How percent grade and degrees relate
A percent grade is the tangent of the slope angle, expressed as a percentage. Degrees are the angle itself, measured from horizontal.
- percent — slope grade as a percentage (rise ÷ run × 100)
- degree — slope angle from horizontal, in degrees
More detail
Why percent and degrees diverge at steep grades
At gentle slopes the two scales track closely — 10% is about 5.7°. But they diverge fast: 100% grade is 45°, not 90°, because percent is a ratio (rise/run) while degrees measure the angle directly. A 45° slope already reads as a "vertical wall" in percent terms (100%), which trips up anyone assuming the scales are linear against each other.
Quick check. 100% grade always equals exactly 45°, since tan(45°) = 1. Use that pair to sanity-check either direction of this calculator.
Frequently asked questions
What angle is a 100% slope?
45°, since percent grade is tan(angle) × 100 and tan(45°) = 1. Switch to "Percent → degree" above and enter 100 to confirm.
How do I convert a percent grade to degrees?
Take the arctangent of the grade divided by 100: degree = atan(percent ÷ 100). A 20% grade is atan(0.2) ≈ 11.31°.
Why is there no percent value at 90 degrees?
Percent grade is tan(degree) × 100, and tan(90°) is undefined (the slope is a vertical wall with no horizontal run to divide by). Angles at or beyond ±90° return no result.
Can the slope be negative?
Yes — a negative percent or degree represents a downhill grade. This calculator accepts negative and zero values on both sides; only ±90° and beyond is undefined.