Roof Pitch Calculator
Pitch ratio, angle, slope and common-rafter length.
How it works
Pitch is rise divided by horizontal run. The calculator normalizes that ratio to inches of rise per 12 inches of run, then converts the same ratio to degrees and percent slope.
Rafter length is the hypotenuse of a right triangle. It is geometric length only and does not size the rafter or include ridge, tail, birdsmouth, plumb-cut, seat-cut or connection allowances. Verify the roof design and fall protection with qualified local professionals.
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How the Roof Pitch Calculator works
The roof pitch calculator converts any rise/run pair into the familiar X:12 pitch, degrees, percent slope and pitch multiplier. Add the horizontal distance from wall plate to rafter end to get total rise and the geometric common-rafter length.
Rise and run describe one ratio
Pitch is vertical rise divided by horizontal run. A 6 in rise over a 12 in run is 6:12, a ratio of 0.5, a 50% slope and an angle of arctan(0.5), or about 26.57°. The pitch multiplier is √(1 + 0.5²), about 1.118.
The ratio fields can use any matching units because they cancel. The horizontal roof run is entered separately in feet and means the one-way plan distance from the wall plate to the rafter end, not the full building width.
What rafter length does and does not include
Geometric rafter length is horizontal run multiplied by the pitch multiplier. The diagram makes the right triangle explicit and is useful for checking that run and rise were not reversed.
This result does not size a rafter or add ridge, tail, birdsmouth, plumb-cut, seat-cut or connection allowances. Structural loads, member selection and roof work protection must be established for the actual project. Continue to the roofing calculator for covering area and purchasing units.
FAQ
What angle is a 6:12 roof? expand_more
Divide 6 by 12 and take arctan(0.5). The result is approximately 26.57° and the pitch multiplier is approximately 1.1180.
Is roof run half the building width? expand_more
It often is for a centered gable without overhang, but not always. Enter the actual horizontal distance from the wall plate to the rafter end for the rafter being estimated.
Can this calculator give a rafter cut length? expand_more
No. It gives the right-triangle line length only. Ridge, tail, birdsmouth, plumb cuts, seat cuts and connection details require the actual framing layout.
Does pitch determine rafter size? expand_more
No. Rafter size and spacing depend on span, species and grade, dead load, snow and wind loads, bracing, connections and the locally adopted code.