Roof Pitch Calculator

Roof pitch is the roof's steepness — the angle a roof surface makes with horizontal, or equivalently how many inches it rises for every 12 inches it runs across. Different trades express the same roof three ways, and this calculator converts between all of them at once: pitch ratio, angle in degrees, and percent grade.

The three languages

1. Pitch ratio (X-in-12) — the roofer's shorthand. A 6/12 roof rises 6 inches per 12 inches of run.
2. Angle (degrees) — the geometric truth, measured from the horizontal.
3. Percent grade — rise ÷ run × 100, borrowed from civil engineering.

The math

Ratio = rise ÷ run        (scaled so run = 12)
Angle = arctan(rise ÷ run)  in degrees
Grade = (rise ÷ run) × 100%

Worked example

A roof rising 6 inches over a 12-inch run:

Ratio = 6-in-12
Angle = arctan(6 ÷ 12) ≈ 26.6°
Grade = (6 ÷ 12) × 100 = 50%

So "6/12", "26.6°" and "50%" are three ways of saying the same roof, and the calculator reports all three so any trade can read it in its own unit.

Why run is 12 inches

Half a foot is the traditional unit of horizontal run in roofing because it makes pitches easy to eyeball (a 6-in-12 roof rises half its run) and keeps on-roof arithmetic simple. Roofing materials, flashing details and installation guidelines are engineered around pitch classes — 3/12, 4/12, 6/12, 9/12 and 12/12 being the milestones most contractors carry in their heads.

What pitch means practically

A steeper roof sheds rain and snow faster and can earn usable attic height, but it costs more to build and is riskier to walk on. Many building codes also set minimum pitches per material — 4/12 is the usual baseline for standard asphalt shingles.

Measuring it yourself

Hold a level true at the 12-inch mark along the run, then read the vertical drop to the roof surface with a ruler or tape — that drop, in inches, is your pitch. Two cautions:

• Measure the rise over a known run, never along the sloped rafter; the slope length exaggerates the pitch.
• Keep units consistent — rise in inches against a run in centimetres breaks the ratio entirely.

Common mistakes

• Using the sloped length of the rafter as the run — always the horizontal run.
• Reading a 45° roof as "45-in-12" — a 45° roof is a 12/12 pitch with a 100% grade.
• Confusing grade and angle: 50% does not mean 50°, and the two diverge more as the roof steepens.
• Scaling the ratio wrongly — a 3-inch rise over 24 inches of run is 3/24 of 12, i.e. a 1.5-in-12 pitch, not a 3-in-12.

Design checks worth running

• Gable and hip framing: use pitch to compute common rafter length — run ÷ cos(angle).
• Snow load: steeper pitches shed snow, reducing structural load in cold climates.
• Materials budget: a steeper roof has more surface area than the floor area beneath it — two pitches with the same floor plan can need very different material quantities.

For the same trigonometry applied to ramps and roads — in degrees or percent grade — see the elevation change calculator.