Percent · Degrees · Ratio
Slope to degrees converter.
Type into any one box and the rest follow. Percent grade, permille, degrees, ratio and slope all describe the same steepness — this converts between them instantly.
Moderate — Within the 1:12 limit the ADA sets for a ramp on an accessible route.
Equivalent fall of 1″ per ft and 83.3 mm per m.
Jump to a Common Slope
Slope Conversion Table
Percent grade, permille, degrees, ratio and fall per foot for the slopes that come up most often. Rows in bold are values fixed by a code or a convention rather than round numbers.
| Percent Grade | Permille | Degrees | Ratio | Fall per Foot (in) | Where You See It |
|---|---|---|---|---|---|
| 0.50% | 5.0‰ | 0.29° | 1 : 200 | 0.060″ | — |
| 1.00% | 10.0‰ | 0.57° | 1 : 100 | 0.120″ | — |
| 2.00% | 20.0‰ | 1.15° | 1 : 50 | 0.240″ | — |
| 2.08% | 20.8‰ | 1.19° | 1 : 48.1 | 0.250″ | Drain pipe minimum (¼″ per foot) |
| 3.00% | 30.0‰ | 1.72° | 1 : 33.3 | 0.360″ | — |
| 4.00% | 40.0‰ | 2.29° | 1 : 25 | 0.480″ | — |
| 5.00% | 50.0‰ | 2.86° | 1 : 20 | 0.600″ | — |
| 6.00% | 60.0‰ | 3.43° | 1 : 16.7 | 0.720″ | Typical maximum highway grade |
| 8.33% | 83.3‰ | 4.76° | 1 : 12 | 1.000″ | ADA ramp maximum (1:12) |
| 10.00% | 100.0‰ | 5.71° | 1 : 10 | 1.200″ | — |
| 12.50% | 125.0‰ | 7.13° | 1 : 8 | 1.500″ | — |
| 15.00% | 150.0‰ | 8.53° | 1 : 6.7 | 1.800″ | — |
| 20.00% | 200.0‰ | 11.31° | 1 : 5 | 2.400″ | — |
| 25.00% | 250.0‰ | 14.04° | 1 : 4 | 3.000″ | — |
| 33.30% | 333.0‰ | 18.42° | 1 : 3 | 3.996″ | 4/12 roof pitch |
| 50.00% | 500.0‰ | 26.57° | 1 : 2 | 6.000″ | — |
| 57.70% | 577.0‰ | 29.98° | 1 : 1.7 | 6.924″ | — |
| 75.00% | 750.0‰ | 36.87° | 1 : 1.3 | 9.000″ | — |
| 100.00% | 1,000.0‰ | 45.00° | 1 : 1 | 12.000″ | 45° — rise equals run |
Why Percent and Degrees Do Not Line Up
The single biggest source of confusion in this topic is the assumption that percent grade and degrees scale together. They do not. Percent grade is a ratio — rise divided by run — while degrees measure an angle, and the two are connected by a tangent, which is anything but linear.
At gentle slopes the two happen to track each other closely enough to fool you: a 5% grade is 2.86°, and a 10% grade is 5.71°, near enough to double. But the relationship bends as the slope steepens. A 50% grade is 26.6°, not 28.6°. A 100% grade is 45°. And no percent grade, however large, ever reaches 90° — vertical is the one slope that has no percentage at all.
The conversions in both directions are:
degrees = arctan(grade ÷ 100)
grade = tan(degrees) × 100
Which Unit Belongs Where
- Percent grade — roads, driveways, site drainage and treadmills. Road signs and earthworks drawings are almost always in percent.
- Degrees — anything measured with a digital level or an inclinometer, and most engineering and machining work.
- Ratio (1 : N) — accessibility, drainage and rail. Written as 1:12 or "1 in 12", it is the clearest form when the rise is fixed and you need to know how much room the run will take.
- Pitch (x/12) — roofing only. See the roof pitch calculator for that convention.
Reading a Ratio the Right Way Round
A ratio written 1:12 means one unit up for twelve along — the small number is the rise. Because the run is the larger number, a bigger second number means a gentler slope. 1:20 is flatter than 1:12, which is flatter than 1:8. This trips people up because every other measure of steepness gets larger as the slope gets steeper.
Common Questions
What is permille (‰) and how does it relate to percent?
Permille means parts per thousand, so it is simply the percent grade multiplied by ten: a 1.5% grade is 15‰. It is the usual way to specify drainage falls, railway gradients and road grades outside the United States. One permille is also exactly one millimetre of fall per metre of run, which is why a drainage drawing marked 22‰ and one marked 22 mm/m are asking for the same thing.
How do I convert percent slope to degrees?
Divide the percent by 100 to get the slope as a decimal, then take the inverse tangent: degrees = arctan(percent ÷ 100). A 10% grade is arctan(0.10) = 5.71°. The two scales are not proportional, so you cannot simply divide or multiply by a fixed number.
Is a 100% grade the same as vertical?
No — a 100% grade is 45°, exactly halfway to vertical. Percent grade is rise divided by run, so 100% means the rise equals the run, which is a 45° angle. A truly vertical face has no percent grade at all, because the run is zero and the division is undefined.
How steep is a 45% grade?
About 24.2°. This is the conversion people misjudge most often, because the number 45 suggests 45 degrees. A 45% grade rises 45 units for every 100 units of horizontal travel, which is considerably gentler than a 45° angle.
What does a 1:12 slope mean?
It means one unit of rise for every twelve units of horizontal run — an 8.33% grade, or 4.76°. It is the maximum running slope the ADA allows for a ramp on an accessible route, and one of the most widely quoted ratios in construction.
What is the difference between grade, slope and pitch?
They describe the same steepness in different units. Slope is the plain ratio of rise to run, grade is that ratio written as a percentage, and pitch is the roofing convention of rise per 12 units of run. A slope of 0.5 is a 50% grade and a 6/12 pitch.