Elevation Grade Percentage Calculator
Grade describes how steep a road, ramp or trail is as the rise (vertical change) over the run (horizontal distance), expressed as a percentage. A 6 percent grade climbs 6 units for every 100 units of horizontal distance. This calculator takes the rise and the horizontal run in the same units, then reports the grade percentage, the slope angle in degrees, and the slope expressed as a 1 in N ratio. It follows the engineering convention of using horizontal run, the basis for highway grade limits and ADA ramp rules.
Grade percentage formula
Grade (%) = (rise / run) * 100
Slope angle = atan(rise / run) in degrees
Ratio N = run / rise (expressed as 1 in N)
Grade uses the horizontal run by convention. A 100 percent grade equals a 45 degree angle, because rise then equals run.
Grade context
- A 6 percent grade rises 6 units per 100 units of horizontal distance.
- The ADA limits accessible ramps to a maximum 8.33 percent running slope (1 in 12).
- Highway maximum grades commonly range from 6 to 12 percent by terrain and road class.
- A 100 percent grade is a 45 degree angle, not vertical.
- The ratio form (1 in N) is common in rail and accessibility standards.
Grade percentage: frequently asked questions
What does grade percentage mean?
Grade percentage is the rise (vertical change) divided by the run (horizontal distance), multiplied by 100. A 6 percent grade rises 6 feet for every 100 feet of horizontal distance. It is the standard way roads, ramps and trails describe steepness.
How do I convert grade to an angle?
The slope angle equals the arctangent of rise divided by run. For example a 100 percent grade (rise equals run) is 45 degrees, not 90 degrees. This calculator reports the angle in degrees alongside the percentage.
Is grade based on horizontal run or slope distance?
By engineering convention, grade uses the horizontal run, not the distance measured along the slope. This calculator follows that convention. If you only have the slope distance, use a slope distance calculator first to recover the horizontal run.
What is a typical maximum road grade?
Federal and state highway design limits commonly fall between 6 and 12 percent depending on terrain and road class, with steeper grades allowed on low-volume mountain roads. The ADA limits accessible ramps to a maximum running slope of 8.33 percent (a 1 in 12 ratio).
How is the ratio form calculated?
The ratio expresses the slope as 1 in N, where N is the run divided by the rise. A 1 in 12 ramp has a rise of 1 for every 12 of run, equal to about 8.33 percent. The calculator outputs N for the given rise and run.
Official sources
- U.S. Access Board (ADA): U.S. Access Board.
- Federal Highway Administration: Federal Highway Administration.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.