Convert between rise & run, percentage grade, degrees and ratio — the four ways slope appears on drawings, road signs, ramps and drainage plans. One tool, every format, with a live triangle you can actually read.
- Rise & Run
- Percent Grade
- Degrees
- Ratio (1:n)
- Ramp Check
- Drainage Check
Percent grade = (rise ÷ run) × 100. It is not the angle in degrees. 100% grade is a 45° slope, not a 100° slope.
Angle = arctan(rise ÷ run). A 1:12 ramp is about 4.76°, not 8.33°.
A smaller n means a steeper slope. 1:12 is steeper than 1:20.
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Slope Conversion Table
The four slope formats side by side — the quickest way to check a drawing against a road sign or a spec sheet.
| Ratio (1:n) | Grade (%) | Angle (°) | Typical use |
|---|---|---|---|
| 1:200 | 0.50% | 0.29° | Land drainage, highway camber |
| 1:100 | 1.00% | 0.57° | Drainage pipe minimum (large diameter) |
| 1:80 | 1.25% | 0.72° | Sewer lateral minimum (150 mm) |
| 1:60 | 1.67% | 0.95° | Drainage pipe minimum (100 mm) |
| 1:50 | 2.00% | 1.15° | Pavement crossfall, car park drainage |
| 1:48 | 2.08% | 1.19° | ADA cross slope maximum |
| 1:40 | 2.50% | 1.43° | Path drainage, patio fall |
| 1:20 | 5.00% | 2.86° | Gentle walkway, driveway approach |
| 1:12 | 8.33% | 4.76° | ADA/IBC ramp maximum |
| 1:8 | 12.50% | 7.13° | OSHA ramp maximum (cleats required) |
| 1:6 | 16.67% | 9.46° | Steep site access, temporary works |
| 1:4 | 25.00% | 14.04° | Very steep — check vehicle capability |
| 1:2 | 50.00% | 26.57° | Extreme — embankments only |
| 1:1 | 100.00% | 45.00° | 45° — not a ramp, a slope face |
How to Calculate Slope
Slope is the relationship between how far something rises and how far it runs horizontally. The same slope can be written four ways. This is how each one is calculated.
Rise & Run
Measure the vertical difference (rise) and the horizontal distance (run) in the same unit.
Slope = Rise ÷ Run
Percent Grade
Multiply the slope ratio by 100. This is what road signs and drainage specs use.
Grade (%) = (Rise ÷ Run) × 100
Degrees
The angle of the slope from horizontal, using the inverse tangent.
Angle (°) = arctan(Rise ÷ Run)
Ratio (1:n)
Common on UK road signs and construction drawings. A smaller n means steeper.
n = 100 ÷ Grade (%)
An 8.33% grade is a 4.76° angle. A 45° slope is 100% grade. Confusing the two is the most common mistake on site and in exams. The relationship is θ = arctan(% ÷ 100).
Slope Percentage and Ratio — Worked Examples
| Task | Given | Calculation | Result |
|---|---|---|---|
| Ramp design check | Rise 0.6 m, Run 7.2 m | 0.6 ÷ 7.2 = 0.0833 | 8.33% — 1:12, meets ADA |
| Drainage pipe | Run 30 m, fall 0.45 m | 0.45 ÷ 30 × 100 | 1.5% — check pipe size minimum |
| Roof pitch | Rise 6 ft, Run 12 ft | 6 ÷ 12 = 0.5 | 50% — 6:12 pitch, 26.57° |
| Road gradient | Rise 4 m, Run 100 m | 4 ÷ 100 × 100 | 4% — within motorway limit |
| Car park fall | Rise 0.1 m, Run 5 m | 0.1 ÷ 5 × 100 | 2% — 1:50, standard crossfall |
| Path crossfall | Rise 0.02 m, Run 1 m | 0.02 ÷ 1 × 100 | 2% — 1:50, ADA cross slope OK |
| Trench invert | Run 45 m, fall 0.9 m | 0.9 ÷ 45 × 100 | 2% — 1:50, good for 100 mm pipe |
| Stair angle | Rise 2.7 m, Run 3.6 m | arctan(2.7 ÷ 3.6) | 36.87° — steep stair, check code |
Where Slope Calculations Are Used in Real Life
Slope is not an abstract geometry exercise. It governs access, safety, drainage and cost on every project.
Wheelchair ramps
ADA and IBC limit running slope to 1:12 (8.33%). Cross slope is capped at 1:48 (2.08%). Getting this wrong fails inspection.
