How to Calculate Roof Pitch

The Four Pitch Formulas

All four values below describe the same slope, just in different notations:

Why the multiplier works: the roof surface is the hypotenuse of a right triangle with legs rise and run. The Pythagorean theorem gives the hypotenuse length, and dividing by the run normalizes it to a factor per unit of horizontal distance.

Worked Example 1 — 6/12, the standard case

1. Measured: rise 6 in over a 12-in run.
2. Pitch: (6 ÷ 12) × 12 = 6/12.
3. Angle: atan(0.5) = 26.57°.
4. Slope: 0.5 × 100 = 50%.
5. Multiplier: √(1 + 0.5²) = 1.118. A 1,500 sq ft footprint → 1,677 sq ft of roof.

Worked Example 2 — 4/12, converting the other way

1. Measured: rise 4 in per 12-in run.
2. Angle: atan(4/12) = atan(0.3333) = 18.43°.
3. Slope: 33.3%.
4. Multiplier: √(1 + 0.1111) = 1.054. A 2,000 sq ft footprint → 2,108 sq ft of roof.
5. Reverse check: a 24° reading on a phone app → 12 × tan(24°) ≈ 5.3, so roughly a 5/12 pitch.

Worked Example 3 — non-12 run

You measured 7 inches of rise over a 16-inch rafter section (run 16). Pitch is always normalized to a 12-inch run: (7 ÷ 16) × 12 = 5.25/12. Everything else follows from the ratio 0.4375: angle atan(0.4375) = 23.63°, slope 43.75%, multiplier √(1 + 0.1914) = 1.091.

The 4 Most Common Pitch Mistakes

• Flipping rise and run. Pitch is rise over run — 6/12 is very different from 12/6 (which isn't even valid notation, since run is fixed at 12).
• Confusing slope percentage with degrees. A 50% slope is 26.57°, not 50°. The percentage is rise/run; the angle is atan(rise/run). They diverge fast on steep roofs: 12/12 is 100% but only 45°.
• Measuring run from the wrong point. For a gable roof, run is half the building width — one roof plane, not both. Using the full width doubles the run and halves the pitch.
• Ignoring the overhang. Pitch doesn't change with overhang, but area does — add overhang to the footprint before applying the multiplier, not after.

Using the Result

The pitch multiplier is the bridge from geometry to materials: multiply your footprint by it to get roof surface area, then feed that into the Roofing Squares Calculator or Shingle Calculator. For measurement instructions in the field, see How to Measure Roof Pitch.