Degree To Percent Slope Converter
A 3 degree slope is a 5.24 percent grade, because the tangent of 3 degrees is 0.0524.
Quick answer: Take the tangent of the angle and multiply by 100. For example, 3 deg slope is 5.241 %, 8 deg slope is 14.054 % and 20 deg slope is 36.397 %.
The degree to percent slope formula
The percent slope equals the tangent of the angle times 100.
Percent slope is rise divided by run, times 100.
Take 3 deg slope. tan(3 deg) × 100 gives 5.241 %.
Take 8 deg slope. tan(8 deg) × 100 gives 14.054 %.
From an angle to a grade
Slope is often given as a grade in percent. The grade is rise over run times 100, and it equals 100 times the tangent of the slope angle (Wikipedia: Grade (slope)).
A 3 degree slope is a small climb, but it is a steady 5.24 percent grade over a long distance.
How to convert degree to percent slope step by step
- Read the angle in degrees.
- Find its tangent on a calculator in degree mode.
- Multiply by 100.
- Write the answer as a percent.
Example 1: 3 deg slope
- Start with 3 deg slope.
- tan(3 deg) × 100 = 5.241.
- The slope is 5.241 %.
3 deg slope = 5.241 %
Example 2: 8 deg slope
- Start with 8 deg slope.
- tan(8 deg) × 100 = 14.054.
- The slope is 14.054 %.
8 deg slope = 14.054 %
Example 3: 20 deg slope
- Start with 20 deg slope.
- tan(20 deg) × 100 = 36.397.
- The slope is 36.397 %.
20 deg slope = 36.397 %
The three examples below use common sizes.
Each one shows the sum in full.
degree to percent slope conversion table
| Angle | Slope (%) | Run per 1 rise |
|---|---|---|
| 0.5 deg slope | 0.8727 % | 114.59 to 1 |
| 1 deg slope | 1.746 % | 57.29 to 1 |
| 1.5 deg slope | 2.619 % | 38.188 to 1 |
| 2 deg slope | 3.492 % | 28.636 to 1 |
| 3 deg slope | 5.241 % | 19.081 to 1 |
| 4.8 deg slope | 8.397 % | 11.909 to 1 |
| 6 deg slope | 10.51 % | 9.514 to 1 |
| 8 deg slope | 14.054 % | 7.115 to 1 |
| 12 deg slope | 21.256 % | 4.705 to 1 |
| 20 deg slope | 36.397 % | 2.747 to 1 |
| 35 deg slope | 70.021 % | 1.428 to 1 |
The highlighted row is the default of the calculator. The last column gives to 1.
A quick mental shortcut for degree to percent slope
Multiply the degrees by 1.75 for a quick guess. 3 degrees gives about 5.25 percent.
Use the exact sum for steeper slopes.
Wheelchair ramps and drives
Ramp and driveway rules are usually stated as a percent or a ratio. A rule written as 1 in 12 is an 8.33 percent grade, which is about 4.76 degrees.
Use this page to check an angle on a plan against the rule.
Long gentle slopes
Trains, canals and rural roads often have grades under 5 percent. At those levels the percent is close to 1.75 times the degrees.
The gap grows as the slope gets steeper.
Quick conversion answers
| Conversion | Result |
|---|---|
| 0.5 deg slope | 0.8727 % |
| 3 deg slope | 5.241 % |
| 8 deg slope | 14.054 % |
| 20 deg slope | 36.397 % |
Where this conversion is used
Designers and inspectors check a ramp or drive against a percent rule.
Surveyors turn an angle reading into a grade.
Common mistakes to avoid
- Multiplying the angle by 100. You must use the tangent.
- Calculator in radian mode. Use degree mode.
- Treating 45 degrees as 45 percent. It is 100 percent.
- Using the slope length. Grade uses horizontal run.
Related converters
More slope angles
0.25 deg slope is 0.4363 %. 0.75 deg slope is 1.309 %. 2.5 deg slope is 4.366 %.
5 deg slope is 8.749 %. 7 deg slope is 12.28 %. 9 deg slope is 15.84 %.
14 deg slope is 24.93 %. 25 deg slope is 46.63 %. 40 deg slope is 83.91 %.
Doubling the first number
0.5 deg slope is 0.8727 %. 1.5 deg slope is 2.619 %. 5 deg slope is 8.749 %.
10 deg slope is 17.63 %. 14 deg slope is 24.93 %. 18 deg slope is 32.49 %.
28 deg slope is 53.17 %. 50 deg slope is 119.2 %. 80 deg slope is 567.1 %.
Doubling and halving
Small angles are close to proportional. 1.5 degrees is about 2.62 percent, and 3 degrees is 5.24 percent.
At large angles this stops working. 40 degrees is 83.9 percent, not twice 20 degrees at 36.4 percent.
Use these rules to catch slips.
Checking the answer
Divide the percent by 100 and take the arctangent. You should get the angle you started with.
For 5.24 percent, that gives about 3 degrees.
Common ramp and road angles
Here are some gentle angles with their grade and gradient.
0.5 degrees is 0.87 percent, or 1 in 114.6. 1 degrees is 1.75 percent, or 1 in 57.3. 2 degrees is 3.49 percent, or 1 in 28.6.
3 degrees is 5.24 percent, or 1 in 19.1. 4 degrees is 6.99 percent, or 1 in 14.3. 5 degrees is 8.75 percent, or 1 in 11.4.
6 degrees is 10.51 percent, or 1 in 9.5. 8 degrees is 14.05 percent, or 1 in 7.1.
Rounding the answer
Plans usually show one or two decimals of a percent. For example, 5.2408 percent is 5.24 percent.
Round only at the end. Rounding early can add a small error to the final number.
Why grade is not the slope length
Grade uses the flat distance, not the distance along the hill. For a gentle slope the two are almost the same.
For a steep slope they differ, so use the horizontal run.
Frequently asked questions
How do I convert a slope angle to percent grade?
Take the tangent of the angle and multiply by 100.
What grade is a 3 degree slope?
About 5.24 percent.
What is 1 in 12 in degrees?
About 4.76 degrees, or 8.33 percent.
How do I go from percent to degrees?
Divide by 100 and take the arctangent.
Is a 100 percent grade 100 degrees?
No. It is 45 degrees.
Does grade use slope length?
No. It uses horizontal run.
Sources
- Wikipedia: Grade (slope) (en.wikipedia.org)
