment down to 2/12 and specialised low-slope systems below that.
Why the angle matters
Steep roofs shed water and snow quickly and last longer, but cost more in material — the rafter length grows as 1 ÷ cos θ while the plan area does not, so a 45° roof carries about 41% more surface than its footprint. Shallow roofs need fewer materials and stronger waterproofing, and they collect debris.
Below about 10° the surface stops being self-cleaning and standing water becomes the design case. That is where membranes, tapered insulation and proper falls take over from simple shingle rules.
Measuring an existing roof
In the attic, measure horizontally from the top plate to a point under the ridge, and vertically from the top plate to the underside of the ridge board. Both in the same unit, and the ratio is the answer. On the outside, a level held 12 inches along the slope with a tape down to the roof surface gives the pitch per 12 directly.
The calculator assumes a straight slope. A curved or multi-pitch roof has to be measured section by section, and the number you compute is the slope, not the rafter length — that needs the run multiplied by 1 ÷ cos θ.
Frequently Asked Questions
What angle is a 3.6/12 pitch?
16.7 degrees. Rise over run is 3.6 ÷ 12, and the arctangent of 0.3 is 16.7°.
How do I convert pitch to degrees?
Divide the rise by the run and take the arctangent. 30 rise over 100 run is 0.3, which is 16.7°.
What is the minimum slope for shingles?
Most asphalt shingle makers require 4/12, with a double underlayment allowed down to 2/12. Below that you need a low-slope membrane system.
Does a steeper roof cost more?
Yes. Rafter length grows with 1 ÷ cos θ, so a 45° roof has 41% more surface than its footprint, and more material and labour go into it.
Is slope percentage the same as pitch?
No. Slope is rise over run as a percentage (30%), pitch is the same ratio expressed over 12 (3.6/12). They describe the same roof.
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