The conversion
1:60, 1.67% and 0.95° are the same slope. A fall or a gradient is one slope written three ways: a ratio, a percentage, or an angle in degrees. Drainage falls are usually given as a ratio or in millimetres per metre. Ramp gradients come as a ratio. Some tools and site levels read out in degrees.
All three come from the same fraction: rise ÷ horizontal run. Measure the run horizontally, not along the sloping surface. Use degree mode for the angle formulas. A level surface is 0% and 0°; it has no finite 1:X ratio.
- Ratio (1:X). For every 1 unit of rise, there are X units of run. “1 in X” and “1:X” mean the same thing.
- Percentage. Rise over run × 100. A 1:100 slope is (1 ÷ 100) × 100 = 1%.
- Degrees. The angle whose tangent is rise over run. Find it with arctan (tan⁻¹). A 1:100 slope is arctan(1 ÷ 100) = 0.57°.
Here is every conversion in one place.
| Convert | Formula |
|---|---|
| Ratio → percentage | % = (1 ÷ X) × 100 |
| Ratio → degrees | angle° = arctan(1 ÷ X) |
| Percentage → ratio | X = 100 ÷ %, giving 1:X |
| Percentage → degrees | angle° = arctan(% ÷ 100) |
| Degrees → ratio | X = 1 ÷ tan(angle°), giving 1:X |
| Degrees → percentage | % = tan(angle°) × 100 |
One more conversion is worth knowing on site: millimetres of fall per metre of run. Since 1 m = 1000 mm, a ratio of 1:X falls 1000 ÷ X millimetres for every metre it runs. That number lines up with a tape measure and a string line. It is often the easiest one to set out with.
Quick reference
| Ratio | Percentage | Degrees | mm fall per m |
|---|---|---|---|
| 1:100 | 1.00% | 0.57° | 10.0 mm |
| 1:80 | 1.25% | 0.72° | 12.5 mm |
| 1:60 | 1.67% | 0.95° | 16.7 mm |
| 1:40 | 2.50% | 1.43° | 25.0 mm |
| 1:20 | 5.00% | 2.86° | 50.0 mm |
| 1:14 | 7.14% | 4.09° | 71.4 mm |
| 1:12 | 8.33% | 4.76° | 83.3 mm |
| 1:10 | 10.00% | 5.71° | 100.0 mm |
Work it out by hand — drainage fall
For this example, a plan specifies 1:60 over a 6 m horizontal run. How much does it drop? And what is that as a percentage and an angle?
- Turn the ratio into a rate. 1000 mm ÷ 60 = 16.7 mm of fall per metre of run.
- Multiply by the run. 16.7 mm/m × 6 m ≈ 100 mm of total fall over the 6 m pipe run. Exact check: 6000 mm ÷ 60 = 100 mm.
- As a percentage. (1 ÷ 60) × 100 = 1.67%.
- As degrees. arctan(1 ÷ 60) = 0.95°.
Over 6 m of horizontal run, that slope drops 100 mm. Check the level difference with suitable site equipment. This example converts a chosen gradient; it does not set the required drainage fall.
Work it out by hand — ramp gradient
An example ramp rises 300 mm over a 4.2 m horizontal run. What is that gradient in each format?
- Ratio. Run ÷ rise = 4200 ÷ 300 = 14, so the ratio is 1:14.
- Percentage. (300 ÷ 4200) × 100 = 7.14%.
- Degrees. arctan(300 ÷ 4200) = arctan(0.0714) = 4.09°.
Same fraction, three labels. Whichever one your plans or your inspector asks for, you only ever do one division. Degrees adds one arctan on top.
Calculate and keep your working
Use the free web tool or download the Chippy Tools printable reference.
Related
- Pillar: Concrete Calculations: The Complete On-Site Guide, every concrete sum in one place.
- Each country’s building code sets its own maximum ramp and walkway gradients. Check your local ramp-gradients page for the legal minimum/maximum before you build to a number from this page.
Sources
These conversions follow from the right-triangle relationship tan(angle) = rise ÷ horizontal run. The examples show arithmetic, not permitted drainage or ramp gradients. Use the adopted code and approved plans to choose the gradient before converting it.