Gradient Of A Hill Calculator

Work out gradient of a hill instantly with clear inputs, formula shown and shareable results.

About Gradient Of A Hill Calculator

Gradient is vertical rise over horizontal run: 120 m over 1600 m is 7.5%, or 4.29 degrees, or 1 in 13.3. The slope distance is slightly longer than the horizontal run - 1604.5 m here - which is why map distances understate walked distance in hilly ground.

Formulas

Gradient

gradient = rise / horizontal run

Slope distance

slope = sqrt(rise^2 + run^2)

Worked example

With the default values below, Gradient Of A Hill Calculator returns Gradient of 7.50%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Vertical rise: 120 m
Horizontal distanceminimum 0 m: 1,600 m

Results

Gradient: 7.50%
Gradient In Degrees: 4.289 deg
Railway-Style Ratio: 1 in 13.33
Distance Along The Slope: 1,604.5 m

Step by step

1Values used
2Gradient
3Slope distance
4Gradient= 7.50
5Gradient In Degrees= 4.289 deg
6Railway-Style Ratio= 1 in 13.33
7Distance Along The Slope= 1,604.5 m

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why do railways use 1 in n?

Because it reads directly as the distance needed per unit of climb, which is what matters for locomotive haulage capacity.

Is the horizontal run or slope distance used?

Gradient conventionally uses horizontal run. On slopes under about 15% the difference from slope distance is under 1%.