Slope and Grade Calculator

Welcome to the Slope and Grade Calculator, a comprehensive tool for calculating slope percentage, angle, ratio, and grade from rise and run measurements — or reverse-calculating missing dimensions from a known slope. Whether you are designing an ADA-compliant wheelchair ramp, grading a drainage system, planning a driveway, checking roof pitch, or working on any construction or engineering project, this calculator provides instant results with step-by-step solutions and professional recommendations.

What is Slope?

Slope describes how steep a surface is. It is the ratio of vertical change (rise) to horizontal distance (run). Slope can be expressed in several equivalent ways:

• Percentage (%): Rise divided by run times 100. Example: a 2% slope rises 2 units per 100 units of horizontal distance.
• Ratio: Expressed as rise:run (e.g., 1:12 means 1 unit of rise for every 12 units of run).
• Angle (degrees): The angle of inclination measured from horizontal. Calculated using arctan(rise/run).
• Grade: Same as slope percentage, commonly used for roads and land.
• Pitch: Rise per 12 units of run, used specifically for roofs (e.g., 6:12 pitch).

Key Formulas

How to Use This Calculator

1. Choose your calculation mode: Select what you want to calculate — slope from rise and run, find a missing rise or run from a known slope, or convert between slope formats.
2. Select your application: Choose ramp, drainage, driveway, roof, landscaping, or general purpose for tailored recommendations.
3. Enter your measurements: Input known values with the appropriate unit (feet, inches, meters, centimeters, or yards).
4. Review results: Get slope percentage, angle, ratio, slope length, steepness classification, a proportional diagram, compliance checking, and step-by-step math.

Slope vs. Grade vs. Pitch

Slope and grade both express the ratio of rise to run, typically as a percentage. The term "grade" is more commonly used in civil engineering and road construction (e.g., "a 6% grade"). Pitch is specific to roofing and expresses rise per 12 units of run (e.g., "6:12 pitch" means 6 inches of rise for every 12 inches of run, which is a 50% slope).

Common Slope Standards

Frequently Asked Questions

How do I calculate slope from rise and run?

Slope percentage = (Rise / Run) × 100. For example, a rise of 6 inches over a run of 12 inches gives a 50% slope. You can also express slope as an angle using arctan(Rise/Run), or as a ratio like 1:2.

What is the maximum slope for an ADA wheelchair ramp?

The ADA requires a maximum slope of 1:12 (8.33%) for wheelchair ramps. This means 1 inch of rise for every 12 inches of run. Steeper ramps are allowed only in existing buildings where space is limited: up to 1:10 for a rise of 6 inches or less, and up to 1:8 for a rise of 3 inches or less. Landings are required after every 30 inches of rise (about 30 feet of run at 1:12) and at changes of direction.

What is the difference between slope, grade, and pitch?

Slope, grade, and pitch all describe incline but are used in different contexts. Slope is rise over run expressed as a ratio or percentage. Grade is typically the same as slope percentage, used for roads and land. Pitch specifically refers to roof slope, expressed as rise per 12 units of run (e.g., 6:12 pitch).

What slope is needed for proper drainage?

The minimum slope for proper drainage is 1% (approximately ⅛ inch per foot). The recommended slope for patios and sidewalks is 2% (¼ inch per foot). Underground drain pipes typically use 1-2% slope. Avoid exceeding 5% for surface drainage to prevent erosion.

How do I convert slope percentage to degrees?

Use the formula: Angle = arctan(Slope% / 100) × (180/pi). For example, a 100% slope equals 45°, a 50% slope equals 26.57°, and a 10% slope equals 5.71°. Note that slope percentage and angle are not linearly proportional.

What is the steepest driveway allowed?

The maximum comfortable driveway slope is 10-15% for daily use. The International Fire Code limits fire apparatus access roads, which can include long driveways, to a 10% grade unless the fire official approves more. Slopes over 12% may require traction improvements for winter conditions. Always check local building codes as requirements vary by jurisdiction.

Additional Resources

• Grade (slope) - Wikipedia
• Roof Pitch - Wikipedia