Slope Percent To Degrees Calculator

Work out slope percent to degrees instantly with clear inputs, formula shown and shareable results.

About Slope Percent To Degrees Calculator

Percentage slope is rise divided by horizontal run times 100, and the angle is its arctangent. 15% is 8.53 degrees, or 1 in 6.67. The two scales diverge sharply on steep ground: 100% is only 45 degrees, and a vertical face is infinite percentage - which is why highway signs use percentage and climbers use degrees.

Formulas

Percent to degrees

angle = arctan(percent / 100)

Degrees to percent

percent = tan(angle) x 100

Worked example

With the default values below, Slope Percent To Degrees Calculator returns Slope In Degrees of 8.531. Change any input above and every figure here is recalculated in your browser.

Inputs used

Slope: 15 %
Convertone of Percent to degrees, Degrees to percent: Percent to degrees

Results

Slope In Degrees: 8.531 deg
Slope As A Percentage: 15.00%
Expressed As A Ratio: 1 in 6.67
Rise Over 100 Metres Of Run: 15.00 m

Step by step

1Values used
2Percent to degrees
3Degrees to percent
4Slope In Degrees= 8.531 deg
5Slope As A Percentage= 15.00
6Expressed As A Ratio= 1 in 6.67
7Rise Over 100 Metres Of Run= 15.00 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

Is 100% slope vertical?

No, it is 45 degrees - equal rise and run. Vertical would be infinite percentage, which is why the scale is unhelpful for cliffs.

What slope is a steep road?

Highway grades rarely exceed 7%. Anything over 12% is exceptionally steep for a public road and over 20% needs specialist vehicles.