Angle of Depression Calculator

This angle of depression calculator will help you solve the angle by which a line of sight deviates from the horizontal in a downward direction.

Grade20%11.3099° from horizontal

Angle11.30993°

Ratio1 in 5

Rise per 12 of run2.4the roofing and stair convention

Rise100 ft30.48 m

Run500 ft152.4 m

Slope length509.902 ftalong the surface, not the horizontal

ADA ramp limittoo steepa wheelchair ramp may not exceed 1 in 12, or 8.33%

Maximum ADA run without a landing98 ftand no more than 30 in of rise between landings

Ladder 4:1 rule75.96° is the targeta ladder should stand one out for every four up — 75.96°

The formula

grade = rise ÷ run × 100%; angle = atan(rise ÷ run)

Four ways to say the same thing

Grade as a percentage, an angle in degrees, a ratio of 1 in N, and rise per 12 of run are all the same quantity dressed differently. Road engineers use per cent, roofers use rise per 12, drainage uses 1 in N, and only surveyors routinely use degrees.

Note that a 100% grade is 45°, not vertical. The percentage is rise over run, not over the slope length, so it has no upper bound — a 200% grade is a perfectly meaningful 63.4°.

Two limits worth remembering: a wheelchair ramp may not exceed 1 in 12, and a leaning ladder wants 1 out for every 4 up, which is about 76°.