Convert between slope as a percentage, angle in degrees, ratio and rise over run for drainage, ramps and ground works.
Slope can be written as a percentage (rise divided by run times 100), as an angle in degrees, or as a ratio such as 1:40. A 100% grade is a 45° angle. These are just different ways of describing the same steepness.
Drainage falls are often 1:40 to 1:80, a wheelchair ramp should be no steeper than 1:12 (about 8%), and a domestic stair is roughly 30–42°.
Take the arctangent of the percentage divided by 100. For example a 10% grade is arctan(0.1), which is about 5.7 degrees. The calculator does this automatically.
It means the surface drops 1 unit for every 40 units of length, equal to a 2.5% grade. It is a common minimum fall for drainage pipes and patios.
A 45 degree angle is a 100% grade, because the rise equals the run. Grades above 100% are steeper than 45 degrees.
Guidance is usually no steeper than 1:12, which is about 8.3%. Gentler slopes such as 1:15 or 1:20 are easier to use where space allows.
A fall of around 1:40 to 1:80 is typical for patios and paths so water runs off without pooling. Always slope away from buildings.
