Convert vertical rise and horizontal run to matching units, then calculate grade percentage and inclination angle.
Complete the required fields and select the calculate button.
Run means horizontal distance, not the sloping surface length. A negative rise represents a downhill grade.
Slope percentage expresses vertical rise or fall as a percentage of horizontal run. The calculator converts each measurement to metres, then reports both grade percentage and the corresponding angle in degrees.
Grade percentage is not the same number as degrees. A 100% grade means rise equals horizontal run and corresponds to 45°, while a 100° angle would describe something entirely different.
Negative rise returns a negative grade and angle for a descent. Unit conversion lets rise and run use different length units, but each menu must match the number entered.
Slope percentage = rise ÷ horizontal run × 100
Angle = arctan(rise ÷ horizontal run)
The run must be greater than zero. The angle is reported in degrees and lies between −90° and 90° for the allowed positive run.
| Item | Meaning |
|---|---|
| Rise | Signed vertical elevation change, converted to metres. |
| Run | Positive horizontal distance, converted to metres. |
| Grade | Rise per run multiplied by 100 percent. |
| Angle | Arctangent of rise/run, reported in degrees. |
| Sloped length | The surface or hypotenuse distance, which is not entered here. |
Enter a rise of 0.6 m and a run of 12 m. The ratio is 0.6 ÷ 12 = 0.05, so slope is 5%. Angle = arctan(0.05) = about 2.86°.
If rise were −0.6 m with the same run, outputs would be −5% and approximately −2.86°, indicating descent in the chosen direction.
A sign states direction, while magnitude states steepness. Ten percent means ten units of vertical change per 100 equal horizontal units. It does not mean the surface is ten percent longer or that the angle is ten degrees.
Road, ramp, drainage, roof, and accessibility requirements use specific definitions, measurement methods, and limits. Survey error matters over short runs. Use project drawings, applicable codes, and a qualified professional for construction or safety decisions.
To find sloped surface length after obtaining rise and run, use the Pythagorean relationship: length = √(rise² + run²). That length should exceed the horizontal run whenever rise is nonzero. It should not be substituted back into the grade denominator.
Measurement direction establishes the sign. Surveying from low point to high point gives positive rise; reversing direction gives negative rise while physical steepness remains the same magnitude. State direction when a sign could affect drainage or travel.
Small grades are sensitive to level and endpoint errors. Over a 100-metre run, a 0.1-metre elevation error changes grade by 0.1 percentage point. For drainage, accessibility, earthwork, or roadway decisions, calibrated survey equipment and the governing definition are more reliable than casual tape measurements.
Ratios such as 1:20 can be misunderstood because some fields use rise:run while others phrase “one in twenty.” Write both quantities and units beside the ratio.
To plan multiple segments, calculate each grade from its own elevation change and horizontal run. The overall grade is total signed rise divided by total horizontal run, not the simple average of segment percentages unless their runs are equal. A short steep segment can matter for safety even when the overall average looks gentle.
Reported precision should match measurement quality. Showing hundredths of a percent from rough endpoints may suggest accuracy the survey does not support. Record the endpoints, direction, instrument, and units so another person can reproduce the calculation.
Keep the original inputs beside the result for a clear, reproducible record.
No. Rise equals horizontal run, producing a 45-degree angle. A vertical line has zero horizontal run and an undefined percentage.
Yes. A negative value describes descent in the selected direction and returns negative grade and angle.
Grade is defined from vertical change divided by horizontal distance. Using surface length produces a different ratio.
Yes. Select each correctly and the page converts both to metres before division.
For a nonzero grade magnitude, N equals 100 divided by the percentage. A 5% grade is a 1-in-20 rise or fall.
No. Applicable codes may specify measurement, landings, cross-slope, handrails, and other requirements. Use official rules and professional verification.
Angle uses arctangent, a nonlinear function. They are close only for small slopes when expressed in radians versus decimal grade.