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

GradeDegreesContext 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

Frequently Asked Questions

What does percent grade mean?

Percent grade = (rise / run) x 100. A 10% grade means 10 feet of elevation change for every 100 feet of horizontal distance.

What is a steep road gradient?

Most public roads are designed for grades under 6%. Mountain highways may reach 8-12%. The steepest public roads in the world approach 35% (about 19°).

Ready to run the numbers?

Open Gradient to Degrees Converter