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Elevation Grade from Rise and Horizontal Run

Convert signed rise over positive horizontal run into a slope ratio, percentage and principal angle.

  • Formula & worked example
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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.

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

Formula and method

A 1 m rise over20 m horizontal run is0.05, or5%, at about2.8624 degrees.

g=rise/run; percentage=100g; angle=atan(g). The displayed reciprocal is rounded to two decimals.

Worked example

Enter these known values and leave the other values blank.

Vertical distance ("rise")
1 m
Horizontal distance ("run")
20 m
Grade
0.05
Grade in percentage
5 %
Angle of elevation
2.8624 deg

Assumptions and limitations

  • Horizontal run is positive; positive rise climbs and negative rise descends. Level rise gives zero grade. A vertical line has no finite grade in this model.
  • The principal angle lies strictly between−90 and90 degrees. Clear the unknown measurement before using an inverse. Zero grade and zero rise do not identify a unique horizontal run.
  • Metric defaults are1 m rise and20 m run; imperial defaults are1 ft rise and20 ft run. The angle defaults to degrees for metric and radians for imperial. Every captured unit remains available.
  • The reciprocal display rounds the reciprocal of the retained decimal grade to the nearest hundredth with ties toward positive infinity, using integer quotient and remainder before rounding. Exceptionally large reciprocals use a 64-significant-digit scientific representation of that rounded value. This is a rounded display, not a new exact measurement.
  • Extremely small or large finite values use scientific notation when ordinary decimal formatting exceeds its display range. This changes display only and does not impose a minimum physical length.

Common questions

Is5% the same as5 degrees?

No. A5% grade is a ratio of0.05, whose angle is atan(0.05), about2.8624 degrees.

References

Translate the captured reciprocal helper to nearest hundredth with ties toward positive infinity by exact quotient and remainder of the retained decimal grade. Avoid tolerant floor and rounded intermediate division at half-cent boundaries. Represent exceptionally large rounded reciprocals at 64 significant digits using a bounded leading-digit computation, without changing global precision or excluding tiny grades. Require positive horizontal run and the principal slope-angle interval, retaining signed rise and level grade. Use the existing source-pinned scientific fallback when relative decimal formatting overflows; preserve tiny nonzero values without imposing a physical minimum. Enforce strict signs using sign(...) rather than tolerance-based zero comparisons.

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