Slope calculator: per cent, degrees, 1 in X, ramps and roof pitch

A slope in per cent is the rise divided by the horizontal run, times 100. A 100% slope is 45°, 1% means 10 mm of rise per metre, and a gradient of 1 in 20 is a 5% slope.

Four ways to write the same slope

The same slope can be written in several ways. Roofers give a pitch in degrees, drainage drawings give gradients such as 1 in 40 or 1 in 80, plumbers talk about millimetres of fall per metre, and many data sheets use a percentage. A 2% slope is a rise of 20 mm for every metre measured horizontally, which is also a gradient of 1 in 50.

The formula is: slope in % = rise ÷ horizontal run × 100. A roof slope with a 4 m run that rises 1.20 m is at 1.20 ÷ 4 × 100 = 30%. Both measurements must be in the same unit: 1,200 mm over 4,000 mm still gives 30%. To turn a percentage into 1 in X, divide 100 by it: 5% is 1 in 20.

Conversion table: percentage, degrees, mm per metre and 1 in X

Each row gives the same slope written four ways. Example: a 30% slope is 16.70°, a rise of 300 mm for every metre measured horizontally, or 1 in 3.3. A ramp at 1 in 12 is 8.33%.

From percentage to degrees

Degrees are not proportional to the percentage. The angle is the arctangent of the slope: 30% is 16.70°, 50% is 26.57° and 100% is exactly 45°, where the rise equals the run. The other way round, the slope in % is the tangent of the angle times 100: a 35° roof pitch is a 70.02% slope.

The classic mistake is to read 30% as 30°. A roof pitched at 30° has a slope of 57.74%, almost twice as steep. Always check which unit a quote or a data sheet is using.

Roof pitch and rafter length

For a pitched or lean-to roof you need two figures: the pitch, which decides which tiles or sheets you can use, and the true length of the slope, used to order rafters, battens and membrane. The true length comes from Pythagoras: a 4 m run with a 1.20 m rise gives √(4² + 1.20²) = 4.18 m.

A lean-to with a 4 m run and a 2.80 m rise is at 70%, a pitch of 34.99°. The minimum pitch of a tile or a sheet depends on the product and on how exposed the roof is, and it is printed on the manufacturer's data sheet, so the calculator does not apply one figure to every roof.

Access ramps: Approved Document M, Table 1

In England, Approved Document M (Volume 2, buildings other than dwellings) links the steepest gradient to the going of each flight: 1 in 12 for a going of 2 m (166 mm rise at most), 1 in 15 for 5 m (333 mm) and 1 in 20 for 10 m (500 mm). Between 2 m and 10 m you may interpolate, which gives 1 in 14 for a 4 m going and 1 in 19 for a 9 m going. No flight should have a going of more than 10 m or a rise of more than 500 mm. Landings at the foot and head must be at least 1.2 m long, intermediate landings at least 1.5 m, and a total rise of more than 2 m calls for another way up, such as a lift. Wales and Scotland publish their own guidance.

Example: a 280 mm rise over a 4 m going is 7%, or 1 in 14.3, within the 1 in 14 allowed for that going. The same rise over 3 m would be 9.33%, steeper than the 1 in 13 allowed at 3 m. An approach less steep than 1 in 20 is treated as a gently sloping approach rather than a ramp, with a level landing for every 500 mm of rise.

Waste pipes: Approved Document H, Table 2

Unventilated branch pipes have their own limits in Approved Document H. A WC branch is laid at 18 to 90 mm of fall per metre and can run up to 15 m. A 30 mm washbasin or bidet branch also starts at 18 mm per metre, but its upper limit drops as the pipe gets longer: 87 mm per metre up to 0.7 m, 44 mm up to 1.1 m and 22 mm up to 1.7 m. Beyond the table, the branch needs venting.

Example: a WC 3 m from the stack laid at 20 mm per metre needs 3 × 20 = 60 mm of fall. Below ground, Table 6 of the same document gives 1 in 40 as the flattest gradient for a 100 mm drain with a peak flow under 1 litre per second, and 1 in 80 above that flow when at least one WC is connected.

Common mistakes

• Measuring along the slope instead of horizontally: on a 30% roof, the 4.18 m slope length would give 28.7% instead of 30%.
• Mixing units: 60 mm over 3 m is 2%, not 20%. The calculator lets you pick a unit for each measurement.
• Confusing degrees and per cent, especially above 20%, where the gap grows quickly.
• Reading 1 in 12 as 12%: it is 8.33%.

For the next steps, the mitre angle calculator turns a roof pitch into rafter cuts, the wall area calculator helps when ordering materials, and the cubic metres to tonnes converter works out the gravel for a path.