Gradient to Degrees Converter Formula

Understand the math behind the gradient to degrees converter. Each variable explained with a worked example.

Use the Gradient to Degrees Converter

Formulas Used

Degrees

degrees = atan(value / 100) * 180 / pi

Radians

radians = atan(value / 100)

Rise per Foot of Run

rise_per_foot = value / 100 * 12

Variables

VariableDescriptionDefault
valueGradient (% Grade)(%)10

How It Works

Gradient (Percent Grade) to Degrees

Angle = arctan(Gradient / 100)

A 100% grade means the rise equals the run (45°). A 10% grade is a relatively steep road.

Common Grades

| Grade | Degrees | Context | |---|---|---| | 1% | 0.57° | Gentle drainage slope | | 5% | 2.86° | Moderate road grade | | 10% | 5.71° | Steep road grade | | 45% | 24.2° | Very steep trail | | 100% | 45° | Rise equals run |

Worked Example

Convert a 10% road grade to degrees.

value = 10
  1. 01Angle = arctan(10/100) = arctan(0.1)
  2. 02Angle = 5.71°
  3. 03Rise per foot of run = 0.1 x 12 = 1.2 inches

Ready to run the numbers?

Open Gradient to Degrees Converter