Calculate pitch, slope, angle, and diagonal length from rise and run measurements.
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Enter rise and run to get pitch, slope %, angle, and diagonal.
Enter rise and run to calculate.
Slope compares vertical rise with horizontal run. Enter the rise and run to calculate the construction pitch, slope percentage, angle, and diagonal distance between the two points. Construction pitch is commonly expressed as the amount of rise for every 12 inches of horizontal run — a 6:12 pitch rises 6 inches for every 12 inches of run.
Pitch = (Rise ÷ Run) × 12
Slope % = (Rise ÷ Run) × 100
Angle = atan(Rise ÷ Run)
Diagonal = √(Rise² + Run²)
The diagonal is the geometric straight-line distance between the two points. It does not include overhangs, ridge adjustments, or material cuts.
A rise of 6 ft over a run of 12 ft:
6 ÷ 12 × 12 = 6
Pitch: 6:126 ÷ 12 × 100
Slope: 50%atan(6 ÷ 12)
Angle: ≈ 26.57°√(6² + 12²) = √180
≈ 13.42 ft
Diagonal: ≈ 13 ft 5 inThe vertical change between two points.
The horizontal distance between the same two points.
The amount of rise for every 12 inches of horizontal run.
The straight-line distance between the start and end points.
Construction pitch is typically expressed as rise per 12 units of horizontal run, such as 6:12 — the surface rises 6 units vertically for every 12 units of run.
Slope expresses the same relationship as a percentage: a 6:12 pitch equals a 50% slope. Angle expresses it in degrees: a 6:12 pitch is approximately 26.57°.
These are different ways of describing the same rise-to-run relationship, and the calculator reports all three from the same measurements.
Roof layout: convert measured rise and run into roof pitch and angle.
Framing: determine geometric slope and diagonal dimensions during layout.
Ramps: calculate slope percentage and angle from rise and run.
Drainage and grade: convert vertical change and horizontal distance into slope percentage.
| Pitch | Slope · Angle |
|---|---|
| 1:12 | 8.33% · 4.76° |
| 2:12 | 16.67% · 9.46° |
| 3:12 | 25% · 14.04° |
| 4:12 | 33.33% · 18.43° |
| 5:12 | 41.67% · 22.62° |
| 6:12 | 50% · 26.57° |
| 8:12 | 66.67% · 33.69° |
| 10:12 | 83.33% · 39.81° |
| 12:12 | 100% · 45° |
Divide the rise by the run and multiply by 12. A rise of 6 feet over a run of 12 feet produces a 6:12 pitch.
A 6:12 pitch means the surface rises 6 units vertically for every 12 units of horizontal run.
Divide the pitch rise by 12 and multiply by 100. A 6:12 pitch equals a 50% slope.
A 6:12 pitch is approximately 26.57 degrees.
Square the rise and run, add the results, and take the square root. This gives the straight-line diagonal between the two points.
They describe the same rise-to-run relationship in different formats. Construction pitch is commonly expressed as rise per 12 units of run, while slope is often expressed as a percentage.
Yes. Enter the roof rise and horizontal run to calculate pitch, slope, angle, and geometric diagonal length. Roofing details and structural requirements should still be verified separately.
The calculator can determine the geometric slope from rise and run, but allowable or required slopes depend on the project and applicable requirements.
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