Every way of writing a slope comes from one number, the rise divided by the run. A ramp that climbs 1 for every 12 across has a slope of 1 ÷ 12 = 0.0833: that is 8.33%, 4.76°, a ratio of 1 : 12 and a pitch of 1 in 12. Type the slope in the form you have – two lengths, a percent, an angle, a ratio or a roof pitch – and the calculator gives all the others, with the steps.
Common slopes in every form
| Where you meet it | Percent | Degrees | Ratio | Pitch |
|---|---|---|---|---|
| Walking surface, steepest before it counts as a ramp (ADA, 1 : 20) | 5% | 2.86° | 1 : 20 | 0.6 in 12 |
| Steepest ramp run (ADA, 1 : 12) | 8.33% | 4.76° | 1 : 12 | 1 in 12 |
| Small drain pipe, ¼ in per foot | 2.08% | 1.19° | 1 : 48 | 0.25 in 12 |
| Steep road sign, 10% | 10% | 5.71° | 1 : 10 | 1.2 in 12 |
| Low-slope roof, 4/12 | 33.33% | 18.43° | 1 : 3 | 4 in 12 |
| Common roof, 6/12 | 50% | 26.57° | 1 : 2 | 6 in 12 |
| Steep roof, 12/12 | 100% | 45° | 1 : 1 | 12 in 12 |
Degrees and percent are not proportional
| Degrees | Percent |
|---|---|
| 1° | 1.75% |
| 5° | 8.75% |
| 10° | 17.63% |
| 15° | 26.79% |
| 30° | 57.74% |
| 45° | 100% |
| 60° | 173.21% |
For small slopes, one degree is close to 1.75%, so a 2° patio is about 3.5%. Beyond 10° the rule of thumb breaks down fast: doubling the angle from 30° to 60° triples the percent.
Which form to use
Road signs in most of the world and gradient maps use percent; US and Canadian roofers speak in pitch, inches of rise per 12 of run; accessibility rules and drain designers use 1 : n ratios; surveyors, physics problems and angle finders use degrees. For a roof, the length along the slope (in the results) tells you how long the rafters and the roof covering are: a 6/12 roof is 11.8% longer along the slope than in plan.
The converter runs on your device and works offline, useful on a roof or a building site with no signal.
Frequently asked questions
How do I turn a percent slope into degrees?
Divide the percent by 100 and take the arctangent. 8% is arctan(0.08) = 4.57°. The two are not proportional: 100% is 45°, not 90°.
How do I turn degrees into a percent slope?
Take the tangent and multiply by 100. 5° is tan(5°) × 100 = 8.75%; 30° is 57.74%.
What does a 1 : 12 slope mean?
One unit up for every 12 across: 8.33%, or 4.76°. It is the steepest running slope allowed for a ramp under the 2010 ADA Standards in the United States.
What is a 6/12 roof pitch in degrees?
6 in of rise for every 12 in of run: a slope of 50%, or 26.57°. A 12/12 roof is 45°.
Can a slope be more than 100%?
Yes. 100% is 45°; anything steeper is over 100%, and 60° is 173%. A vertical wall has no percent, because the run is zero.
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