Roof Pitch Calculator
Enter the vertical rise and the horizontal run to get the roof pitch angle in degrees — plus the slope as a percentage — and see why steeper roofs shed water and snow faster.
Angle and slope at once
Enter the rise and the run and the calculator returns the pitch angle in degrees (arctan of rise over run) and the slope as a percentage together.
Measure the run flat
The run is the horizontal distance along the ground, not the slanted rafter length — measuring along the rafter overstates the run and flattens the pitch.
What is a roof pitch calculator?
Rise, run, and the angle they make
A roof pitch calculator turns two measurements — how far a roof rises vertically and how far it runs horizontally — into the slope of the roof. It returns the pitch as an angle in degrees and as a slope percentage, the two numbers roofers, builders, and DIYers use to size materials, choose a roofing system, and check that a roof drains the way it should. Give it any rise and run in the same unit and it does the trigonometry for you.
Enter the vertical rise and the horizontal run to get the roof pitch angle in degrees and the slope percentage instantly.
The pitch angle is the arctangent of the rise divided by the run, and the slope percentage is that same ratio multiplied by 100.
angle = arctan(rise ÷ run)Roof pitch is conventionally written as rise-per-12, like "6:12", meaning the roof climbs 6 units for every 12 units of horizontal run. The arctangent converts that ratio into an angle, and multiplying the ratio by 100 gives the slope as a percentage. Use the same unit for both the rise and the run — the units cancel in the ratio, so only their proportion matters.
Suppose a roof rises 6 over a run of 12 — the classic 6:12 pitch.
Form the ratio
6 ÷ 12 = 0.5 — the rise-over-run ratio that defines the slope.
Take the arctangent
arctan(0.5) = 26.57° — the pitch expressed as an angle.
Convert the ratio to a percentage
0.5 × 100 = 50 % — the slope as a percentage.
The two outputs describe the same slope in two languages. The angle (26.57° for the 6:12 roof above) is the geometric tilt, handy for cutting rafters and reading a protractor; the slope percentage (50 %) is the rise per hundred of run, the form drainage and accessibility codes tend to use. Roof pitch is usually quoted in the x:12 convention, so a 6:12 reads as "six in twelve". The steeper the pitch, the faster the roof sheds water and snow — flat and low-slope roofs (under about 4:12) pond water and need membrane systems, while steep roofs (12:12 and up, a full 45°) drain almost instantly and suit shingles and tiles but are harder and more dangerous to walk. Doubling the rise from 6:12 to 12:12 takes the angle from 26.57° to 45° and the slope from 50 % to 100 %.
The trigonometry is exact, but a couple of practical points are worth keeping in mind.
Measure the horizontal run, not the rafter
This calculator needs the horizontal run — the flat distance the roof covers — not the slanted length of the rafter. Measuring along the rafter overstates the run and reports a shallower pitch than the roof really has. Keep the rise and run in the same unit so the ratio is correct, and remember the figures describe the slope geometry only, not loading, materials, or building-code compliance.