Free · Coordinate geometry calculators

Rise, Run, Percent Grade & Slope Angle

Convert signed rise and positive horizontal run to slope percentage and angle.

  • Formula & worked example
  • Private in your browser
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A rise of 1 m over 1 m of horizontal run is a 100% grade and a 45° angle. A 100% grade does not mean 90°.

Grade (%) = 100 × rise ÷ horizontal run; angle = arctan(rise ÷ run)

Worked example

Enter these known values and leave the other values blank.

Signed vertical rise
1 m
Positive horizontal run
1 m
Slope angle
45 deg
Grade in the selected unit
100 %

Assumptions and limitations

  • Run is the horizontal distance, not the sloping surface length, and must be positive. Rise can be negative for a descent.
  • The angle is restricted to strictly between −90° and 90°. A vertical line has zero run and no finite percentage grade.
  • Length fields may use different units; the calculation converts them before taking their ratio. The grade selector offers percent and per mille.
  • This is geometry only. It does not decide accessibility, road design or construction compliance limits.

Common questions

Why is 100% slope only 45°?

A 100% grade means the rise equals the horizontal run. The tangent of 45° is 1; 90° would require an infinite ratio.

Can a grade exceed 100%?

Yes. If rise exceeds the positive run, the grade exceeds 100% and the angle exceeds 45° while remaining below 90°.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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