Slope Percentage Calculator
Express vertical rise as a percentage of horizontal run and convert that grade into an angle above level ground.
How the result changes
Only vertical rise changes; all other inputs stay at your current values. The line illustrates the formula across the shown range. This is not a forecast of real-world outcomes.
About this calculation
Slope Percentage Calculator: Express vertical rise as a percentage of horizontal run and convert that grade into an angle above level ground. Enter vertical rise, horizontal run; the reported quantities are slope grade (%), slope angle (degrees). The equations and examples below show how those inputs lead to the result and where the model's assumptions matter.
Formula
grade = rise / run × 100
Worked example
With Vertical rise: 2 m, Horizontal run: 20 m, slope grade is 10 %.
Method and inputs
Measure elevation change and horizontal distance in the same length unit. Divide rise by run to obtain grade as a ratio, then multiply by one hundred for percent grade. The arctangent of the ratio gives the corresponding angle above horizontal.
Worked example
A path that climbs 2 meters across a horizontal run of 20 meters has a grade of 10 percent. Its angle is arctan(0.1), about 5.71 degrees. Ten percent grade is therefore not the same as a ten-degree angle.
For a ramp that rises 1 meter across 12 meters of horizontal run, grade is about 8.33 percent. Its surface length is slightly more than 12 meters, so using that diagonal in the denominator would give a slightly smaller number. The distinction grows on steeper slopes.
How to read the result
A grade of 100 percent means rise equals horizontal run and corresponds to 45 degrees. The horizontal distance is the projection onto level ground, not the distance walked along the slope. Both outputs describe the same right-triangle geometry.
The angle output can help compare a drawing that specifies degrees with a road sign that specifies percent grade. Conversion is nonlinear: doubling a 10-percent grade does not exactly double its angle. If a route climbs and descends, calculate each section separately before deriving a net or average rise.
Assumptions and checks
This model treats the segment as straight and uses a nonnegative rise. It is suitable for a single incline rather than an entire route with repeated uphill and downhill sections. Survey measurements may need correction for local terrain.
Using the sloped surface length as run understates the percentage. Mixing feet for rise and meters for run also invalidates the ratio. Divide before converting to percent, and distinguish grade from gradient stated as one in ten.
Common questions
What does the slope percentage calculator calculate?
It reports both rise divided by horizontal run as a percentage and the matching angle in degrees. It provides a common way to compare road, ramp or terrain steepness.
When should I recalculate or check another method?
Recalculate whenever the rise or horizontal run changes. For building access design or road engineering, compare the result with the applicable local standard and use surveyed dimensions rather than a visual estimate.
Inputs
- Vertical rise (m)
- Horizontal run (m)