How to use
- Enter the elevation change. Uphill is positive. Downhill is negative, and the percent will be negative.
- Enter the horizontal distance, not the distance you walked on the slope, unless the slope is gentle enough that you accept the approximation.
- Keep both numbers in the same unit. The menu labels the slope distance; it does not convert the inputs.
- Press Calculate. Percent grade is rise ÷ run × 100. Angle is the arctangent of rise ÷ run.
How it's calculated
Angle in degrees = arctan(rise ÷ run) × 180 ÷ π
Slope distance = √(rise² + run²)
Percent and degrees are different scales. A 45 degree angle is a 100 percent grade, because rise equals run. A 10 percent grade is only about 5.7 degrees. People mix those up when a sign says “10%” and they picture a 10 degree ramp.
If you have a list of elevations rather than one rise and one run, total the climbs on the elevation gain calculator first. Time for that climb is Naismith’s rule, not a grade. Roof slope in rise-over-run for a building, which is the same geometry with a different job, is the ClearQuip roof pitch calculator.
Worked example
A trail that climbs 500 feet over 1 mile of horizontal distance uses a run of 5,280 feet. The grade is 500 ÷ 5,280 × 100 = 9.47 percent. The angle is arctan(500 ÷ 5,280) ≈ 5.41 degrees. The slope distance is √(500² + 5,280²) ≈ 5,304 feet, only a little longer than the horizontal mile because the grade is moderate.
Assumptions and sources
The percent grade is the definition used on roads and trails: vertical change divided by horizontal distance. Some people divide by the slope distance instead; that is a different ratio and this page does not use it. The angle is the inverse tangent, in degrees. Inputs are assumed to share a unit. A negative rise is a descent and produces a negative percent.
FAQ
Is 10 percent the same as 10 degrees?
No. Ten percent is a rise of 10 for a run of 100, which is about 5.7 degrees. Ten degrees is about an 18 percent grade.
What if I measured the distance along the trail?
The formula wants the horizontal run. On a steep trail the walked distance is longer. If you only have the slope distance, the horizontal run is √(slope² − rise²), when the slope is longer than the rise.
Can the grade be downhill?
Yes. Enter a negative elevation change. The percent and the angle come out negative. The slope distance stays positive.
Does a higher percent mean a harder hike?
Steepness is one part of effort. Distance, pack weight, altitude, and surface matter too. The grade is only the geometry.