# Slope conversion: degrees to percent, mm per metre and inches per foot

Source: https://ssbyte-apps.web.app/guides/degrees-to-percent-slope-mm-per-m-in-per-ft/
Last updated: 2026-10-01

**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](/guides/use-phone-as-spirit-level-and-calibrate/) and [Engineer Tools](/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.