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Conversion

Slope / Grade Converter (Percent ↔ Degrees ↔ Rise:Run)

A single ramp can be described three ways: (1) percent grade — rise ÷ run × 100 % (8 % means 8 m rise per 100 m horizontal run); (2) angle — arctan(rise ÷ run), expressed in degrees; (3) ratio — "1 : N" reads as "rise 1 unit over a run of N units". This tool converts in all three directions and also surfaces radians and the rise / run pair. Use negative values for downhill.

Percent grade

10.0000%

Given

Degrees

5.7106°

Computed

Ratio 1 : N

1 : 10

Computed

Angle in radians

0.0997

For every 1 unit of rise, how much horizontal run?

1 m / 10 m

Formulas

G(%) = (rise/run) × 100; θ = arctan(G/100); 1 : N → G = 100 / N

Road signs and highway design typically quote percent grade (5% = 5 m rise per 100 m). Hiking and cycling use percent or degrees. Accessibility ramps and roof pitch are usually given as a 1 : N ratio (ADA caps an accessible ramp at 1 : 12 ≈ 8.33% ≈ 4.76°). Negative values mean downhill. This tool converts freely between all three forms and also shows radians and the rise/run pair.

Formula

G(%) = (rise / run) × 100 θ° = arctan(rise / run) = arctan(G / 100) 1:N → G(%) = 100 / N G(%) → 1:N = 1 : (100 / G)

Frequently asked

Which is steeper: an 8 % grade or an 8° angle?

8° is significantly steeper than 8 %. An 8 % grade means rise / run = 0.08, so angle = arctan(0.08) ≈ 4.574°. Conversely 8° corresponds to grade = tan(8°) × 100 ≈ 14.05 %. The two are close for small slopes (5 % ≈ 2.86°) but diverge quickly. Road signs, hiking and cycling apps tend to use percent (unitless, linear, easy mental math); surveys, technical drawings and accessibility standards prefer degrees or 1 : N. Mixing them up can almost double your perceived slope.

Why is 1 : 12 such a famous ramp slope?

The US ADA Standards §405 cap the slope of an accessible public ramp at 1 : 12 (≈ 8.33 % ≈ 4.764°), meaning every 1 unit of rise needs 12 units of horizontal run. The cap is set so that a person in a manual wheelchair can self-propel up the ramp without excessive strain, and rest landings must be added every 30 in of cumulative rise. The UK (BS 8300-1:2018), ISO 21542:2011 and Hong Kong's Buildings Department barrier-free guidelines all converge on the same neighbourhood, with some defaulting to a gentler 1 : 14 or 1 : 16. When designing new buildings, "1 : 12" is the number to remember.

What does a US "6/12 roof pitch" mean in degrees?

A "6/12 pitch" reads as "6 in of rise per 12 in of horizontal run" — rise/run = 0.5, which is a 50 % grade, an angle of arctan(0.5) ≈ 26.565° and a 1 : 2 ratio. North American roof categories: low-pitch 2/12 to 4/12 (9.46°–18.43°), standard 4/12 to 9/12 (18.43°–36.87°), steep 9/12 to 12/12 (36.87°–45°). Europe and most of Asia quote pitch directly in degrees ("a 30° roof"). To work back to a degree value enter 50 in percent mode (or 26.565 in degrees mode) in this tool.

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