Degrees To Percent Converter
A 5 degree slope is an 8.75 percent grade, because the tangent of 5 degrees is 0.0875.
Quick answer: Take the tangent of the angle and multiply by 100. For example, 5 deg slope is 8.749 %, 10 deg slope is 17.633 % and 30 deg slope is 57.735 %.
The degrees to percent formula
The percent slope equals the tangent of the angle times 100.
Percent slope is rise divided by run, times 100.
Take 5 deg slope. tan(5 deg) × 100 gives 8.749 %.
Take 10 deg slope. tan(10 deg) × 100 gives 17.633 %.
Why tangent
Grade is the vertical rise divided by the horizontal run, times 100. It equals 100 times the tangent of the angle of the slope (Wikipedia: Grade (slope)).
At 45 degrees the rise equals the run, so the grade is exactly 100 percent. Steeper slopes go past 100 percent.
How to convert degrees to percent 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: 5 deg slope
- Start with 5 deg slope.
- tan(5 deg) × 100 = 8.749.
- The slope is 8.749 %.
5 deg slope = 8.749 %
Example 2: 10 deg slope
- Start with 10 deg slope.
- tan(10 deg) × 100 = 17.633.
- The slope is 17.633 %.
10 deg slope = 17.633 %
Example 3: 30 deg slope
- Start with 30 deg slope.
- tan(30 deg) × 100 = 57.735.
- The slope is 57.735 %.
30 deg slope = 57.735 %
The three examples below use common sizes.
Each one shows the sum in full.
degrees to percent conversion table
| Angle | Slope (%) | Run per 1 rise |
|---|---|---|
| 1 deg slope | 1.746 % | 57.29 to 1 |
| 2 deg slope | 3.492 % | 28.636 to 1 |
| 3 deg slope | 5.241 % | 19.081 to 1 |
| 4 deg slope | 6.993 % | 14.301 to 1 |
| 5 deg slope | 8.749 % | 11.43 to 1 |
| 7 deg slope | 12.278 % | 8.144 to 1 |
| 10 deg slope | 17.633 % | 5.671 to 1 |
| 15 deg slope | 26.795 % | 3.732 to 1 |
| 20 deg slope | 36.397 % | 2.747 to 1 |
| 30 deg slope | 57.735 % | 1.732 to 1 |
| 45 deg slope | 100 % | 1 to 1 |
The highlighted row is the default of the calculator. The last column gives to 1.
A quick mental shortcut for degrees to percent
For small angles, percent is about 1.75 times the degrees. So 4 degrees is about 7 percent.
The rule gets less exact as the angle grows.
Roads, ramps and roofs
Road signs and ramp rules give a slope in percent, while a tool or map may show degrees. This sum links the two.
The same math fits a hill, a drain pipe or a roof.
Not a straight line
Percent and degrees do not scale evenly. Doubling the angle does not double the percent.
45 degrees is 100 percent, but 90 degrees would be infinite.
Quick conversion answers
| Conversion | Result |
|---|---|
| 1 deg slope | 1.746 % |
| 5 deg slope | 8.749 % |
| 10 deg slope | 17.633 % |
| 45 deg slope | 100 % |
Where this conversion is used
Builders and drivers turn an angle into a percent slope.
Hikers and cyclists compare climb figures.
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 angles
0.5 deg slope is 0.8727 %. 1.5 deg slope is 2.619 %. 2.5 deg slope is 4.366 %.
6 deg slope is 10.51 %. 8 deg slope is 14.05 %. 12 deg slope is 21.26 %.
25 deg slope is 46.63 %. 35 deg slope is 70.02 %. 40 deg slope is 83.91 %.
Doubling the first number
1 deg slope is 1.746 %. 3 deg slope is 5.241 %. 5 deg slope is 8.749 %.
12 deg slope is 21.26 %. 16 deg slope is 28.67 %. 24 deg slope is 44.52 %.
50 deg slope is 119.2 %. 70 deg slope is 274.7 %. 80 deg slope is 567.1 %.
Doubling and halving
Small angles are close to proportional. 2.5 degrees is about 4.37 percent, and 5 degrees is 8.75 percent.
At large angles this stops working. 30 degrees is 57.7 percent, not twice 15 degrees at 26.8 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 8.75 percent, that gives about 5 degrees.
Common angles in percent
Here are some usual angles and their percent slopes.
1 degrees is a 1.75 percent slope. 2 degrees is a 3.49 percent slope. 3 degrees is a 5.24 percent slope.
5 degrees is a 8.75 percent slope. 1 degrees is a 17.63 percent slope. 15 degrees is a 26.79 percent slope.
2 degrees is a 36.4 percent slope. 25 degrees is a 46.63 percent slope. 3 degrees is a 57.74 percent slope.
45 degrees is a 100 percent slope.
Going the other way
To turn percent back into degrees, divide by 100 and take the arctangent.
A 5 percent slope is 2.86 degrees. A 1 percent slope is 5.71 degrees. A 2 percent slope is 11.31 degrees.
A 5 percent slope is 26.57 degrees. A 1 percent slope is 45 degrees.
Rounding the answer
Slopes are usually given to one or two decimals. For example, 8.7489 percent is 8.75 percent.
Round only at the end. Rounding early can add a small error to the final number.
Frequently asked questions
How do I convert degrees to percent?
Take the tangent of the angle and multiply by 100.
What percent is 45 degrees?
Exactly 100 percent.
Why not multiply by 100 directly?
Because slope depends on the tangent, not the angle itself.
How do I go from percent to degrees?
Divide by 100 and take the arctangent.
What is the run per 1 rise?
It is 1 divided by the tangent of the angle.
Does it use run or slope length?
Run, which is the horizontal distance.
Sources
- Wikipedia: Grade (slope) (en.wikipedia.org)
