Slope & Grade
How to Convert Percent Grade to Degrees (and Back)
Convert slope percent to degrees with arctan, degrees to percent with tan, a full conversion chart from 0.5% to 100%, and why the two scales aren't proportional.
Percent and degrees describe the same slope in different mathematics - a ratio versus an angle - and the conversion trips up everyone who assumes they scale together. For gentle grades they nearly do (each 1% ≈ 0.57°), which builds a false intuition that shatters on steep ground: doubling 50% grade doesn't give 90°, it gives 45°… going to 100% only reaches 45°.
The two formulas
Grade (%) = tan(Degrees) × 100
On a phone: rotate to scientific mode; use tan⁻¹ (sometimes atan) for the first, tan for the second. Make sure the calculator is in degree mode, not radians - the classic error that returns 0.0997 instead of 5.71.
Conversion chart
| Grade % | Degrees | Ratio | Context |
|---|---|---|---|
| 0.5% | 0.29° | 1:200 | Practical minimum for pipe flow |
| 1% | 0.57° | 1:100 | Drain pipe standard minimum |
| 2% | 1.15° | 1:50 | Patio/pavement drainage |
| 3% | 1.72° | 1:33 | Lawn drainage, comfortable walk |
| 5% | 2.86° | 1:20 | Foundation grading; gentle driveway |
| 8.33% | 4.76° | 1:12 | ADA ramp maximum |
| 10% | 5.71° | 1:10 | Steep driveway feel begins |
| 15% | 8.53° | 1:6.7 | Common code max for driveways |
| 25% | 14.04° | 1:4 | Mower stability limits near |
| 33% | 18.26° | 1:3 | Typical max mowable bank |
| 50% | 26.57° | 1:2 | Common max cut slope, good soil |
| 67% | 33.7° | 1:1.5 | Typical rock-fill slope |
| 100% | 45° | 1:1 | Rise equals run |
| 200% | 63.4° | 2:1 | Steeper than repose of most soils |
Why the scales diverge (30-second geometry)
Grade divides rise by horizontal run, and as slopes steepen, each added degree of angle demands more and more rise per unit of run - tan grows without bound. At 89°, grade is 5,700%; at 90°, run is zero and percent grade is undefined. Meanwhile near zero the curve is almost straight, which is why the ×0.57 shortcut works below ~10% and quietly fails beyond it (at 30%, the shortcut is off by 4%; at 100%, by 22%).
Worked conversions
Driveway check: code caps your driveway at 12%. Your inclinometer app reads 6.2°. tan(6.2°) × 100 = 10.9% - compliant, with margin.
Equipment chart: a mower's manual says "do not operate across slopes over 15°." Your bank measures 28% grade: arctan(0.28) = 15.6° - over the line; mow up-down or don't.
Roof pitch bonus: pitch 4:12 = 4 ÷ 12 × 100 = 33.3% = 18.4°. Same math, different clothing.
The slope calculator converts both directions and adds ratio, slope length, and fall tables.
Open the Slope CalculatorCommon mistakes
Calculator in radian mode. If arctan(0.1) returns 0.0997, switch to degrees. Expected: 5.71.
Assuming 100% = vertical. It's 45°. Vertical is unreachable in percent notation.
Mixing conventions mid-project. Excavation notes in percent, equipment limits in degrees, roof specs in rise:12 - convert everything to one system at the start, convert back at the end.
When to call a professional
Conversions are arithmetic; judgments about steep slopes are not. Cut-and-fill slopes above roughly 2:1 (50%), any slope showing movement, and retaining decisions at slope toes involve soil mechanics - a geotechnical engineer's chart of safe angles for your soil beats every generic table, including this one.
Frequently Asked Questions
How do I convert percent grade to degrees?
Degrees = arctan(percent / 100). For 10%: arctan(0.10) = 5.71 degrees. On any phone calculator with scientific mode: divide percent by 100, then use tan-inverse.
How do I convert degrees to percent grade?
Percent = tan(degrees) x 100. For 15 degrees: tan(15) = 0.268, so 26.8% grade.
What is a 45-degree slope in percent?
100%. At 45 degrees, rise equals run, so grade = 1 x 100 = 100%. This is the reference point that surprises people - 100% is not vertical.
Why isn't 50% grade half of vertical?
Because grade is a ratio (rise/run), not a fraction of 90 degrees. 50% grade is arctan(0.5) = 26.6 degrees. Vertical would be infinite percent - run shrinks to zero.
Which should I use, percent or degrees?
Construction, drainage, and road work speak percent; roof pitch uses rise-per-12 ratios; equipment stability charts and some surveying instruments use degrees. Use your document's convention and convert at the end, not midway.