Hill Grade Angle CalculatorFree online fitness & health calculator — instant results, no sign-up
Calculate training hill grade and angle from rise and horizontal run.
For general information only. This is not medical advice, diagnosis, dosing guidance or a treatment recommendation. Talk to a doctor or other qualified health professional about your health, pregnancy, or diet.
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About the Hill Grade Angle Calculator
The Hill Grade Angle Calculator converts a hill's vertical rise and horizontal run into a percentage grade and a slope angle in degrees. Use it to describe the steepness of a hill for running, walking, or other uphill training. With a vertical rise of 50 m and a horizontal run of 500 m, it reports Grade = 10 % and Slope angle = 5.71 degrees.
- Vertical rise (m)
- The elevation gain from the bottom to the top of the measured hill segment, in meters, with a default of 50 m.
- Horizontal run (m)
- The horizontal distance covered by the same hill segment, rather than the distance along its sloping surface, in meters, with a default of 500 m.
Formula and method
G = (h / r) × 100; θ = arctan(h / r) × 180 / π. For h = 50 m and r = 500 m: G = (50 / 500) × 100 = 10 %; θ = arctan(50 / 500) × 180 / π ≈ 5.71 degrees.
- hVertical rise in meters.
- rHorizontal run in meters; it must be greater than zero.
- GHill grade expressed as a percentage.
- θSlope angle measured above the horizontal, in degrees.
- πThe mathematical constant pi, used to convert radians to degrees.
Divide vertical rise by horizontal run to obtain the slope ratio. Multiply that ratio by 100 to calculate percentage grade. Take the inverse tangent of the same ratio and convert the result from radians to degrees to calculate the slope angle. For the default inputs, the ratio is 0.1, producing a grade of 10 % and an angle rounded to 5.71 degrees.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Vertical rise50 m
- Horizontal run500 m
Results
- Grade10 %
- Slope angle5.71 degrees
How to use the Hill Grade Angle Calculator
- 1Choose the hill segment you want to assess and identify its starting and ending elevations.
- 2Enter its elevation gain in Vertical rise (m); keep 50 for the default example.
- 3Enter its horizontal distance in Horizontal run (m); keep 500 for the default example and ensure the value is greater than zero.
- 4Read the calculated Grade and Slope angle outputs; the default inputs give 10 % and 5.71 degrees.
- 5Use both outputs to describe the segment's overall steepness when planning or comparing hill-training routes.
Reading your result
The Grade row expresses vertical rise as a percentage of horizontal run: 10 % means the rise is 10 % of the horizontal distance. The Slope angle row expresses that same steepness as an angle above level ground: 5.71 degrees for the default inputs. These are two descriptions of the same slope, not interchangeable numerical values; a 10 % grade is not a 10-degree angle.
Limitations
The calculation treats the selected segment as a uniform slope and does not reveal steeper pitches or flatter sections within it. Use horizontal run, not distance traveled along the hill surface, and measure rise and run over the same segment. A zero horizontal run makes the grade undefined. Elevation and distance measurement errors affect both outputs. Grade and angle alone do not predict training effort or safety, which also depend on pace, surface, weather, and individual fitness.
Common questions
Can I use the distance recorded while traveling up the hill as horizontal run?+
Only if that distance represents horizontal distance. Distance measured along the sloping surface is longer than horizontal run; using it directly will underestimate both grade and slope angle. Check how your mapping tool or device defines distance.
Why does a 10 % hill grade correspond to 5.71 degrees rather than 10 degrees?+
Percentage grade is 100 times the rise-to-run ratio, while angle is the inverse tangent of that ratio. For a rise of 50 m and horizontal run of 500 m, the ratio is 0.1, and arctan(0.1) is approximately 5.71 degrees.
Should I enter total accumulated ascent for a route with several climbs and descents?+
Not when calculating the slope between a segment's endpoints. Use the elevation difference and matching horizontal run for one continuous climb. Total accumulated ascent across an undulating route does not describe a single hill angle.
Does this calculator show the steepest part of my training hill?+
No. It reports the overall slope for the rise and run you enter. To assess a steep section, measure that section's own vertical rise and horizontal run separately.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.