Slope Angle From Gradient Calculator

Work out slope angle from gradient instantly with clear inputs, formula shown and shareable results.

About Slope Angle From Gradient Calculator

Gradient is rise divided by run, and the slope angle is its arctangent. A grade quoted as a percentage is simply the gradient times 100, so a 1-in-12 ramp is an 8.33% grade at about 4.76°.

Formulas

Slope angle

θ = arctan(rise / run)

Grade

grade % = 100 × rise / run

Worked example

With the default values below, Slope Angle From Gradient Calculator returns Slope angle of 14.0362. Change any input above and every figure here is recalculated in your browser.

Inputs used

Rise (vertical): 3
Run (horizontal)minimum 0: 12

Results

Slope angle: 14.0362 °
Grade: 25.0000 %
Gradient (rise ÷ run): 0.25000000
Slope length along the incline: 12.3693

Step by step

1Values used
2Slope angle
3Grade
4Slope angle= 14.0362 °
5Grade= 25.0000 %
6Gradient (rise ÷ run)= 0.25000000
7Slope length along the incline= 12.3693

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 8 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

Rise 3 in a run of 12?

Gradient 0.25, grade 25% and an angle of arctan 0.25 ≈ 14.0362°.

Is a 100% grade a vertical wall?

No, it is 45°. A vertical drop has an infinite gradient, which is why grades above about 30% are rare on roads.