Elevation Grade Calculator
Grade describes the steepness of a slope: how much it rises (or falls) over a given horizontal distance. It is used for roads, trails, ramps, railways, drainage, and trenching. Grade is most often given as a percentage, the rise divided by the run times 100, but it can also be read as an angle in degrees or as a ratio. This tool takes the vertical rise (the elevation change) and the horizontal run and returns the grade percentage, the slope angle, the slope ratio, and the true slope-distance length along the incline. Enter rise and run in the same unit. A negative rise represents a downhill grade.
Slope grade formula
grade percent = rise / run * 100
angle = atan(rise / run) in degrees
ratio = run / rise (expressed as run : 1)
slope distance = sqrt(rise^2 + run^2)
Grade as a percentage is the rise divided by the run, multiplied by 100, so a 1-unit rise over a 100-unit run is a 1 percent grade. The slope angle is the arctangent of rise over run. The ratio expresses how many units of horizontal run accompany one unit of rise. The slope distance is the actual length measured along the incline, found by the Pythagorean theorem from rise and run.
Worked example
A road climbs 10 metres of elevation over 100 metres of horizontal distance. Grade = 10 / 100 * 100 = 10.00 percent. The angle is arctan(10 / 100) = arctan(0.1) = 5.71 degrees. The ratio is 100 / 10 = 10.00, written 10 to 1. The slope distance is sqrt(10 squared + 100 squared) = sqrt(10,100) = 100.50 metres, slightly longer than the horizontal run.
Frequently asked questions
What is the difference between grade percent and angle?
Grade percent is rise divided by run times 100, while the angle is the arctangent of rise over run in degrees. They are not the same scale: a 100 percent grade is a 45-degree angle, not 90. For gentle slopes the two are numerically close, but they diverge as the slope steepens, so always note which one a figure refers to.
Is grade measured against horizontal or slope distance?
Standard grade, as used for roads and this calculator, is rise over horizontal run. Some fields define grade as rise over the slope distance (the actual length along the incline). The two agree for gentle grades but differ as slopes steepen. This tool uses the horizontal-run convention and also reports the slope distance separately.
What does a slope ratio like 10:1 mean?
A 10 to 1 ratio means the slope drops or rises one unit for every ten units of horizontal distance, which is a 10 percent grade. Ratios are common in landscaping, drainage, and earthworks. A larger first number means a gentler slope; 4 to 1 is steeper than 10 to 1.
Can I use this for a downhill grade?
Yes. Enter a negative rise to represent a descent, and the grade percentage and angle will come out negative, indicating downhill. The ratio and slope distance use the magnitude. Keep rise and run in the same unit so the percentage and slope distance are correct.
Official sources
- U.S. Federal Highway Administration: roadway grade and geometric design.
- U.S. Access Board: accessible ramp slope requirements.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.