Slope calculator

How it works

Slope as a percentage is the rise divided by the horizontal length, times 100. Degrees come from the arctangent of the same ratio.

Example

An accessible ramp should not exceed 8% (about 4.6°); a comfortable staircase is around a 60-70% riser/tread ratio.

Percentage, degrees and ratio: three ways of saying the same thing

The percentage is the rise divided by the horizontal distance: ten per cent means ten centimetres of climb for every metre travelled on the flat. Degrees are the true angle, and they are not proportional: 100% is not ninety degrees but forty-five, because at forty-five degrees you rise exactly as much as you advance. The ratio, written as 1:20, says how many horizontal units are needed for one vertical.

The three forms coexist through trade habits: roads and cycle paths speak in percentages, roofs in degrees or ratios, drains in ratios or millimetres per metre. Confusing them is the mistake that leads to building a ramp three times steeper than intended.

On the horizontal distance, not the sloping one

The formula asks for the plan projection, not the length of the ramp. On gentle slopes the difference is negligible: at ten per cent the sloping length exceeds the horizontal one by barely half a per cent. But on roofs and stairs, where thirty degrees are exceeded, the error becomes serious and distorts the material calculation.

The practical way to take the right measurement, when the ground slopes, is to hold the tape level and measure vertically from there to the ground: it is the method used on site with a rod and a spirit level, and it requires no trigonometry.

The values that actually matter, by context

For an accessible ramp, the Italian reference in DM 236/1989 is eight per cent, with steeper gradients allowed only on short runs and under precise conditions; the figure comes from how much a person in a wheelchair can climb unaided. For a bathroom drain the practical reference is around one to two per cent: any less and water stands, much more and the water runs ahead leaving the solids behind, which is the commonest cause of blockages in a badly rebuilt system.

For a roof the pitch depends on the covering: tiles usually want at least thirty per cent, sheet metal and membranes cope with far lower values. And for a terrace one per cent towards the outlets is enough, provided it is constant.

The sign, and the sum you must not make

A negative gradient is not an error: it is a descent, and in calculating excavation volumes or water run-off the sign is everything. What cannot be done, instead, is adding gradients up: two stretches at five per cent do not make one at ten. For an average gradient over several stretches you add the rises and add the distances, and divide one sum by the other.

It is the same reason the average gradient of a climb on a bicycle says so little: it hides the hard stretches, and those are the ones the legs feel.

Nearby tools

For the rise-and-going ratio of a staircase there is Stair calculator. For measurements and areas Room area and volume and Areas and perimeters, and for angles Scientific calculator.