Enter the gradient of a slope (rise over run) into the calculator to convert it to degrees. The calculator will provide the angle in degrees based on the gradient input.

Gradient To Degrees Formula

The following formula is used to convert a gradient to degrees:

degrees = atan(gradient) * (180 / π)


  • Gradient is the ratio of the rise to the run (rise/run).
  • Degrees is the angle in degrees that corresponds to the gradient.

To convert a gradient to degrees, take the arctangent of the gradient and then convert the result from radians to degrees by multiplying by 180/π.

What is Gradient?

Gradient is a measure of the steepness or incline of a slope. It is often expressed as a ratio of the vertical rise to the horizontal run. For example, a gradient of 1 means that for every unit of horizontal distance, there is a rise of 1 unit. Gradients are used in various fields such as civil engineering, road construction, and geography to describe the incline of surfaces.

How to Calculate Gradient to Degrees?

The following steps outline how to convert the gradient of a slope to degrees:

  1. First, determine the gradient of the slope (rise over run).
  2. Next, use the formula: degrees = atan(gradient) * (180 / π).
  3. Finally, calculate the angle in degrees.
  4. After inserting the gradient and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge.

Gradient (rise/run) = 0.5

Using the formula, the degrees would be calculated as:

degrees = atan(0.5) * (180 / π) ≈ 26.57 degrees