Geometry
Rise, run, slope & rake
- where
- sloping length (m)
- horizontal run (m)
- vertical rise or fall (m)
- angle (°)
- gradient (%)
- ratio denominator, 1:n
Explain this equation
Describes a slope four ways from its horizontal run and vertical rise: the sloping length, the angle, the percentage gradient and the 1:n ratio. Use it for ramps, paths, rakes and sloping members.
x is the horizontal distance and y the vertical rise, in metres. A fall can be entered as a negative y. L is the length measured along the slope. θ is the angle from horizontal. G is the rise as a percentage of the run. n means 1 unit of rise in n units of run.
Run, rise and slope form a right-angled triangle, so L = √(x² + y²) by Pythagoras and θ = arctan(y/x). G is just y/x as a percentage, and n is the same ratio turned upside down.
A 1 m rise over 4 m is 25%, 1:4, about 14° and 4.12 m along the slope. A 1:12 ramp is about 8.3% and 4.8°.
Watch out: with a zero rise the ground is level and there is no 1:n ratio, so the calculator shows 0 for n.
Calculate a rake or fall from horizontal run and vertical rise.
Enter your values to see the result.
Good to know
Rise may be negative to represent a fall. Zero rise is level; a 1:n ratio is then not applicable.
Sources
- Geometry / arithmetic
This is a calculation aid, not a structural design or compliance certificate. Every default is an example, not a specification for your project.