Geometry
Rise, run, slope & rake
- where
- slope length (m)
- horizontal run (m)
- vertical rise or fall (m)
- angle (degrees)
- gradient (%)
- gradient as 1 in n
Explain this equation
This turns a horizontal run and a vertical rise into the sloping length, the angle, the percentage gradient and the 1 in n ratio.
x is the horizontal run and y the vertical rise, both in metres; a negative y means a fall. L is the length measured along the slope. θ is the angle from horizontal in degrees. G is the gradient as a percentage, and n is the run per unit of rise, as in 1 in n.
The run, rise and slope form a right-angled triangle, so L comes from Pythagoras and θ from the tangent, rise over run. The gradient is rise over run expressed per hundred, hence × 100. 1 in n is that ratio inverted.
A 4 m run with a 1 m rise gives a 4.12 m slope, about 14°, 25%, or 1 in 4. Doubling the rise roughly doubles the gradient but does not double the angle.
Watch out: with zero rise the slope is level and 1 in n has no meaning, so the calculator shows 0. A falling slope gives negative values.
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
Estimates are not design approval or British Standards compliance checks. Structural arch, retaining-wall, wind, foundation, lintel and masonry-capacity design are not performed. Use the project engineer’s specification.