About

Architects and contractors often encounter mixed units in blueprints. While road signs and accessibility ramps define gradients in percentages (e.g., 8.33%), miter saws and roof framing squares require angular degrees. A conversion error here results in poor water drainage, non-compliant wheelchair ramps, or structural misalignment.

This tool facilitates the bidirectional conversion between percentage grade and angular degrees. It utilizes the trigonometric tangent relationship. To aid professionals, common building code thresholds (such as maximum ADA ramp slopes) are integrated into the reference table, providing immediate context for the calculated values.

Formulas

Percentage grade is the tangent of the angle multiplied by 100.

Percent = tan(Deg) × 100

To find the angle from a percentage:

Deg = arctan(Percent100)

Reference Data

Slope (%)	Angle (°)	Ratio (Rise:Run)	Context
0%	0.0°	--	Flat
2%	1.15°	1:50	Min drainage (ext)
5%	2.86°	1:20	Walkways (No rails)
8.33%	4.76°	1:12	Max ADA Ramp
10%	5.71°	1:10	Steep Driveway
25%	14.0°	3:12	Low Slope Roof
50%	26.6°	6:12	Common Roof Pitch
100%	45.0°	12:12	45 Degree

Frequently Asked Questions

No. This is a common misconception. 100% slope means the Rise equals the Run (e.g., 1 meter up for every 1 meter forward), which corresponds to a 45° angle. Vertical is infinite percent.

The input is capped below 90°. At 90°, the tangent function is undefined (infinite slope), making a percentage representation impossible.

Yes. Highway grades are almost exclusively measured in percent. Most interstate highways are capped at 6% or 7%.

Convert the ratio to a decimal first. For 4:12, divide 4 by 12 (0.333), multiply by 100 (33.3%), and input that value into the Percentage field.