The requirement
A fall or a gradient is the same slope written three different ways — a ratio (1:60), a percentage (1.67%), or an angle in degrees (0.95°). Drainage falls are usually specified as a ratio or in millimetres per metre, ramp gradients as a ratio, and some tools and site levels read out in degrees. Converting between them is just rise-over-run, presented differently.
All three come from the same fraction: rise ÷ run.
- Ratio (1:X) — for every 1 unit of rise, there are X units of run. Written as “1 in X” or “1:X” — they mean the same thing.
- Percentage — the rise-over-run fraction × 100. A 1:100 slope is (1 ÷ 100) × 100 = 1%.
- Degrees — the angle whose tangent is the rise-over-run fraction, found with arctan (tan⁻¹). A 1:100 slope is arctan(1 ÷ 100) = 0.57°.
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’s the number that lines up with a tape measure and a string line, so it’s often the easiest one to actually 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’s that as a percentage and an angle?
- Convert the ratio to 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 total fall over the 6 m pipe run (6000 mm ÷ 60 = 100 mm exactly).
- 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 — enough to check with a spirit level and a straightedge, or a laser level reading 0.95° off the horizontal.
Work it out by hand — ramp gradient
A ramp rises 300 mm over a 4.2 m run. What’s 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’re never doing more than one division and — for degrees — one arctan.
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.