Slope grade calculator
This reports the slope you enter, in percent, degrees and ratio. It does not set the grade your job needs — minimum falls for drainage, ramps, driveways and pipes are fixed by the relevant standard and your authority, not by this tool. Check the required figure against that standard before you cut or fill to it.
Enter the rise and the run — any matching units — and the tool gives the grade as a percentage, the angle in degrees and the reduced ratio, all from the one relationship of rise over run. Add a distance in the last field and it also tells you how far the ground drops over that run at this grade.
Worked example
A yard that falls 2 ft over a 50 ft run is a grade of 2 ÷ 50 = 0.04, or 4%. As an angle that is arctan(0.04) ≈ 2.29°, and as a ratio it is about 1:25. Over a 30 ft path at that same grade the drop is 0.04 × 30 = 1.2 ft — the number you set your string line to.
The formula
grade% = (rise ÷ run) × 100 · angle = arctan(rise ÷ run)
Rise over run is a pure ratio, so its units cancel and the grade is the same whether you measured in feet or metres. Multiply the ratio by 100 for a percent, take its arctangent for the angle, and invert it for the 1:x ratio. The drop over a distance is simply that ratio times the distance.
Questions
- How do I calculate the grade of a slope?
- Divide the rise (the vertical change) by the run (the horizontal distance) and multiply by 100 for a percentage. A drop of 2 ft over 50 ft of run is 2 ÷ 50 = 0.04, or a 4 percent grade. This tool takes your rise and run and reports the grade, the angle and the ratio at once.
- What is the difference between grade, angle and ratio?
- They are three languages for the same steepness. Grade is rise over run as a percent, the angle is that ratio in degrees (the arctangent of rise ÷ run), and the ratio is written like 1:25, meaning one unit up for every 25 along. Earthworks talk in percent, surveyors in ratios, and a level or inclinometer reads degrees.
- What grade do I need for drainage?
- This tool reports whatever slope you enter — it does not prescribe a minimum, because the right fall depends on the surface, the pipe and your local rules. A common rule of thumb for surface drainage is a fall of around 1 to 2 percent away from a building, but confirm the figure your job actually requires with the relevant standard.
- How much does a slope drop over a given distance?
- Multiply the grade fraction by the distance. At a 4 percent grade, over 30 ft the drop is 0.04 × 30 = 1.2 ft. Enter a distance in the projection field and the tool works out the fall for you, in the same units as your run, which is handy for setting string lines and marking batter boards.
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