Ramp Gradient: Percent, Degrees, and the 1 in 12 Rule

From the rise and the run, finds the gradient as a percentage, the angle, and the run for a rise of 1. Japanese accessibility rules require 1/12 or gentler indoors.

Explanation

This works out how steep a ramp is from two numbers: the rise, or how far it climbs, and the run, the horizontal distance it covers. You get three answers, because ramps are described in three different ways: as a percentage, as an angle, and as a ratio such as 1 in 12. The third is the form accessibility standards are written in.

\text{gradient}\ (\%) = \dfrac{h}{d} \times 100

\theta = \arctan\left(\dfrac{h}{d}\right)

$h$ is the rise and $d$ is the run. The run for a rise of 1 is $d / h$ , and when that comes out at 12 the ramp is 1 in 12. Enter both in the same unit, since the ratio cancels them.

Example

Take the defaults, a rise of 1 and a run of 12.

\text{gradient} = \dfrac{1}{12} \times 100 = 8.33\ldots\ \%

\theta = \arctan\left(\dfrac{1}{12}\right) = 4.76\ldots\ \text{degrees}

The gradient is about 8.33%, the angle about 4.76 degrees, and the run for a rise of 1 is 12. That is the classic 1:12 ramp.

Notes

1:12, about 8.3%, is the usual benchmark for a ramp a wheelchair user can manage unaided. Japan's accessibility rules lean on it, and so does the ADA in the United States. What actually binds depends on the building, the height climbed and local rules, so check the standard that applies to your project.
The run is horizontal, not the length of the sloping surface. A ramp rising 1 over a run of 12 has a sloping face of about 12.04.
Length grows in step with height. At 1:12, climbing 75 cm takes 9 m of run, and a long ramp needs level landings at intervals for resting. Check early that it fits the site, because this is what usually kills a design.
Percent and degrees are easy to confuse: 8.33% is about 4.76 degrees, not 8.33 degrees.