The formula
gradient % = rise ÷ horizontal distance × 100
Where it comes from
A gradient compares how much you climb with how far you travel horizontally, not with the distance along the slope. That distinction matters: on a steep hill the two differ noticeably, and using the wrong one understates the gradient.
How to work it out by hand
- Divide the rise by the horizontal distance
- Multiply by 100 for the percentage
- For degrees, take the arctangent of the same fraction
- For the ratio, divide both by the rise: 1 in something
What is worth knowing
The percentage and the angle are not proportional, which is where road signs mislead. A 100 % gradient is 45°, not 90°, and the percentage keeps climbing without limit while the angle never reaches vertical. Accessibility standards are strict about this: most jurisdictions cap a wheelchair ramp at 8 %, about 4.6°, and 5 % is the comfortable figure. Roads sign anything above 10 % as steep, and the steepest public roads in the world sit around 35 %. Roofers usually work in a ratio instead, which is why a roof is quoted as 1 in 4 rather than 25 %.