Angle to Slope Percent
Percent grade is how much you rise for every 100 you travel horizontally: the tangent of the angle times 100. Angle and percent are not proportional.
Your numbers
Grade (%)
57.74%
Ratio
0.5774
Radians
0.5236rad
Formula
Grade (%) = tan(Angle (°)) × 100
45 degrees is 100%. The 10% you see on a road sign is only 5.7 degrees, and grades above 100% are still just over 45 degrees.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Angle (°) (°)An angle in degrees; a full turn is 360°. | 30 | 0 ~ 89 |
Step by step
Quick reference table
Results when only Angle (°) (°) changes and everything else stays put.
| Angle (°) (°) | Grade (%) (%) | Ratio | Radians (rad) |
|---|---|---|---|
| 15 | 26.79 | 0.2679 | 0.2618 |
| 22.5 | 41.42 | 0.4142 | 0.3927 |
| 30 | 57.74 | 0.5774 | 0.5236 |
| 45 | 100 | 1 | 0.7854 |
| 60 | 173.21 | 1.7321 | 1.0472 |
What each result means
| Result | At default values |
|---|---|
| Grade (%) (%)How far you rise over 100 of horizontal run. | 57.74 |
| RatioThe trigonometric ratio to invert, between −1 and 1. | 0.5774 |
| Radians (rad)An angle in radians; a full turn is 2π. | 0.5236 |
Common mistakes
45 degrees is 100%. The 10% you see on a road sign is only 5.7 degrees, and grades above 100% are still just over 45 degrees.
Glossary
- Angle (°)
- An angle in degrees; a full turn is 360°.
- Grade (%)
- How far you rise over 100 of horizontal run.
- Ratio
- The trigonometric ratio to invert, between −1 and 1.
- Radians
- An angle in radians; a full turn is 2π.
Frequently asked questions
Q. How is Angle to Slope Percent calculated?
Grade (%) = tan(Angle (°)) × 100 — Percent grade is how much you rise for every 100 you travel horizontally: the tangent of the angle times 100. Angle and percent are not proportional.
Q. Can you walk through an example?
With Angle (°) 30°, the answer is Grade (%) 57.74%.
Q. What do I need to enter?
Enter Angle (°). The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only Angle (°) (°) moves the answer to Angle (°) (°) 15 → Grade (%) (%) 26.79 and Angle (°) (°) 60 → Grade (%) (%) 173.21. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
45 degrees is 100%. The 10% you see on a road sign is only 5.7 degrees, and grades above 100% are still just over 45 degrees.
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