Choose the roof measurement you actually know
A roof can be described by rise and horizontal run, rise per 12, or its angle above level. This form accepts those practical starting points and derives the other notations. Use dimensions when they come from a reliable section drawing or direct measurement; use degrees when the starting value came from an inclinometer or a clearly side-on visual check.
Pitch x/12 means x units of vertical rise for every 12 equal units of horizontal run. It is not the sloped rafter length. The central relation is tan(θ)=rise/run: θ=atan(rise/run), percent grade=100×rise/run, and pitch rise=12×rise/run.
Calculate from pitch, dimensions, or angle
- For a written 6/12 pitch, enter 6 as roof rise per 12; the denominator is already represented by the form.
- For field or drawing dimensions, enter vertical rise and horizontal run in the same unit. Do not substitute rafter length for run.
- For an angle reading, enter degrees measured from a verified level reference, then calculate the equivalent pitch.
- Keep the input type with any copied result so another reader knows whether it came from dimensions, notation, or a visual reading.
Worked roof examples and rounding
- A 6/12 roof has rise/run=6/12=0.5. atan(0.5)=26.565°, grade is 50%, and the pitch remains 6/12.
- A section with 30 inches of rise over 72 inches of horizontal run has slope 0.4167, angle about 22.62°, and pitch about 5/12.
- A measured 33.69° angle has tan(θ)≈0.667, corresponding to about 8/12; source uncertainty may make 7.9/12 more honest than rounding immediately.
- Equal units cancel in a ratio, but mixed feet and inches must be converted before division.
- Material quantities, rafter cuts, loads, drainage, and local requirements need inputs beyond this geometric conversion.
When each input route is appropriate
- Use rise per 12 to translate common trade notation on a roof schedule.
- Use rise and run for a scaled section or measurements taken from level references.
- Use degrees to translate a sensor reading, while keeping its calibration and placement uncertainty.
- Compare two proposals in a consistent notation before discussing them with a qualified contractor.
- Keep visual photo estimates separate from values stated on authoritative plans.
Reading a roof result
Degrees describe rotation from horizontal, percent grade describes rise per 100 units of run, and x/12 describes rise per 12 units of run. They are equivalent only when they refer to the same straight slope and trustworthy baseline.
- Label decimal pitch values instead of implying a standard nominal pitch.
- Do not infer a complete roof geometry from one photographed edge.
- Use plan dimensions or direct field measurement when ordering or fabricating.
Geometry is not a roof assessment
The calculation relates pitch notation, slope, and angle only. It does not inspect framing, sheathing, sag, load paths, weather exposure, material limits, drainage details, or code requirements. Verify site dimensions and safety-critical decisions with appropriate instruments and qualified people.