Slope Calculator
Enter a slope in any one form and get all the others at once: percent grade, angle, ratio (1 : n) and rise ÷ run. You can also work from a rise and a run.
How a slope is expressed and calculated
Let r be the rise divided by the run. The slope can be written in these ways:
- Grade (%) = r × 100 (rise ÷ run × 100).
- Angle = atan(r), the inverse tangent of r, in degrees. Conversely, r = tan(angle).
- Ratio (1 : n): a rise of 1 for a run of n, where n = 1 ÷ r.
At 45° the rise equals the run (r = 1), so the grade is 100%. A grade above 100% is steeper than 45°.
From a rise and a run
Choose "Rise and run" to find the slope from two lengths. The rise and the run can each have their own unit (km, m, cm, mm, in, ft, yd). If the units differ, the lengths are converted exactly by their definitions before dividing.
- A rise of 30 cm over a run of 1 m gives r = 0.3 (a 30% grade, about 16.6992°).
- A run of 0 cannot be calculated (the surface would be vertical). A rise of 0 is level (0%, 0°).
Precision
Grade and ratio conversions use exact fractions and are rounded only once, at the end. The angle involves tan and atan, which are irrational, so it uses an ordinary numerical approximation and the result is rounded for display.
Examples
- A 10% grade is about 5.7106° (a ratio of 1 : 10).
- 45° is a 100% grade, a ratio of 1 : 1.
- A ratio of 1 : 12 is about an 8.33% grade, about 4.7636°.
- A rise of 1 m over a run of 5 m is a 20% grade, about 11.3099°.
- A roof that rises 4 inches for every 12 inches of run (a "4 in 12" pitch): enter a rise of 4 in and a run of 12 in to get a 33.33% grade, about 18.4349°.
Notes
- Decimal numbers are accepted (up to 12 digits before the decimal point and 6 after). Use a period as the decimal separator; commas are accepted only as thousands separators.
- Enter an angle of 0 or more and less than 90. A 90° surface is vertical and has no defined slope.
- For a very steep slope (almost vertical), the angle is shown with more digits so that it is not rounded up to 90. If it is too steep for the 8 decimal places the tool can show, it reads "Just under 90° (almost vertical)" and the angle cannot be copied.
- When n in the ratio is smaller than 0.01, it is shown as "less than 0.01".
- A slope worked out from an angle is an approximation, so digits beyond 12 significant figures are not shown.
- This tool only converts the way a slope is written. Limits for ramps, roofs, roads and so on depend on the standard or code that applies and are not covered here.
- To convert between degrees and radians, use the Degrees and Radians Converter.
Frequently asked questions
What is 45 degrees as a percent grade?
100%. At 45° the rise equals the run, because tan 45° = 1.
What angle is a 10% grade?
About 5.7106°, the inverse tangent of 0.1 in degrees.
What is a 1:12 slope as a percent?
About 8.33% (1 ÷ 12 × 100), or about 4.7636°.
Can the rise and the run be in different units?
Yes. For example, a rise of 30 cm over a run of 1 m gives 30% (about 16.6992°) once you pick each unit.