Drainage and sewer pipes
Minimum gradients depend on pipe diameter — 100 mm pipe needs about 1:60 (1.67%), 150 mm about 1:80 (1.25%). Too flat and solids settle; too steep and water outruns solids.
Roof pitch
Roof pitch determines the roofing material, the rafter length, and whether the roof sheds water or snow. Low pitch (1:12 to 4:12) needs different membranes than steep pitch (8:12+).
Roads and highways
Motorways are capped at 3–4%, rural roads at 6–8%, and residential streets at 12%. Steeper than that and heavy vehicles lose traction, fuel consumption climbs, and drainage becomes critical.
Site grading and cut & fill
Grading plans specify slope as a percentage. A 2% fall across a car park is 1:50. Get the slope wrong and you either pond water or move more earth than you budgeted.
Stairs and stepped access
Stair angle is a slope. Comfortable stairs sit between 30° and 37°. Steeper than 42° and they become ladder-like; shallower than 26° and they feel like a ramp.
Excavation and trenching
Trench walls are battered back at a safe slope — typically 1:1 for stable soil, flatter for loose fill. OSHA and local codes set the allowed angles by soil type.
Bicycle and pedestrian paths
Shared paths are usually capped at 5% (1:20) for comfort and safety. Steeper gradients need handrails, landings or alternative accessible routes.
Slope Regulations and Standards
The key documents that set slope limits in construction. Check the project spec for which applies.
ADA Standards §405
US accessible design. Ramp running slope max 1:12 (8.33%), cross slope max 1:48 (2.08%).
IBC 1012.2
International Building Code ramp provisions. Max 1:12 running slope, 1:48 cross slope.
OSHA 29 CFR 1926.451
Construction ramps and walkways. Max 1:3 (20°) for walkways; steeper than 1:8 needs cleats.
OSHA 29 CFR 1910.25
General industry walking-working surfaces. Pedestrian ramps typically capped at 1:12.
AS 1428.1
Australian Standard for access and mobility. Ramp gradients and landings for public buildings.
BS 8300
UK accessible design. Ramp slope limits and landing requirements for buildings.
DIN 18040
German accessible construction standard. Ramp slopes for public and residential buildings.
NBC India Part 3
National Building Code of India. Ramp slope for accessibility and parking gradients.
SANS 10400-S
South African accessibility standard. Ramp slopes and crossfall limits.
Eurocode 1 (EN 1991-1-1)
Actions on structures — roof pitch influences imposed load categories.
People Also Ask
What is a 1:12 slope in percentage and degrees?
1:12 is 8.33% grade and approximately 4.76° angle. It is the maximum running slope allowed for accessible ramps under ADA and IBC.
What is the difference between slope percentage and degrees?
Percent grade is rise ÷ run × 100. Degrees is the angle from horizontal, calculated as arctan(rise ÷ run). They are not the same number. 100% grade is a 45° angle, not 100°.
How do I convert a ratio like 1:20 to a percentage?
Grade (%) = 100 ÷ n. So 1:20 = 100 ÷ 20 = 5%. 1:12 = 100 ÷ 12 = 8.33%. A smaller n means a steeper slope.
What roof pitch is 6:12 in degrees and percentage?
6:12 pitch means 6 units rise per 12 units run. That is 50% grade and approximately 26.57° angle.
What is the minimum slope for drainage pipe?
It depends on pipe diameter. A common rule: 100 mm pipe needs about 1:60 (1.67%), 150 mm pipe about 1:80 (1.25%), and larger pipes can be flatter. Always check the local sewer authority standard.
What is the maximum slope for a wheelchair ramp?
1:12 (8.33%) for ADA and IBC in the United States. Some countries allow 1:10 for short ramps in existing buildings, but 1:12 is the international benchmark. Cross slope is limited to 1:48 (2.08%).
What is the maximum road gradient?
Motorways: 3–4%. Rural roads: 6–8%. Residential streets: 12% (14% for very short sections). Steeper than 12% and heavy vehicles struggle, especially in wet conditions.
How do I measure slope on site without a level?
Use two string lines and a line level, or a laser level. Measure the vertical difference (rise) between two points a known horizontal distance apart (run). Divide rise by run and multiply by 100 for percent grade. A smartphone clinometer app can give a quick angle check, but verify with a physical level for anything critical.
Why is 100% slope equal to 45 degrees?
100% grade means rise equals run. When the rise and run of a right triangle are equal, the angle is 45°. The tangent of 45° is 1, and 1 × 100 = 100%. That is why 100% grade is 45°, not 90° or 100°.
Related Calculators
Verify every slope against the project specification and local code before construction.