How do I calculate roof pitch from rise and run?
Divide vertical rise by horizontal run and multiply by 12 to express the slope as x:12. Roof angle is atan(rise ÷ run), while slope percentage is rise ÷ run × 100. A 6-ft rise over a 12-ft run gives a 6:12 pitch, a 26.57° angle and 50% slope.
Understand vertical rise and horizontal run
Rise is the change in height between two points on a straight slope. Run is the horizontal distance between those same points. Neither value is the length measured along the sloping roof surface. Confusing run with sloped length changes the ratio and produces an incorrect angle.
Enter rise and run in the same unit. This tool uses feet for both in imperial mode and meters for both in metric mode. A 6-inch rise over 12 inches has the same slope as 6 ft over 12 ft, but its sloped length is different. If working from inches in the imperial fields, convert both values to feet first.
Roof pitch, angle and slope percentage
A pitch ratio expresses rise for every 12 units of horizontal distance. An angle expresses the same incline in degrees above horizontal. Slope percentage uses a 100-unit horizontal reference. The three forms describe an incline differently, so their numerical values should not be substituted for one another.
For example, 6:12 means the rise is half the run. That corresponds to 50%, not 6%. Its angle is about 26.57°, not 50°. Use the output label as well as the number when transferring a result into a drawing, note or product inquiry.
Roof pitch calculator formulas
Pitch per 12 = 12 × rise ÷ run. Angle in degrees = atan(rise ÷ run) × 180 ÷ π. Slope percentage = 100 × rise ÷ run. Sloped length = √(rise² + run²). The run must be greater than zero; a zero rise represents a horizontal line.
The sloped length is the geometric hypotenuse for the exact endpoints entered. It does not automatically extend past either endpoint. Overhangs, ridge details, fascia positions and cut allowances are separate. For a longer run at the same pitch, the angle stays constant while the sloped length increases proportionally.
Worked example: a 6:12 roof slope
Enter a rise of 6 ft and a horizontal run of 12 ft. The ratio is 6 ÷ 12 = 0.5, so multiplying by 12 returns a 6:12 pitch. The angle is atan(0.5) ≈ 26.565°, displayed as 26.57°. Multiplying the ratio by 100 gives a 50% slope.
The sloped length is √(6² + 12²) = √180 ≈ 13.416 ft. With a 3-ft rise over a 6-ft run, the pitch and angle stay the same, but the sloped length becomes about 6.708 ft. This is why pitch alone cannot give the length of a roof slope.
| Pitch ratio | Angle | Slope | Length for 12-ft run |
|---|---|---|---|
| 3:12 | 14.04° | 25% | 12.37 ft |
| 6:12 | 26.57° | 50% | 13.42 ft |
| 9:12 | 36.87° | 75% | 15 ft |
| 12:12 | 45° | 100% | 16.97 ft |
Compare roof pitch ratios in consistent units
The comparison table below fixes horizontal run at 12 ft so each row can be checked directly. It is a geometry comparison, not a classification of which roofing product should be installed. Requirements for underlayment, slope limits and fastening come from the relevant roofing system.
A single pitch also does not establish the area of a whole roof. Different planes may have different dimensions or inclines. Hips, valleys, dormers and overlaps need a measured takeoff. Use this tool to resolve the rise-and-run relationship for one straight slope, then use a project-specific layout for quantities.
Record the result without implying a structural design
Download the estimate to keep rise, run, angle and sloped length together. If you are comparing sketches, use a consistent reference for each run. An apparent difference can come from measuring to different endpoints rather than from a change in slope. Check the original dimensions before adjusting materials.
This calculator does not size rafters, beams or connections, and it does not establish roof load capacity. For lumber volume after member dimensions are specified, use the board foot calculator. For a deck-surface estimate on a separate outdoor project, use the deck material calculator; neither tool replaces a structural design.
Owens Corning describes roof slope using vertical rise followed by a 12-inch horizontal run. The angle and sloped-length examples here are calculated from that ratio. Owens Corning explanation of roof slope.
Frequently asked questions
Is a 12:12 pitch a vertical roof?
No. A 12:12 pitch rises 12 units over a horizontal run of 12 units, creating a 45° angle. A vertical line has zero horizontal run and is outside this calculator’s supported rise-and-run model.
Can I enter a roof angle instead of rise and run?
This version accepts rise and horizontal run, not an angle input. If your drawing provides only an angle, obtain the corresponding dimensions before using the tool. Do not enter degrees in a length field.
Does the sloped length include an overhang?
Only if the rise and run you enter already extend to the overhang endpoint. The calculator adds no overhang, ridge deduction or cutting allowance of its own.
Written by Velour Trends · Updated 7 November 2026. Worked examples use the calculator’s stated formulas and rounding model. Our editorial approach · Report a calculation issue.