Road Gradient Calculator Formula

Understand the math behind the road gradient calculator. Each variable explained with a worked example.

Use the Road Gradient Calculator

Formulas Used

Gradient

gradient_pct = rise / run * 100

Slope Ratio (1 in N)

ratio = run / rise

Slope Distance

slope_length = sqrt(pow(rise, 2) + pow(run, 2))

Variables

VariableDescriptionDefault
riseVertical Rise(m)5
runHorizontal Run(m)100

How It Works

Road Gradient Calculation

Gradient expresses how steep a road is.

Formulas

Gradient (%) = (Rise / Run) x 100

Slope ratio = 1 in (Run / Rise) (e.g., 1 in 20)

Slope distance = sqrt(Rise^2 + Run^2)

Design guidelines typically limit residential roads to 8-12% and highways to 3-6% depending on terrain and design speed.

Worked Example

A road rises 5 m over a horizontal distance of 100 m.

rise = 5run = 100
  1. 01Gradient = 5/100 x 100 = 5%
  2. 02Slope ratio = 1 in 100/5 = 1 in 20
  3. 03Slope distance = sqrt(25 + 10000) = sqrt(10025) = 100.12 m

Ready to run the numbers?

Open Road Gradient Calculator