How do I convert degrees to percent slope?

Take the tangent of the angle and multiply by 100. A 10° slope is tan(10°) × 100 ≈ 17.6%. The two are not the same scale: a 45° slope is 100%, not 50%, because percent is rise over run rather than a share of a right angle.

How do I convert percent grade back to degrees?

Take the arctangent of the grade written as a decimal. A 25% grade is arctan(0.25) ≈ 14.0°. This tool does it live in both directions and also shows the figure as rise-per-12, the way a roofer reads pitch.

Why is a 45° slope 100% and not 50%?

Because percent grade compares vertical rise to horizontal run, and at 45° the rise equals the run — one unit up for one unit across, which is 100%. Degrees measure the angle out of 90, so the two only line up loosely at the shallow end.

What is rise-per-12 and where is it used?

It is the same slope written as inches of rise for every 12 inches of run, which is how roof pitch is called out. A 4/12 roof rises 4 in per foot, works out to about 18.4°, and a 33% grade. The tool shows all three so you can talk to whichever trade is asking.

Degrees to percent slope

This converts between an angle, a grade percentage and a rise-per-12 pitch. It describes steepness only — it does not set a drainage fall, a ramp limit or an accessible gradient, all of which are governed by codes you should check for the job.

Type an angle in degrees and read the grade percentage, or type a grade and read the angle — both update as you go. The pitch line reports the same slope as rise-per-12, the framing-square language, and the ratio line gives it as rise:run.

Worked example

A survey shows a 10° bank. tan(10°) ≈ 0.176, so that is a 17.6% grade, which is about a 2.1/12 pitch. Working the other way, a road sign warning of a 6% grade is arctan(0.06) ≈ 3.4° — gentle to the eye but real on a loaded truck.

The formula

percent = tan(angle) × 100 · angle = arctan(percent ÷ 100)

Grade is the rise divided by the run, and the tangent of an angle is exactly that ratio, so the two are the same quantity in different clothes. Multiply the ratio by 12 for the roofing pitch. The scales diverge because degrees run to 90 while grade has no ceiling — a vertical face is 90° but an infinite percent.

Questions

How do I convert degrees to percent slope?: Take the tangent of the angle and multiply by 100. A 10° slope is tan(10°) × 100 ≈ 17.6%. The two are not the same scale: a 45° slope is 100%, not 50%, because percent is rise over run rather than a share of a right angle.
How do I convert percent grade back to degrees?: Take the arctangent of the grade written as a decimal. A 25% grade is arctan(0.25) ≈ 14.0°. This tool does it live in both directions and also shows the figure as rise-per-12, the way a roofer reads pitch.
Why is a 45° slope 100% and not 50%?: Because percent grade compares vertical rise to horizontal run, and at 45° the rise equals the run — one unit up for one unit across, which is 100%. Degrees measure the angle out of 90, so the two only line up loosely at the shallow end.
What is rise-per-12 and where is it used?: It is the same slope written as inches of rise for every 12 inches of run, which is how roof pitch is called out. A 4/12 roof rises 4 in per foot, works out to about 18.4°, and a 33% grade. The tool shows all three so you can talk to whichever trade is asking.

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