Calculators/Roof pitch & rafter

Roof pitch and common rafter calculator

Pitch to angle and slope factor, and the common rafter length for a simple gable — with the ridge deduction and the overhang tail taken off separately, the way you actually cut it.

The roof

Building width, outside to outside
ft
in

Enter 6 for a 6/12 roof, 4 for a 4/12, and so on.

Half comes off the run. Use 0 for none.

Measured level, not along the slope.

The rafter

6/12

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Check the result against the job. This does the arithmetic from the values you enter. Building codes, span tables and material specifications vary by jurisdiction and by product, and the governing document is your approved drawings and your local code. Nothing you type here leaves your browser: the calculation runs on your device and we never receive it.

How this is checked. Every formula on this site runs from one shared calculation engine, and every one has a test fixture whose expected answer was worked out from the geometry or taken from a figure the trade already publishes — never from what the code returns. Some land exactly, which is the point: a 6/12 hip over a 144″ run is exactly 216″, a 45° crown in a square corner bevels at exactly 30°, and a 30° conduit bend has a multiplier of exactly 2. Where a number is a convention rather than arithmetic — a code limit, a waste allowance, bundles per square — it is an input with a stated default rather than a hidden constant. Found something wrong? Tell us at [email protected] and we will fix it and say so.

How the numbers come out

Pitch is a ratio, not an angle: rise over a run of 12. Everything else follows from it by right-triangle geometry.

  • Angle is the arctangent of rise over 12. A 6/12 is 26.57°, a 12/12 is exactly 45°.
  • Slope factor is √(rise² + 144) ⁄ 12 — the hypotenuse of that triangle per unit of run. Multiply any level length by it to get the length along the slope.
  • Run is half the building width, less half the ridge thickness.
  • Rafter line length is run × slope factor. That is the length from the plumb cut at the ridge to the plumb cut at the wall, measured along the top edge — before the birdsmouth is cut into it.
  • The tail is the overhang × the same slope factor, which is why a level 12 inch overhang needs more than 12 inches of rafter.

The slope factor also converts area. A 1,000 sq ft footprint under a 6/12 roof is about 1,118 sq ft of actual roof surface — which is the number that matters when you are ordering shingles rather than framing.

For the table of every common pitch with its angle and slope factor, see the roof pitch reference, and for why pitch is written this way at all, the guide to roof pitch.

Common questions

How do you calculate common rafter length?

Multiply the run by the slope factor. The run is half the building width less half the ridge thickness, and the slope factor is the square root of the rise squared plus 144, divided by 12. A 6/12 roof has a slope factor of about 1.118, so a 143.25 inch run gives a rafter line length of about 160 1/8 inches.

What is a roof slope factor?

The slope factor is the number you multiply a horizontal length by to get the length along the slope. It is also how you turn a flat footprint area into a real roof area: a 1,000 square foot footprint under a 6/12 roof has about 1,118 square feet of roof surface.

Why subtract half the ridge thickness from the run?

The ridge board sits in the middle of the span and takes up its own thickness, so each rafter stops half a ridge short of the building centreline. On a 1 1/2 inch ridge that is 3/4 of an inch off each run — small, but it is the difference between a tight ridge and a gap.

What angle is a 6/12 roof pitch?

A 6/12 pitch is 26.57 degrees from horizontal. Pitch is the arctangent of rise over run, so 4/12 is 18.43 degrees, 6/12 is 26.57, 8/12 is 33.69 and 12/12 is exactly 45 degrees.

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