The requirement
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 ÷ run.
- 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
A drain needs to fall at 1:60 across a 6 m 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°.
So a 6 m length of drain laid to a 1:60 fall drops 100 mm from one end to the other. That is easy to check with a spirit level and a straightedge. A laser level would read 0.95° off the horizontal.
Work it out by hand — ramp gradient
A ramp rises 300 mm over a 4.2 m run. What is that gradient in each format?
- Ratio. Run ÷ rise = 4200 ÷ 300 = 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.
Do it in 5 seconds
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
- Engineering ToolBox, “Slope – Degree, Gradient and Grade Converter” — ratio, percentage and degree conversion formulas.
- ASPE, Plumbing Engineering Design Handbook — drainage fall rates and how they’re conventionally expressed on site.
- There’s no code number to cite for the conversion itself — arctan and rise-over-run are the same maths everywhere. What changes by country and building class is the maximum allowed gradient, which is a separate, jurisdiction-specific rule.