Slope Converter
Enter rise and run to get the slope as a percentage, in degrees, as a ratio and as rise per metre.
Quick answer
With the default inputs: Rise 1 · Run 10Slope 10.00%
Edit the inputs below to recalculate.Inputs
Result
Slope
10.00%
| Percentage | 10.00% |
| Angle | 5.71° |
| Ratio | 1 : 10.00 |
| Rise per metre | 100.0mm/m |
| Slope length | 10.050m |
| Per mille | 100.0‰ |
Slope = rise ÷ run, independent of slope length. Always set out using horizontal distance, not a length measured along the slope.
Reverse: known result, work out one input
Enter a target result; the other inputs stay fixed and this one is worked out.
Formula
| Slope | i = rise ÷ run |
| Percentage | slope % = i × 100 |
| Angle | θ = arctan(i) |
| Ratio | 1 : n where n = 1 ÷ i |
| Slope length | L = √(rise² + run²) |
A 1 m rise over 10 m run: 10% slope, 5.71°, ratio 1:10, 100 mm per metre, and a slope length of 10.05 m.
Slope conversion table
| Slope | Angle | Ratio | Rise per metre | Typical use |
|---|---|---|---|---|
| 0.5% | 0.29° | 1:200 | 5 mm | Surface drainage |
| 1% | 0.57° | 1:100 | 10 mm | Gutters and eaves |
| 2% | 1.15° | 1:50 | 20 mm | Flat roof falls |
| 3% | 1.72° | 1:33.3 | 30 mm | Structural falls |
| 5% | 2.86° | 1:20 | 50 mm | Profiled metal roofs |
| 10% | 5.71° | 1:10 | 100 mm | Max. accessible ramp |
| 20% | 11.31° | 1:5 | 200 mm | Asphalt shingle roofs |
| 33% | 18.26° | 1:3 | 330 mm | Plain tile roofs |
| 50% | 26.57° | 1:2 | 500 mm | Steep pitched roofs |
| 100% | 45.00° | 1:1 | 1000 mm | 45° pitched roof |
How to work it out
- Confirm what the rise and the run each mean. Rise is the level difference between two points; run is the horizontal projection, not the length measured along the slope. Confusing these three is the leading cause of slope errors.
- Base gradient i = rise ÷ run. One metre of rise over ten metres of run gives i = 0.1.
- As a percentage: i × 100% = 10%. That is what a stated 2% fall means — 2 m of rise per 100 m of horizontal run.
- As an angle: θ = arctan(i). At i = 0.1 the angle is 5.71°, not 10°. Percentage and angle are close at shallow gradients but diverge rapidly beyond about 15%.
- As a ratio 1 : n, where n = 1 ÷ i. So i = 0.1 is 1 : 10. The 1:12 required for accessible ramps is i = 0.0833, or 8.33%.
- Slope length = √(rise² + run²), used for ramp finishes, roof tiles and inclined pipe runs.
Where it goes wrong
- Reading a percentage as an angle. A 10% gradient is 5.71°, not 10°; a 20% gradient is 11.3°, still not 20°. This is the most widespread confusion on site.
- Using the slope length as the run. The slope length is longer, so the computed gradient comes out low. With 3 m rise over 10 m run the true figure is 30%, but using the 10.44 m slope gives 28.7%.
- Designing a 2% roof fall but building it flat. When the fall is formed in screed the thinnest point may be only 20 mm, and the achieved gradient often falls below 1% — which is where ponding comes from.
- Assuming steeper is better for drainage. See the drain slope calculator: over-steep falls separate solids from liquid and block more readily.
- Reading 1:12 for an accessible ramp as 12%. It is 8.33%, and building 12% produces a ramp a wheelchair cannot climb.
Material and cost
The cost of a slope error depends on location: insufficient roof fall causes ponding and leakage, and rectification means stripping membrane and insulation at 150-300 CNY/m²; an under-sloped drain blocks and breaking tiles to fix it runs to hundreds or thousands per location; an over-steep accessible ramp means rebuilding the whole base.
On site
- Gradients worth memorising: structural roof fall 2-3%, bathroom floor fall 1-1.5%, horizontal drainage 0.5-3.5% by diameter, accessible ramp 1:12 (8.33%), vehicle ramps not steeper than 15% on straights, cycle ramps not steeper than 8%.
- Different trades express gradient differently: architecture and drainage use percentages, steel and mechanical use degrees, accessibility and roads use ratios. Check the convention before reading a drawing.
- The practical way to check a fall on site is a spirit level with feeler gauges, or a laser level measuring level difference between two points. Eyeballing cannot distinguish 1% from 3%.
- The direction of fall is more error-prone than the value. State which drain a floor falls to, and draw the watershed lines on drawings with multiple falls.
Basis
- GB 50345-2012 Technical code for roof engineering, roof drainage design
- GB 50763-2012 Code for accessibility design, accessible ramps
- GB 50015-2019 Standard for design of building water supply and drainage, hydraulic calculation
FAQ
Should I use percent or degrees?
Percent (or per mille) suits earthworks, roads and drainage because you can compute fall directly from horizontal distance, which is how you set out. Degrees suit steelwork and machine installation where the angle between members matters. Roofs are usually given as a ratio. The conversion is percentage = tan(angle) × 100, so 45° is 100%, not 90%.
What roof slopes are typical?
Flat roofs are graded at least 3% structurally or 2% with a screed, and gutters need at least 1% longitudinal fall. Tiled roofs depend on the covering: plain tiles about 20-50%, asphalt shingles at least 20%, profiled metal at least 5%. Insufficient fall on flat roofs is the single biggest cause of leaks.
What is the most common setting-out mistake?
Using the slope length as the run. Measuring 10 m along the slope when the horizontal distance is only 9.96 m makes the gradient read high. Measure the run horizontally with a level or total station, or derive l = rise ÷ i first. Also check that drainage falls toward the outlet, not away from it.
Cite this page
Use this format in reports, method statements or coursework. The link is permanent.
Building Calculator. Slope Converter. 2026-10-25. https://jianzhujisuan.com/en/slope-converter
Results are estimating aids only and are not a design basis. Construction and final accounts must follow the drawings, the applicable standards and an approved method statement. Anything affecting structural safety, shoring or falsework must be checked by a suitably qualified engineer.