Use this Roof Pitch Calculator to calculate roof pitch, rise, run, rafter length, slope percentage, and roof angle. Enter the rise and horizontal run, or enter an x:12 pitch with a known run.

Roof Pitch Formulas

Pitch (x:12) = (rise ÷ run) × 12

Pitch percent = (rise ÷ run) × 100

Roof angle = arctan(rise ÷ run)

Rafter length = √(rise² + run²)

When the x:12 pitch and run are known:

Rise = run × (pitch ÷ 12)

In x:12 notation, a 6:12 roof rises 6 units for every 12 units of horizontal run.

Example

Suppose a roof has a rise of 6 ft and a horizontal run of 12 ft.

Pitch = (6 ÷ 12) × 12 = 6:12

Pitch percent = (6 ÷ 12) × 100 = 50%

Roof angle = arctan(6 ÷ 12) ≈ 26.57°

Rafter length = √(6² + 12²) ≈ 13.42 ft

The roof therefore has a 6:12 pitch, a 50% slope, and an angle of approximately 26.57°.

Important Notes

• Run means the horizontal distance, not the sloped roof or rafter length.
• Use compatible units for rise and run.
• The calculated rafter length does not include roof overhang, ridge adjustments, birdsmouth cuts, or construction allowances.
• Roofing-material requirements and minimum permitted slopes vary by product and building regulations.
• Use approved plans and applicable building requirements for structural or safety-critical roof construction.

Sources

• U.S. Geological Survey — Percent Slope and Angle of Slope
• OSHA — Roof Slope Definitions