Slope Percentage Calculator
Turn rise and run into percent grade, an angle in degrees, and a 1-in-N ratio. Enter rise and run in any single unit (feet, meters, inches), or start from a percent grade or an angle and convert the other way.
Example: with I know... Rise and run · Rise (vertical change) 6 · Run (horizontal distance, same unit) 100 · Percent grade (if known) 8 · Angle in degrees (if known) 5 → Slope percentage: 6%.
- Angle3.43°
- Ratio1 in 16.67 (1 unit up per 16.67 along)
- Slope as a decimal0.06
Computed by the calculator below using its default values. Change any input to see your own numbers.
Slope % = rise ÷ run × 100. Angle = arctan(rise ÷ run). A 100% grade is a 45° slope, not vertical — percent and degrees are different scales.
Percent grade, degrees, and ratios — three names for one slope
A slope percentage is just rise over run scaled to 100: climb 6 feet over 100 feet of horizontal distance and you are on a 6% grade. The angle comes from trigonometry — the arctangent of rise over run — and the 1-in-N ratio flips the same number around: a 6% grade rises 1 unit for every 16.67 units of horizontal travel. Roads and railways quote percent, roof and ramp specs often use ratios, and surveying tools read out degrees, so converting among the three is a daily chore.
The relationship between percent and degrees is not linear. At gentle slopes they track closely (a 6% grade is 3.43°, roughly 0.57° per percent), but as slopes steepen the angle grows more slowly: 100% is 45°, and no finite percentage ever reaches 90°. That is why a '10% grade' warning sign describes something you can drive, while a 10° slope (17.6%) is noticeably steeper.
How it’s calculated
Slope percentage = rise ÷ run × 100, with rise and run in the same unit and run measured horizontally. Angle = arctan(rise ÷ run) × 180/π. Ratio = 1 in (run ÷ rise). From a percent grade p, the decimal slope is p/100; from an angle θ, slope = tan(θ). Angle inputs must be between −90° and 90°.
Run is the horizontal (map) distance, not the distance measured along the sloped surface — for grades under about 10% the difference is under 0.5%.
Reference slopes
| Slope | Percent grade | Angle |
|---|---|---|
| ADA ramp maximum (1:12) | 8.33% | 4.76° |
| Typical interstate maximum grade | 6% | 3.43° |
| Steep residential driveway | 12% | 6.84° |
| Advanced (black) ski run | 40% | 21.8° |
| 45° slope | 100% | 45° |
Angles computed with θ = arctan(grade/100); ADA ratio from the 2010 ADA Standards for Accessible Design (1:12 max ramp slope).
Common mistakes
- Assuming 100% grade means vertical — it means rise equals run, which is 45°.
- Measuring run along the sloped surface instead of horizontally, which understates the true grade.
- Mixing units — rise in inches with run in feet inflates the slope 12×; convert to one unit first.
- Scaling degrees linearly from percent at steep slopes: 20% is 11.31°, not double-checkable by multiplying 3.43° by anything.
Frequently asked questions
What is the slope percentage formula?
Slope % = rise ÷ run × 100, where rise is the vertical change and run is the horizontal distance in the same unit. A 6-foot climb over 100 horizontal feet is a 6% grade.
Is a 100% slope vertical?
No — this is the most common confusion. 100% means the rise equals the run, which is a 45° angle. Percent grade approaches infinity as a slope approaches vertical, so 90° has no percent equivalent.
How do I convert percent slope to degrees?
Divide the percent by 100 to get the decimal slope, then take the arctangent: angle = arctan(slope). An 8% grade is arctan(0.08) = 4.57°.
What does a 1 in 20 slope mean?
One unit of rise for every 20 units of horizontal run — a 5% grade or 2.86°. Building codes often write ramp and drainage slopes this way.
What is a good slope for a wheelchair ramp?
The ADA maximum for new construction is 1:12 (8.33%, 4.76°), and gentler is better. Landings are required for long runs — check local code before building.