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Slope and Grade Units Explained: Percent, Degrees, and Ratio

Percent, degrees, and ratio all describe the same slope, but they are calculated differently and are not interchangeable by simple proportion.

Percent grade is rise over run

Grade as a percentage is simply (vertical rise Γ· horizontal run) Γ— 100. A 10% grade rises 10 units for every 100 units traveled horizontally, not diagonally.

Degrees use the arctangent of rise over run

The angle in degrees is arctan(rise Γ· run), not the percent value divided by some constant. This is why 100% grade equals a 45Β° angle, not a vertical 90Β° wall, a common point of confusion.

Ratio notation (1:n) states run per unit of rise

Engineering drawings and accessibility codes often write slope as 1:12 or 1:20, meaning 1 unit of vertical rise for every 12 or 20 units of horizontal run. A smaller second number means a steeper slope.

The three scales diverge sharply as slope increases

At low angles, percent and degrees track each other loosely, but they pull apart fast: 50% grade is about 26.6Β°, while 100% grade is 45Β° and 200% grade is nearly 63.4Β° β€” doubling the percentage does not double the angle.

Common real-world slope benchmarks

US accessibility guidelines cap most wheelchair ramps at a 1:12 ratio (about 8.3%). Ordinary road grades rarely exceed 6-8%, while some of the world's steepest public roads reach 30-37%.

Why percent, degrees, and ratio all still coexist

Each notation suits a different audience. Percent grade is intuitive for drivers and cyclists because it maps to a familiar rise-per-distance feel. Degrees are the natural unit for trigonometry and structural engineering calculations. Ratio notation like 1:12 is common in accessibility and construction codes because it directly states a buildable proportion without needing a calculator.

The 100% grade misconception

A surprisingly common mistake is assuming a 100% grade means a vertical drop, since 100% sounds like "all the way." In reality, 100% grade is an equal rise and run, which works out to a 45Β° angle β€” steep, but far from vertical. A truly vertical surface would be an undefined or infinite percent grade.

Frequently Asked Questions

Is a 20% grade twice as steep as a 10% grade?

In terms of rise-per-distance, yes β€” 20% rises twice as much over the same horizontal distance as 10%. But in terms of the actual angle, it is not exactly double: 10% is about 5.7Β° and 20% is about 11.3Β°, close to double only because both angles are still small.

Why does roof pitch use a different convention than road grade?

Roof pitch is traditionally expressed as a ratio like "6 in 12," meaning 6 inches of rise per 12 inches of horizontal run, which is a carpentry-friendly version of the same 1:n ratio notation used in ramps and civil engineering, just phrased in inches instead of an abstract unit.