Calculator
Engineering
MathSlope Calculator
Free online slope calculator to calculate slope percentage, angle, rise over run for roofs, ramps, stairs, drainage, and roads. Convert between degrees, percent, and ratio formats.
What is Slope?
Slope (also called grade, pitch, or gradient) is the measure of steepness or incline of a surface. It's expressed as rise over run (vertical change / horizontal distance), as a percentage, or as an angle in degrees. For example, a 2% slope means 2 feet of rise for every 100 feet of run. Slope is critical in construction for roofs (water drainage), roads (safe driving), ramps (accessibility), drainage pipes (gravity flow), and landscaping. Understanding slope helps ensure proper water runoff, structural stability, and code compliance.
Slope Calculation Formulas
1. Slope % = (Rise / Run) × 100
2. Angle = arctan(Rise / Run) = arctan(Slope %/100)
3. Ratio = Rise : Run (simplified)
4. Slope Length = √(Rise² + Run²)
Common Slopes
Low roof pitch: 2/12 to 4/12 (9.5° to 18.4°)
Standard roof: 4/12 to 8/12 (18.4° to 33.7°)
Steep roof: 8/12+ (33.7°+)
ADA ramp: 1:12 max (8.33%, 4.76°)
Driveway: 10-15% max (5.7° to 8.5°)
Road grade: 6-10% typical (3.4° to 5.7°)
Drainage: 1-2% minimum (0.57° to 1.15°)
Slope Format Examples
Percentage: 25% (25 units rise per 100 units run)
Ratio: 1:4 (1 unit rise per 4 units run = 25%)
Angle: 14.04° (same as 25% or 1:4)
Fraction: 3/12 roof pitch (3" rise per 12" run = 25%)
Common Applications
- Roofing: Pitch affects water drainage, snow load, and material selection
- Ramps: ADA requires max 1:12 (8.33%) for wheelchair accessibility
- Roads: Grade affects vehicle performance, drainage, and safety
- Drainage: Minimum 1-2% slope needed for gravity flow in pipes
- Landscaping: Proper slope prevents water pooling and erosion
- Stairs: Rise/run ratio determines comfort and code compliance
Tips for Slope Calculations
- Minimum roof pitch for shingles: 2/12 (16.7%), for metal: 1/12 (8.3%)
- Maximum driveway slope: 15% (8.5°) for safe vehicle access
- Drainage pipes: 1/4" per foot (2%) minimum for wastewater
- ADA ramps: 1:12 max (8.33%) with landings every 30 feet
- Road grades above 10% are considered steep and may need warnings
- Consider snow/ice in cold climates - limit slopes for safety
- Steeper slopes require more structural support and materials
Building Code Requirements
Building codes specify slope requirements for safety and functionality. Roofs need minimum slope for water drainage (varies by material). Ramps must meet ADA guidelines: maximum 1:12 slope (8.33%), with level landings every 30 feet and at top/bottom. Driveways typically limited to 15% maximum grade. Plumbing drainage requires 1/4 inch per foot (2%) minimum slope for proper flow. Roads may have maximum grades of 6-10% depending on terrain and vehicle types. Always verify local building codes as requirements vary by jurisdiction and application.