Gradient Calculator and Slope Converter

Equivalent gradient formats

A 1:n ratio means one unit of vertical change over n units horizontally. Percentage is vertical change divided by horizontal distance multiplied by 100. Millimetres per metre is the same slope multiplied by 1,000.

Worked gradient examples

1 in 40 fall per metre

A 1 in 40 (1:40) gradient has a slope of 1 ÷ 40 = 0.025. It is exactly 2.5% and 25 mm per horizontal metre, which is approximately 1.4321°. Over 10 m of plan distance, the vertical change is 0.250 m. In practice, a falling level reduces by 0.025 m for every metre travelled in the stated fall direction.

Convert 2 degrees to a gradient

For an angle measured from horizontal, tan(2°) = 0.0349208. This converts to approximately 1:28.6363, 3.4921% or 34.9208 mm/m. Use unrounded values where a level schedule depends on the result, then apply the project’s stated level precision.

Both examples assume horizontal plan distance. The ratio alone gives magnitude, so confirm whether the line rises or falls.

For a quick comparison of common ratios, see the gradient and fall reference table.

Signs and direction

The converter preserves signs for percentage, degrees and millimetres per metre. On drawings, gradients are often written as a positive magnitude with a separate arrow showing the fall direction.

Frequently asked questions