Quick Answer
To convert a degree to a percentage, multiply the tangent of the angle by 100 for slope (30° = 57.74% grade, 45° = 100%) or divide the angle by 360 and multiply by 100 for a share of a circle (90° = 25%). The reverse uses arctangent: degrees = atan(percent ÷ 100), so an 8.33% ADA ramp is 4.76°.
Degree to Percentage Formula: Slope vs Circle Share
“Convert degrees to a percentage” means one of two very different things, and mixing them up is the single most common mistake. For slope, grade or gradient — driveways, ramps, roads, roofs — the percentage is the tangent of the angle. For a share of a circle — pie charts, data visualisation — it is a simple fraction of 360°:
So 30° is a 57.74% grade but 8.33% of a circle — and a 100% grade is exactly 45°, because at 45° the rise equals the run.
Percent slope is rise divided by run, the number posted on US road hill signs and written into ramp specs. It is not a fraction of 90° — that misconception is covered below.
Degrees to Percent Slope Conversion Chart
Common angles with both readings — note how the slope percent races ahead of the circle share as the angle steepens:
| Degrees | Percent slope (grade) | Share of a circle |
|---|---|---|
| 1° | 1.75% | 0.28% |
| 2° | 3.49% | 0.56% |
| 4.76° | 8.33% (ADA ramp max, 1:12) | 1.32% |
| 5° | 8.75% | 1.39% |
| 10° | 17.63% | 2.78% |
| 15° | 26.79% | 4.17% |
| 20° | 36.40% | 5.56% |
| 25° | 46.63% | 6.94% |
| 30° | 57.74% | 8.33% |
| 35° | 70.02% | 9.72% |
| 40° | 83.91% | 11.11% |
| 45° | 100% | 12.5% |
| 50° | 119.18% | 13.89% |
| 60° | 173.21% | 16.67% |
| 70° | 274.75% | 19.44% |
| 80° | 567.13% | 22.22% |
| 90° | vertical — no finite % | 25% |
And the reverse — percent grade to degrees (θ = atan(% ÷ 100)):
| Percent slope | Degrees | Ratio (1 in N) |
|---|---|---|
| 1% | 0.57° | 1 in 100 |
| 2% | 1.15° | 1 in 50 |
| 5% | 2.86° | 1 in 20 |
| 8.33% | 4.76° | 1 in 12 (ADA ramp max) |
| 10% | 5.71° | 1 in 10 |
| 15% | 8.53° | 1 in 6.67 |
| 20% | 11.31° | 1 in 5 |
| 25% | 14.04° | 1 in 4 |
| 33.33% | 18.43° | 1 in 3 |
| 50% | 26.57° | 1 in 2 |
| 100% | 45° | 1 in 1 |
| 200% | 63.43° | 1 in 0.5 |
How to Use the Degree to Percentage Calculator
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Pick the direction.
Tap ° → % to turn an angle into percentages, or % → ° to turn a percent grade back into an angle.
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Type the number.
Enter the angle in degrees (like 30) or the slope in percent (like 8.33). One number is all the tool needs.
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Read both answers.
The big number is the slope percent (or angle); the grid below shows the circle share, the 1-in-N ratio, the roof pitch per 12 and radians — so the pie-chart meaning is never lost.
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Share or reset.
Use Share result to copy a link that reopens with your exact numbers, or Clear all to start over.
Why 45° = 100% (Not 50%): The Percent Slope Misconception
The intuitive guess — that percentage is the angle’s share of 90° — is wrong, and it is why hillside signs surprise people. Percent slope is rise ÷ run × 100 (the tangent). At 45° the rise equals the run, so the grade is 100% while the angle is only half of 90°. The relationship is not linear either: doubling an angle more than doubles its grade, and as the angle approaches 90° the percent runs off to infinity — a vertical cliff has no finite grade at all.
The circle meaning, by contrast, is linear — every 3.6° is exactly 1% of a full turn:
| Angle | Share of a circle | Typical use |
|---|---|---|
| 3.6° | 1% | 1% pie-chart wedge |
| 36° | 10% | decile wedge |
| 90° | 25% | quarter circle |
| 120° | 33.33% | third of a pie |
| 180° | 50% | half circle |
| 270° | 75% | three quarters |
| 360° | 100% | full circle |
Real-World Grades: ADA Ramps, Road Signs & Roof Pitch
The percent form dominates the built world. The US Access Board caps ADA ramp running slope at 1:12 — 8.33%, or 4.76° — with a 1:48 cross slope; US hill warning signs post the grade in percent on plaques under the W7-1 sign (per the MUTCD); and roofers quote pitch as rise per 12 of run, which converts through the same tangent — the Stair Stringer Calculator runs the same rise-over-run math for steps:
| Real-world slope | Percent grade | Degrees |
|---|---|---|
| ADA ramp maximum (1:12) | 8.33% | 4.76° |
| Steep-hill warning territory | 6–10% | 3.43–5.71° |
| 4:12 roof pitch | 33.33% | 18.43° |
| 6:12 roof pitch | 50% | 26.57° |
| 8:12 roof pitch | 66.67% | 33.69° |
| 12:12 roof pitch | 100% | 45° |
Worked Examples: Driveway, Ramp, Pie Chart & Roof
Five conversions exactly as the calculator runs them:
| Scenario | Calculation | Result |
|---|---|---|
| Driveway rising at 10° | tan(10°) × 100 | 17.63% grade — 1 in 5.67 |
| Ramp spec says 8.33% | atan(8.33 ÷ 100) | 4.76° — exactly the ADA 1:12 maximum |
| Pie-chart wedge of 90° | 90 ÷ 360 × 100 | 25% of the circle |
| 6:12 roof pitch | atan(6 ÷ 12) | 26.57° — a 50% slope |
| Hill sign posting 6% | atan(6 ÷ 100) | 3.43° — steep for a road, gentle as an angle |
