Convert slope between grade percentage, angle in degrees and ratio (1-in-N) — for roofs, roads, ramps and trails.
Math • grade ↔ degrees
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Slope can be written three ways: as a grade percentage (rise ÷ run × 100), as an angle in degrees, or as a ratio (1 in N). A 100% grade equals 45°. Builders, roofers, road engineers, hikers and accessibility planners switch between them constantly.
This converter turns a grade percent into degrees and a 1-in-N ratio, and converts an angle back to grade — useful for wheelchair ramps (ADA), roof pitch, driveways and trail gradients.
Slope is expressed three ways depending on trade, and they are not interchangeable numbers. Percentage grade is rise divided by run times 100 — the form on road signs. Degrees measure the angle from horizontal and require an arctangent, not a proportion. Ratio form, written as 1:12 or 4:12, states run per unit of rise, or in roofing the rise per 12 units of run. The critical point is that grade and degrees are not proportional: a 100% grade is 45°, not 90°, because the tangent function is non-linear. Accessibility law works in ratios — the ADA maximum ramp slope is 1:12, or 8.33%.
Grade % = (rise ÷ run) × 100Angle = arctan(rise ÷ run)Ratio = 1 : (run ÷ rise)Roof pitch = rise per 12 of runwhere:
Assumptions: Run is measured horizontally. Using the sloped surface length instead understates the grade, increasingly so as the slope steepens.
Convert a common roof pitch into the other two conventions.
Result4:12 pitch = 33.33% grade = 18.43°
The gap between grade and degrees widens rapidly. At gentle slopes they nearly track — a 5% grade is 2.86° — but by 100% grade the angle is only 45°, and no finite grade ever reaches 90°. Road signs use percent precisely because it is easier to compute from survey data.
Grade percent, degrees and a one-in-N ratio are all the same slope expressed differently, but they are not interchangeable in the places they are used because each field standardised on one. Grade percent is rise over run times a hundred, so a 100% grade is a 45-degree angle rather than vertical — the most common misreading of a road sign. Ratios run the other way, with larger N meaning gentler, which is why railway gradients are quoted as one in a hundred and roofs are not.
Regulated slopes are written in whichever form the regulation chose. Accessible ramps are limited to a 1:12 ratio, which is 8.33% or about 4.76 degrees, and the compliance test is against the ratio rather than the angle. Roofing uses rise over a twelve-inch run, so a 4/12 pitch is 18.43 degrees, and shingle manufacturers set minimum pitches in that notation. Converting into degrees is useful for setting a tool but not for demonstrating compliance, where the original form is what an inspector reads.
Degrees and percent diverge sharply once slopes get steep, which is where intuition fails. They are close for gentle grades — a 10% grade is 5.7 degrees — but the percentage climbs without limit as the angle approaches vertical while the angle cannot exceed ninety. Treating the two as roughly proportional is safe on a road and badly wrong on a roof or an embankment.