Slope and fall
Slope is written differently depending on the trade: 2 % on a sewer, 20 mm per metre on paving, 1 : 50 on a roof. It is the same slope — here you can convert between them.
Your numbers
Answer
Per mille
20‰
Percent
2%
Degrees
1.15°
mm per metre
20mm/m
Ratio
1 : 50
Height difference over 5 m
100mm
How to work it out
- 1‰ = mm/m = % · 10 = 201 % is 10 mm per metre and 10 per mille. % and ‰ are not the same number.
- 2° = tan⁻¹(2 / 100) = 1.15°
- 31 : x = 1 : (100 / 2) = 1 : 50
- 4Height difference = 5 m · 2 / 100 = 0.1 m = 100 mm
The formula
% = rise / length · 100
The slope in per cent is the height difference divided by the horizontal length.
‰ = rise / length · 1000 = mm/m
Per mille is thousandths: 2 % is 20 ‰ and 20 mm per metre.
rise = length · % / 100
The other way round: if you know the fall and the length, you get the height difference.
° = tan⁻¹(% / 100) · 1 : x = 1 : (100 / %)
· The drawing is exaggerated for small slopes so it can be seen. The numbers are correct.
In depth: more numbers and “what if”
Height difference at 2 % over other lengths
| Horizontal length | Height difference |
|---|---|
| 1 m | 20 mm |
| 2 m | 40 mm |
| 5 m | 100 mm |
| 10 m | 200 mm |
| 20 m | 400 mm |
What if the slope is different? (over 5 m)
| Percent | Per mille | Height difference |
|---|---|---|
| 1 % | 10 ‰ | 50 mm |
| 1.5 % | 15 ‰ | 75 mm |
| 2 % | 20 ‰ | 100 mm |
| 2.5 % | 25 ‰ | 125 mm |
| 3 % | 30 ‰ | 150 mm |
More: Workshop maths
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- Density and weightThe weight of plates, bars and pipes — per piece, per running metre and in total.
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