Roof Pitch Explained

Formula

angle° = arctan(X/12) × (180/π). slope% = (X/12) × 100. rise = run × (X/12).

Units

Pitch uses inches of rise per 12 inches of run. Angle in degrees; slope as percent.

Step-by-step

1. Level a 12″ horizontal run on a rafter or rafter square.
2. Measure vertical rise over that run — that number is X in X/12.
3. Convert to degrees or percent if specs require it.
4. Use pitch with run to get rafter length (see related guides).

Reading 7/12

Over 12″ of run you measure 7″ of rise. Angle ≈ 30.26°. Slope ≈ 58.3%. On a 12 ft run, rise = 7 ft.

From angle back to pitch

A 30° roof: tan(30°) ≈ 0.577 → pitch ≈ 0.577 × 12 ≈ 6.93/12 (about 7/12 in the field).

Pitch vs angle vs slope %

Common mistakes

• Calling slope percent “pitch” interchangeably without converting.
• Measuring rise over a non-level 12″ (gives a false pitch).

Practical notes

• Roofing materials often require a minimum pitch — check the product sheet.
• Walkability drops quickly above ~7/12–8/12 without proper fall protection.

Related calculator

Use the free Roof Pitch Calculator to run the same math with your field numbers.

Related tools

• Roof Pitch Calculator — Convert pitch, angle, and slope percent with rafter factors.
• Rafter Calculator — Common rafter length, plumb cut, and seat cut from span or rise/run.

Related guides

• Roof Pitch to Rafter Length — Convert an X/12 pitch into rafter length for a known run.
• How to Calculate Rafter Length — Work out common rafter length from span and pitch or rise and run.
• Common Rafter Formula — The core formula carpenters use for common rafter layout.