Building design

Slope Converter

Convert slope between percent, degrees, radians, rise:run ratio, per mille, mm/m and cm/m with a visual triangle diagram.

Input

Slope value

Unit

Result

Percent

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Degrees

—

Radians

—

Rise : Run

—

Per mille (‰)

—

mm/m

—

cm/m

—

Gradient (tan)

—

Category

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Formula: angle = atan(rise ÷ run). From any unit we derive a single angle, then convert to every other unit.
percent = 100·tan(α) · ‰ = 1000·tan(α) · degrees = α·180/π · 1:N where N = 1/tan(α)

Common slopes — click to load

Conversion table

Percent	Degrees	Radians	Rise : Run	‰	mm/m

FAQ

What is the maximum ADA ramp slope?

The Americans with Disabilities Act (ADA) limits new construction ramp slopes to 1:12 — that is 1 inch of rise for every 12 inches of run. In other units: 8.33% grade, 4.76°, or 83 mm/m. Ramps must also have landings at least every 30 feet of run and on any change of direction.

How do I convert percent to degrees?

Percent is rise divided by run times 100. Degrees come from the arctangent: degrees = atan(percent ÷ 100) · 180/π. A few anchors: 1% ≈ 0.57°, 10% ≈ 5.71°, 45° = 100%, 60° ≈ 173.2%. Degrees and percent grow at different rates — they are equal only near zero.

What is a steep slope?

It depends on context. For highways, anything over 6% is considered steep and usually gets a "steep grade" sign. Forestry roads may go up to 12%. A 1:3 ratio (about 33% or 18.4°) is the usual limit for a lawn mower. Cliffs and scree slopes start around 30–35°.

Percent vs degrees — which is used in construction?

Civil engineers and road designers use percent (grade) because it maps directly to rise per horizontal distance and is easier to add and compare. Surveyors and architects often use degrees. Roofers use "pitch" — a ratio of rise over 12 inches of horizontal run (e.g. 6:12 = 6 inches up per 12 across).

What is per mille (‰) used for?

Per mille — parts per thousand — is common in European rail and road engineering. A 5‰ grade equals 0.5% or 5 mm per meter. Railways typically stay under 40‰, with freight lines under 15‰. Sanitary drainage is often specified in ‰ as well (e.g. 20‰ for house drains).

How are roof pitches written?

In the U.S., roof pitch is written as "rise : 12" where 12 is run in inches. A 4:12 pitch is 4 inches of rise per 12 inches of run — about 33.3%, or 18.43°. Flat roofs run 0:12 to 2:12, standard homes 4:12 to 9:12, steep European roofs go 12:12 (45°) or higher.

Educational conversions. Always follow local building codes, ADA / AASHTO / Eurocode requirements, and professional advice for permitted ramps, road grades and structural slopes.

The Slope Converter turns any slope value into every common unit at once: percent grade, degrees, radians, rise:run ratio (1:N), per mille (‰), mm/m, cm/m and the unitless gradient. Pick your input unit, type the number, and read every equivalent instantly. A triangle diagram redraws to match the angle so you can see how steep the value really is. Built-in presets load typical slopes — ADA ramp (1:12), drainage pipe (1%), highway grade (6%), mountain road (12%), stairs (30°) and a 45° roof. A reference table covers 1° to 60° for quick lookups. Example: enter 6 in percent — result shows 3.43°, 0.0599 rad, 1:16.67 ratio, 60 ‰, 60 mm/m, 6 cm/m. Useful for road design, roof pitch, drainage, ramp accessibility checks and survey work.