Fall from a 1:n gradient

This gives the fall over a run from a gradient written as 1 in n, and the level at the far end. Use it for paving, drainage channels, thresholds or anything laid to a fall.

x is the horizontal run in metres. n is the gradient denominator, so 1 in 80 means n = 80. f is the fall in millimetres. L₁ is the starting level and L₂ the level at the end of the run, both in metres.

A 1 in n gradient drops one unit for every n units across, so the fall over x is x / n. The × 1000 shows the fall in millimetres; the end level is worked in metres, so it uses x / n without that factor.

A 5 m run at 1 in 80 falls 62.5 mm, so a 10.000 m start level ends at 9.9375 m. Halving n, to 1 in 40, doubles the fall.

Watch out: the calculator assumes nothing about what fall is required. Take the gradient from the specification for that detail.