Calculate slope, gradient, angle of inclination, rise and run — expressed as percentage, ratio, degree and fraction for construction and engineering.
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Slope measures the steepness of a surface as the ratio of vertical rise to horizontal run. It can be expressed as a fraction (rise/run = 3/12), a percentage (3/12 × 100 = 25%), a ratio (1:4), or a degree (arctan(3/12) = 14.04°). A slope of 100% means the rise equals the run — a 45° angle. These are all different ways to communicate the same inclination.
For proper drainage: concrete and asphalt paving needs at least 1–2% slope (1/8 to 1/4 inch per foot). Flat roofs require a minimum 2% slope (1/4 inch per foot). Landscaping and lawns need 2% slope away from structures. ADA-compliant ramps are limited to 8.33% (1:12 ratio) maximum. Drainage pipes should slope at least 1% (1/8 inch per foot) for self-cleaning flow.
ADA (Americans with Disabilities Act) limits ramp slopes to 1:12 (8.33%) — for every 1 inch of rise, there must be 12 inches of run. For home ramps without federal requirement, up to 1:8 (12.5%) may be used. A 12-inch rise requires at least 12 feet of ramp at 1:12 slope. Steeper slopes require more upper body strength and can be dangerous for manual wheelchair users.
Slope percentage = (Rise / Run) × 100. Rise is the vertical change; Run is the horizontal distance. For a hill that rises 5 feet over 20 horizontal feet: slope = (5/20) × 100 = 25%. A 100% slope is a 45° angle. On road signs, grade percentages indicate the same thing: a 6% grade means the road rises 6 feet for every 100 feet of horizontal distance.
Degrees = arctan(slope percentage / 100). Percentage = tan(degrees) × 100. Examples: 5% = 2.86°, 10% = 5.71°, 15% = 8.53°, 25% = 14.04°, 50% = 26.57°, 100% = 45°. Degrees and percentage are not proportional — a 10% slope is not twice as steep in degrees as a 5% slope. For construction, percentage is more commonly used; for trigonometry, degrees or radians.
A residential driveway should generally be under 15% slope (about 8.5°) for safe vehicle access in wet or icy conditions. 15–20% is manageable in mild climates with good tyres. Above 20% becomes challenging for low-clearance vehicles and dangerous in winter. Maximum parking slope is typically 5% (ADA spaces require ≤2%). Steep driveways may also affect house insurance and property drainage.
Roof pitch is a form of slope expressed as rise over 12 inches of horizontal run (not 100). A 6:12 pitch = 6 inches of rise per 12 inches of run = 50% slope = 26.6°. Low-slope roofs (under 3:12 = 25%) need waterproof membrane systems. Steep roofs (over 9:12 = 75%) require special anchoring and safety equipment during installation.
For a concrete driveway, best practice is under 15% slope. Above 15%, vehicles may spin tyres in ice and concrete may not cure evenly. The minimum is 1.5–2% slope for proper drainage. Between the house and street, 10–12% is often acceptable in hilly areas. Always check local municipality requirements — some cities limit driveway grades to 12%.
Common methods include: a level and tape measure (measure the run, use the level to find the rise at the other end), a slope gauge or digital inclinometer for quick angle readings, survey levelling equipment for precise grade work, and total stations or GPS for large civil engineering projects. A smartphone clinometer app provides quick approximations for DIY projects.
A 1 in 12 slope (or 1:12 ratio) means 1 unit of rise for every 12 units of horizontal run. In percentage: (1/12) × 100 = 8.33%. As a degree: arctan(1/12) = 4.76°. This is the maximum ramp slope allowed by ADA for accessibility. On roofs, 1:12 is a very low pitch requiring special waterproofing. On driveways, 1:12 (8.33%) is very manageable and generally acceptable.
