Processing math: 100%

Gradient to Degrees Calculator

Formula

The formula to convert a gradient to degrees is:

$\text{degrees} = \arctan(\text{gradient}) \times \left( \frac{180}{\pi} \right)$

Where:

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

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.

Example Calculation 1

Let's assume the following value:

Gradient = 1

Using the formula:

$\text{degrees} = \arctan(1) \times \left( \frac{180}{\pi} \right) = 45$

The angle in degrees is 45°.

Example Calculation 2

Let's assume the following value:

Gradient = 0.5

Using the formula:

$\text{degrees} = \arctan(0.5) \times \left( \frac{180}{\pi} \right) = 26.5651$

The angle in degrees is 26.5651°.