Slope conversion: degrees to percent, mm per metre and inches per foot
Short answer: percent slope = 100 × tan(angle). Millimetres per metre = 1000 × tan(angle). Inches per foot = 12 × tan(angle). A ratio of 1:n means n = 1 ÷ tan(angle). Use the tables below if you would rather look the number up.
The formulas
Slope is the rise divided by the run, and that equals the tangent of the angle. Every other unit is that number scaled:
| You want | Formula |
|---|---|
| Percent slope | 100 × tan(angle) |
| Millimetres per metre | 1000 × tan(angle) |
| Inches per foot | 12 × tan(angle) |
| Ratio 1:n | n = 1 ÷ tan(angle) |
| Angle from percent | arctan(percent ÷ 100) |
Conversion table: angle to slope
| Angle | Percent | mm per metre | in per foot | Ratio 1:n |
|---|---|---|---|---|
| 0.1° | 0.17% | 1.7 | 0.02 | 1:573 |
| 0.25° | 0.44% | 4.4 | 0.05 | 1:229 |
| 0.5° | 0.87% | 8.7 | 0.10 | 1:115 |
| 1° | 1.75% | 17.5 | 0.21 | 1:57 |
| 2° | 3.49% | 34.9 | 0.42 | 1:29 |
| 3° | 5.2% | 52 | 0.63 | 1:19 |
| 5° | 8.7% | 87 | 1.05 | 1:11.4 |
| 10° | 17.6% | 176 | 2.12 | 1:5.7 |
| 15° | 26.8% | 268 | 3.22 | 1:3.7 |
| 20° | 36.4% | 364 | 4.37 | 1:2.7 |
| 30° | 57.7% | 577 | 6.93 | 1:1.7 |
| 45° | 100% | 1000 | 12.00 | 1:1 |
A 45° slope is 100%, not 90%: percent slope keeps growing and becomes infinite at a vertical wall.
Common slopes
| Slope | Percent | Angle |
|---|---|---|
| 1:100 | 1% | 0.57° |
| 2% fall | 2% | 1.15° |
| 1:40 | 2.5% | 1.43° |
| 1:20 | 5% | 2.86° |
| 1:12 | 8.33% | 4.76° |
| 4:12 roof pitch | 33.3% | 18.43° |
| 6:12 roof pitch | 50% | 26.57° |
| 12:12 roof pitch | 100% | 45° |
Roof pitch such as 6:12 means a rise of 6 for every 12 of run, in the same units.
Worked examples
- A drain with a 2% fall: over 5 m of run, it drops 5 × 0.02 = 0.10 m, which is 100 mm.
- A ramp at 1:12: to climb 0.3 m it needs 0.3 × 12 = 3.6 m of run.
- A floor that reads 0.5°: that is 8.7 mm per metre, so 8.7 mm lower at one end of a 1 m shelf and about 17 mm lower over 2 m.
Measure the slope with your phone
Engineer Tools lets you pick the unit you work in, so you can read the tilt directly in degrees, percent, mm/m, in/ft or as a 1:n ratio, without converting. Set a zero point to measure the angle between two surfaces, and calibrate first for an accurate reading. See how to use your phone as a spirit level and Engineer Tools.
Frequently asked questions
How do I convert degrees to percent slope?
Percent slope is 100 times the tangent of the angle. For example, 5 degrees is 100 × tan 5° ≈ 8.7%.
What angle is a 1:12 ramp?
A 1:12 slope is a rise of 1 for every 12 of run, which is 8.33% or about 4.76 degrees.
Which units can Engineer Tools show?
Degrees, percent, millimetres per metre, inches per foot and a 1:n ratio.
More guides
- How to level a motorhome or caravan with your phone
Measure the tilt with a phone, work out how far each wheel must be raised with a simple formula, and level a motorhome or caravan with ramps or blocks.
- How to use your phone as a spirit (bubble) level and calibrate it
How a phone bubble level works, how to place it, and how to calibrate it with a two-point flip so the reading is accurate on any surface.