Roof pitch calculator: ratio, angle and area factor

Roof pitch is written as inches of rise per 12 inches of horizontal run, so a 6/12 roof climbs 6 inches for every foot it travels inward. This calculator converts that ratio into degrees, into the multiplier used for turning plan area into roof area, and into a rafter length for a given run.

Rise (in per 12)

Inches of rise per 12 inches of horizontal run.

Run (optional) (ft)

Used for the rafter length, not the pitch.

Pitch

6.0:12

Angle 26.6 degreesArea factor 1.118 ×Rafter length 13.42 ft

Geometry only. Real roofs have overhangs, valleys and ridge boards that change cut lengths, and a carpenter's framing square beats any estimate for cutting rafters.

The multiplier is the number that matters when ordering material: roof area equals plan area times the multiplier. A 6/12 pitch is 1.118, meaning a 1,000 sq ft footprint has 1,118 sq ft of roof. A 4/12 is 1.054, an 8/12 is 1.202, and a 12/12 is 1.414 — the value that makes steep roofs so much more expensive to cover.

Pitch also decides what materials are allowed. Asphalt shingles need at least 2/12, and anything below 4/12 generally requires a doubled underlayment; below 2/12 the roof is treated as flat and needs a membrane. Above 8/12, most roofing crews want roof jacks or staging, which shows up in the labour price rather than the material list.

How the calculation works

Pitch = rise ÷ run, expressed as rise per 12. Angle = atan2(rise, 12) in degrees. Multiplier = √(144 + rise²) ÷ 12, from Pythagoras on a 12 in run. Rafter length = run (ft) × multiplier.

The multiplier is exactly the secant of the roof angle, which is why it always exceeds 1.

• The roof plane is a straight slope with no sag or curve; a sagging roof has an effective pitch lower than its nominal one.
• Rafter length ignores the ridge board and the birdsmouth cut, so add 12-18 in of tail and plumb allowance when cutting.
• The run is the horizontal distance from the ridge to the wall plate, not the full span of the roof.
• Pitch is uniform across the plane; a gambrel or mansard roof has several, each needing its own calculation.

Sources: Pitch multiplier = √(144 + rise²) ÷ 12 (Pythagoras on a 12 in run); Asphalt shingle minimum pitch: 2/12 with doubled underlayment below 4/12 (manufacturer guidance)

Worked examples

Questions

What does a 6/12 pitch mean?

Six inches of vertical rise for every 12 inches of horizontal run, which is 26.6 degrees. It is the most common residential pitch in the US.

How do I convert pitch to degrees?

Take the arctangent of rise divided by 12. A 6/12 roof is atan(0.5) = 26.6 degrees; a 12/12 roof is 45 degrees.

What is the multiplier for roof area?

For a 6/12 pitch it is 1.118: multiply the footprint by that to get roof area. For 4/12 it is 1.054, 8/12 is 1.202 and 12/12 is 1.414.

What is the minimum pitch for shingles?

2/12 for asphalt shingles with a doubled underlayment from 2/12 to 4/12; below 2/12 you need a flat-roof membrane rather than shingles.

How do I measure pitch from the ground?

Measure 12 inches horizontally along a level held against the roof edge, then measure down to the roof surface. Alternatively hold a level against a gable end and measure rise over a 12 in run.

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Written and maintained by Sam Winters. Last updated 2026-11-04. Every figure is computed in your browser; nothing you enter is sent anywhere. Found an error? Tell me — accuracy reports get fixed first.