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Elevation Grade Calculator

Calculate slope percentage, angle in degrees and slope length from an elevation rise and a horizontal run.

What this tool does

Calculate slope percentage, angle in degrees and slope length from an elevation rise and a horizontal run. You fill in these fields: Rise and Run. It shows grade, angle above horizontal, slope length, and rise divided by run.

Inputs

  • Rise: A number. The vertical change in height. Use a negative number for a downhill slope.
  • Run: A number. Must be greater than 0. The horizontal distance. Enter rise and run in the same unit, such as feet or meters.

How to use

  1. Enter the rise.
  2. Enter the run.
  3. Read the result: grade, angle above horizontal, slope length, and rise divided by run. It appears once every required field has a valid value.

Worked examples

Example 1. Inputs:

  • Rise: 3
  • Run: 12

Results:

  • Grade: 25.00%
  • Angle above horizontal: 14.04 degrees
  • Slope length: 12.369317 same unit as rise and run
  • Rise divided by run: 0.25 (The slope as a plain ratio)

How this is worked out: Grade = rise / run x 100 = 3 / 12 x 100 = 25. Angle = arctan(3 / 12) = arctan(0.25). arctan(0.25) = 0.25 - 0.25^3/3 + 0.25^5/5 - ... = 0.2449787 radians. x 180 / pi = 14.03624 degrees. Slope length = sqrt(3^2 + 12^2) = sqrt(153) = 12.36932.

Example 2. Inputs:

  • Rise: 10
  • Run: 20

Results:

  • Grade: 50.00%
  • Angle above horizontal: 26.57 degrees
  • Slope length: 22.36068 same unit as rise and run
  • Rise divided by run: 0.5 (The slope as a plain ratio)

How this is worked out: Grade = 10 / 20 x 100 = 50. Angle = arctan(0.5) = 26.56505 degrees (a standard value: tan 26.56505 degrees = 0.5). Slope length = sqrt(10^2 + 20^2) = sqrt(500) = 22.36068.

Example 3. Inputs:

  • Rise: -3
  • Run: 12

Results:

  • Grade: -25.00%
  • Angle above horizontal: -14.04 degrees
  • Slope length: 12.369317 same unit as rise and run
  • Rise divided by run: -0.25 (The slope as a plain ratio)

How this is worked out: A negative rise is a downhill slope with the same steepness. Grade = -3 / 12 x 100 = -25. Angle = arctan(-0.25) = -14.03624 degrees, the negative of the 3 and 12 case. Slope length uses the squared rise, so it equals sqrt(153) = 12.36932.

Example 4. Inputs:

  • Rise: 0
  • Run: 5

Results:

  • Grade: 0.00%
  • Angle above horizontal: 0.00 degrees
  • Slope length: 5 same unit as rise and run
  • Rise divided by run: 0 (The slope as a plain ratio)

How this is worked out: Flat ground: rise 0. Grade = 0 / 5 x 100 = 0. Angle = arctan(0) = 0 degrees. Slope length = sqrt(0^2 + 5^2) = 5, the run itself.

Limitations

  • Gives the steepness of one straight line from the rise and run. It does not model ground that bends or changes steepness.
  • The slope length is the straight-line distance along the slope, not the length of a curved path.
  • The result is only as accurate as the rise and run you measure.

FAQs

Q: What is the difference between grade and angle?
A: Grade is the rise divided by the run, times 100. Angle is the arctangent of the same rise divided by run, in degrees above flat ground. A 45 degree angle is a 100 percent grade.
Q: Can the rise be negative?
A: Yes. A negative rise is a downhill slope. The grade and the angle both come out negative, and the slope length stays positive.
Q: Why does the run have to be more than zero?
A: A run of zero would mean a vertical wall, which has no finite grade. Enter a run greater than zero.
Q: Do rise and run have to use the same unit?
A: Yes. Enter both in the same unit, such as feet or meters. The grade and angle do not depend on the unit, and the slope length is in that same unit.

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