Roof Slope Calculator
Determine roof slope percentage, gradient ratio, pitch ratio, and incline angle from rise over run dimensions.
Slope vs. Pitch
Slope is expressed as a percentage (Rise / Run) × 100, whereas Pitch is expressed as a ratio over 12 inches (e.g. 4/12).
How to Use This Calculator
To calculate slope ratios, slope percentages, and incline angles, enter your vertical and horizontal dimensions above:
- Vertical Rise: Vertical elevation change (e.g. 6 inches).
- Horizontal Run: Horizontal base distance (standard US run is 12 inches).
- Measurement Unit: Select inches, feet, centimeters, or millimeters.
Click Calculate Slope to view slope ratio (X:12), slope percentage (%), incline angle (°), and pitch area multiplier.
What Is Roof Slope & How Is It Expressed?
Roof slope defines the steepness of a roof surface. Depending on the industry, slope is expressed in three distinct mathematical formats:
- Slope Ratio (e.g., 6:12): The vertical rise in inches for every 12 horizontal inches. Favored by North American roofing contractors.
- Slope Percentage (e.g., 50%): Calculated by dividing vertical rise by horizontal run and multiplying by 100. Standard in civil engineering and drainage design.
- Incline Angle (e.g., 26.57°): The tilt angle in degrees measured from the horizontal baseline. Used in architectural CAD drafting and solar panel installation.
Formulas & Mathematical Equations
Worked Numerical Example
Let's calculate the slope properties for a roof with a 6-inch rise over a 12-inch run:
- Slope Ratio: 6 : 12 (simplifies to 1 : 2).
- Slope Percentage: (6 / 12) × 100 = 50.0%.
- Incline Angle in Degrees: arctan(6 / 12) = 0.4636 radians × (180 / π) = 26.57°.
- Slope Area Multiplier: √(6² + 12²) / 12 = √180 / 12 = 1.11803.
How to Interpret Your Slope Result
Building codes classify roofs into distinct categories based on slope percentage and ratio:
| Slope Category | Slope Ratio | Slope (%) | Angle (°) | Code & Material Guidelines |
|---|---|---|---|---|
| Flat Roof | 0:12 to 2:12 | 0% – 16.7% | 0° – 9.5° | Single-ply membrane (EPDM, TPO, PVC); shingles prohibited |
| Low Slope | 2:12 to 4:12 | 16.7% – 33.3% | 9.5° – 18.4° | Double underlayment or self-adhering ice membrane required |
| Conventional Slope | 4:12 to 9:12 | 33.3% – 75.0% | 18.4° – 36.9° | Standard architectural shingles, metal, tile; walkable |
| Steep Slope | 9:12 & Above | 75.0% + | 36.9° + | Architectural shingles, slate, tile; requires safety harnesses |
Related Roofing Calculators & Guides
Calculate pitch ratios, incline angles, and slope factors.
Open Tool → Angle DegreesConvert rise and run into precise degree angles for solar & CAD.
Open Tool → Slope GuideExplaining the technical differences between pitch and slope.
Read Guide →Frequently Asked Questions
Roof slope is the ratio of vertical rise over horizontal run (e.g. 6:12). Roof pitch is technically the ratio of vertical rise over total building span (e.g. 6/24 = 1/4 pitch). In standard US trade usage, both terms are often used interchangeably to mean rise over run.
A 50% slope means the roof rises 6 inches vertically for every 12 inches of horizontal run (6/12 pitch), corresponding to an incline angle of 26.57 degrees.
Building codes classify roofs with slopes between 2/12 (16.67%) and 4/12 (33.33%) as low-slope roofs. They require specialized double-underlayment or ice & water shield membranes under shingles.
Steeper slope percentages (above 50% or 6/12 pitch) accelerate rainwater runoff, preventing standing water and ice dam formation near eaves and flashing valleys.