Roof Pitch Calculator

How to use the Roof Pitch Calculator

To measure an existing roof, hold a level horizontally against the slope, mark 12 inches along it, and measure straight down from that mark to the roof surface. That drop is the pitch: a 6 inch drop over 12 inches of level is a 6/12 roof.

To size rafters, enter the full building span. The run of each rafter on a symmetrical gable is half the span, and the calculator adds the overhang on top of the rafter length.

To order roofing, use the footprint of the building and the pitch. The actual sloped area is always larger than the footprint, which is the single most common reason people under-order shingles.

Roof Pitch formula

Pitch is a ratio, and everything else follows from it:

• angle = arctan(rise ÷ run)
• slope % = (rise ÷ run) × 100
• multiplier = √(pitch² + 12²) ÷ 12
• rafter length = run × multiplier
• roof area = footprint area × multiplier
• squares = roof area ÷ 100

Pitch	Angle	Slope	Area multiplier
3/12	14.04°	25%	1.0308
4/12	18.43°	33%	1.0541
5/12	22.62°	42%	1.0833
6/12	26.57°	50%	1.1180
8/12	33.69°	67%	1.2019
10/12	39.81°	83%	1.3017
12/12	45.00°	100%	1.4142

Worked example

A 6/12 pitch:

• Angle: arctan(6 ÷ 12) = 26.57°
• Slope: 50%
• Multiplier: √(36 + 144) ÷ 12 = 13.4164 ÷ 12 = 1.1180

On a 28 ft span, each rafter runs 14 ft horizontally: 14 × 1.1180 = 15.65 ft, or 15 ft 7¹³⁄₁₆ in, plus the overhang. The ridge sits 7 ft above the wall plate.

A 50 ft × 30 ft footprint is 1,500 sq ft on the ground but 1,677 sq ft of roof, 16.77 squares, or 18.45 squares with 10% waste, so order 19 squares.

What the result means

A 12/12 roof is 41 percent bigger than the building it covers. Even a modest 6/12 adds nearly twelve percent. Ordering shingles against the footprint instead of the sloped area is the classic under-order, and the shortfall grows with the pitch.

Roofing is sold in squares of 100 square feet, normally three bundles to the square for standard three-tab or architectural shingles. Suppliers sell whole bundles, so the figure is rounded up.

The waste allowance covers cuts at hips, valleys, rakes and penetrations. Ten percent suits a simple gable; a cut-up roof with several dormers and valleys can need fifteen to twenty.

Pitch also decides what you are allowed to install. Below about 4/12, standard shingles need extra underlayment; below 2/12 they are not permitted at all and the roof needs a membrane system.

Common mistakes

• Ordering against the footprint. The roof is always bigger than the plan area. That is the whole point of the multiplier.
• Measuring the rafter as the full span. Each rafter runs half the span on a symmetrical gable.
• Forgetting the overhang. The rafter is longer than the run to the wall by the eave projection, measured horizontally then multiplied like everything else.
• Confusing pitch with angle. A 6/12 roof is 26.57 degrees, not 6 degrees and not 30. Suppliers and framers use pitch; solar and engineering use degrees.
• Using shingles on a low slope. Under 4/12 needs a double underlayment; under 2/12 shingles are not a permitted roof covering.
• Ignoring the ridge board and bird’s mouth. The calculated length is the theoretical line; the actual cut is shortened by half the ridge thickness.

Frequently asked questions

What angle is a 6/12 pitch roof?

26.57 degrees. The pitch is the tangent of the angle: 6 divided by 12 is 0.5, and the arctangent of 0.5 is 26.57 degrees. It is also a 50 percent slope.

How do I measure roof pitch?

Hold a level horizontally against the roof slope, mark 12 inches along it, and measure vertically down from that mark to the roof. The measurement in inches is the pitch, a 5 inch drop is a 5/12 roof. You can do it from inside against a rafter if getting on the roof is unsafe.

How do I calculate roof area from the footprint?

Multiply the footprint area by the pitch multiplier, which is the square root of pitch squared plus 144, divided by 12. At 6/12 that is 1.1180, so a 1,500 square foot footprint is 1,677 square feet of roof.

How many bundles of shingles are in a square?

Three, for standard three-tab and most architectural shingles. A square covers 100 square feet. Heavier premium shingles can run four or five bundles per square, so check the wrapper.

How long is a rafter for a 28 foot span at 6/12?

Each rafter runs 14 feet horizontally. Multiplied by 1.1180 that is 15.65 feet, or 15 feet 7 and 13/16 inches, before the overhang and before deducting half the ridge thickness.

What is the minimum pitch for shingles?

Two in twelve is the absolute minimum, and between 2/12 and 4/12 the roof needs a doubled underlayment. Below 2/12 asphalt shingles are not permitted and the roof needs a membrane or standing seam system.