Slope, grade & angle converter

The steepness of a slope can be written three ways: as a percent grade (rise divided by run times 100), as an angle in degrees, or as a ratio such as 1:12. Roads use percent, roofs and ramps often use ratios or pitch, and surveying uses degrees. This converter switches between all three.

How to use it

1. Enter the slope in any form: percent, degrees or rise:run.
2. Read the equivalent values.

Formulas

• Grade % = rise / run × 100
• Angle = arctan(rise / run)
• Grade % = tan(angle) × 100

Key equivalents

• 1:12 = 8.33% = 4.76°, the maximum slope for wheelchair ramps under ADA guidelines.
• 1:20 = 5% = 2.86°.
• 10% = 5.71°, a steep road.
• 45° = 100%, where rise equals run.
• 1% = 0.57°, typical drainage fall for pipes and paving.

A common misconception

A 100% grade is not vertical; it is 45°. A vertical wall has an infinite grade. Percent and degrees are only roughly proportional for small slopes: 10% is 5.7°, but 50% is already 26.6°, not 22.5°.

Roof pitch

In the US, roof pitch is written as rise per 12 units of run. A 6/12 roof has a rise:run of 1:2, which is 50% or 26.57°.

Practical uses

• Checking ramp and walkway compliance.
• Setting pipe falls for drainage: often 1:40 to 1:80 for small domestic drains.
• Reading road signs that show grades, such as 12% hills.