Convert slope percent to angle in degrees with ratio and mm/m equivalents.
Common slopes reference
| Application | Percent | Degrees | Ratio |
|---|---|---|---|
| Gentle drainage | 1% | 0.57° | 1 : 100 |
| Patio / flat roof min | 2% | 1.15° | 1 : 50 |
| Driveway comfort max | 5% | 2.86° | 1 : 20 |
| ADA ramp maximum | 8.33% | 4.76° | 1 : 12 |
| Road classified steep | 10% | 5.71° | 1 : 10 |
| Cycling climb, category | 15% | 8.53° | 1 : 6.67 |
| Standard residential roof | 25% | 14.04° | 1 : 4 |
| Steep roof / 6:12 pitch | 50% | 26.57° | 1 : 2 |
| 45° roof / 12:12 pitch | 100% | 45.00° | 1 : 1 |
| Very steep | 200% | 63.43° | 2 : 1 |
Calculation details
Derivation: from rise/run to angle
Slope percent expresses vertical rise as a percentage of horizontal run. Written as a ratio, percent ÷ 100 equals rise ÷ run. By definition the tangent of the angle equals rise divided by run, so:
tan(θ) = rise / run = percent / 100
Solving for θ gives the arctangent relation used here:
θ = atan(percent / 100) — radians, then multiplied by 180 / π to convert to degrees.
Example: 8.33% → atan(0.0833) = 0.08314 rad → 0.08314 × 57.2958 = 4.76°.
The inverse relation: percent = tan(θ) × 100. So 30° gives tan(30°) × 100 = 57.74%.
Frequently asked questions
What is the maximum slope allowed for an ADA-compliant ramp?
The Americans with Disabilities Act (ADA) Standards for Accessible Design limit ramp slope to 1:12, i.e. 8.33% or about 4.76°. Cross slope must stay ≤ 1:48 (about 2.08% or 1.19°). For new construction the preferred slope is 1:16 to 1:20 (6.25% to 5%). Steeper 1:10 or 1:8 ratios are only allowed for limited rise on existing sites under strict exceptions.
How does roof pitch (X:12) translate to percent and degrees?
US roof pitch is given as rise over 12 inches of run. A 6:12 pitch equals 6 ÷ 12 = 50% slope, which converts to atan(0.5) = 26.57°. A 4:12 pitch is 33.33% or 18.43°. The common "45° roof" is a 12:12 pitch — rise equals run, so slope is 100% and the angle is exactly 45°. Low-slope roofs are typically 2:12 (16.67% / 9.46°) or below.
How do I convert a rise and run measurement to slope percent?
Divide the vertical rise by the horizontal run (both in the same unit) and multiply by 100. For example, a deck with 250 mm rise over 3000 mm run has 250 ÷ 3000 × 100 = 8.33% slope. Then atan(0.0833) × 57.2958 ≈ 4.76°. Measure the horizontal distance, not the slope length along the surface.
When does slope percent become impractical or unsafe?
Wheelchair ramps above 8.33% violate ADA. Road grades above 7% require runaway truck precautions; 10–12% is the upper limit on most public highways. Driveways above 15% are hard to drive in snow and may ground low vehicles. Cycling climbs above 10% are rated hors catégorie only on short sections. Roof slopes above 45° (100%) need fall-arrest systems during work and may need extra fastening against wind uplift.
Why does 100% slope equal 45° and not 90°?
Slope percent is a tangent-based measure, not an arc measure. 100% means rise equals run, so tan(θ) = 1 and θ = 45°. A 90° wall would require run = 0, giving tan(θ) = ∞ or infinite percent. This is why slope percent cannot express truly vertical surfaces — use degrees for anything steeper than about 75°.
Turns a slope given in percent into the equivalent angle in degrees using the arctangent relation, and also reports the rise:run ratio, millimetres per metre and inches per foot. Useful for ADA ramp checks, roof pitch conversions, road grade evaluation and cycling climb ratings. Typical examples: 8.33 percent equals 4.76 degrees (the ADA ramp maximum, or a 1:12 ratio), 25 percent equals 14.04 degrees (a standard residential roof slope), and 100 percent equals exactly 45 degrees (a 12:12 pitch where rise equals run). Enter a value, pick the decimal precision, and use the presets to jump to common slopes. A reverse mode converts degrees back to percent for quick cross-checks against architectural drawings.