How do I convert percent grade to degrees?

Percent grade is rise over run times 100. The angle is the arctangent of that ratio: degrees = atan(grade / 100) × 180 / pi. A 100 percent grade is a 45 degree angle, not 90, because it means equal rise and run.

What does a 1-in-X slope mean?

It means one unit of vertical rise for every X units of horizontal run, so 1-in-40 is a fall of one foot over forty feet. It equals a grade of 100 / X percent, so 1-in-40 is 2.5 percent. Plumbing and drainage plans commonly use this form.

What slope do I need for drainage?

A common minimum for surface drainage is about 2 percent (roughly 1-in-50) so water runs off without ponding. Sanitary drain pipe is often pitched 1/4 inch per foot, which is about 2 percent or 1-in-48. Always follow local code for the exact figure.

Is percent grade the same as the angle?

No. They only match for very small slopes. Percent grade is a tangent ratio while the angle is its arctangent, so they diverge as the slope steepens. A 10 percent grade is about 5.7 degrees, not 10 degrees.

What is the maximum slope for a wheelchair ramp?

Accessibility standards generally cap a ramp at 1-in-12, which is about 8.33 percent or 4.76 degrees, with level landings. Enter 12 as the X in the 1-in-X form to confirm a design meets that maximum before building.

Slope & Grade Calculator

Slope is described four different ways depending on the trade — percent grade by surveyors, degrees by carpenters, rise-over-run by roofers, and 1-in-X by drainage engineers. This calculator takes any one of those forms and instantly gives the other three, plus the actual elevation change over a run you specify.

How it works

All four forms describe the same ratio of vertical rise to horizontal run. The percent grade and the 1-in-X ratio are direct ratios, while the angle is their arctangent:

grade %      = (rise / run) × 100
angle (deg)  = atan(rise / run) × 180 / pi
1-in-X       = 1 / (rise / run)  →  X = run / rise
rise over run= rise : run

Going the other way, an angle converts back with the tangent: grade % = tan(angle in radians) × 100. Given a grade and a horizontal run, the vertical change is simply rise = run × grade / 100.

Example and tips

A 2 percent grade is an angle of about 1.15 degrees, a rise-over-run of 0.02 (or 1 in 50), and produces a 1-foot drop over 50 feet of run. Watch the distinction between grade and angle on steep work: a 100 percent grade is 45 degrees, and grades above 100 percent are entirely normal even though an angle can never exceed 90. For drainage, think in 1-in-X — it reads directly as “one unit down for every X along.”