Rafter Calculator: Lengths, Cut Angles and Jack Cut List
Rafter Length and Cut Angle Calculator
Common, hip and jack rafter lengths from span and pitch, with plumb and seat cut angles and a jack rafter cut list. Ridge thickness is deducted and the overhang is added along the slope, not along the plan.
The common rafter multiplier is the hypotenuse of the pitch triangle per foot of run. The hip multiplier uses 288 rather than 144 because a hip runs diagonally across the plan, so its run per foot is the square root of 2 feet, and at a 6/12 pitch that works out to exactly 1.5. Half the ridge thickness comes off the run because the rafter stops at the face of the ridge board, not at the centreline, and forgetting it makes every rafter in the roof long by the same amount.
How to use this tool
Enter the span, the pitch, the overhang and the ridge thickness. The tool returns the common rafter length, the plumb and seat cut angles, the hip rafter, and a jack rafter cut list stepped at your rafter spacing.
Two multipliers, and why the hip one uses 288
A common rafter rises straight across the building, so per foot of run it travels the hypotenuse of a 12 and rise triangle: the square root of 144 plus the rise squared, over 12. That is the common multiplier.
A hip rafter runs diagonally to the corner, so for every foot the common rafter runs, the hip runs the square root of 2 feet in plan. Its triangle therefore has a base of the square root of 2 times 12, whose square is 288, and the multiplier becomes the square root of 288 plus the rise squared, over 12. At a 6/12 pitch that works out to exactly 1.5, which is a satisfying check and a useful one: if your hip multiplier at 6/12 is not exactly 1.5, something is wrong.
The ridge deduction that makes every rafter long
The run is measured to the centreline of the building, but the rafter stops at the face of the ridge board, not at its centre. So half the ridge thickness comes off the run before the multiplier is applied. On a 1.5 inch ridge that is three quarters of an inch of run, which becomes about seven eighths of an inch along a 6/12 slope.
It sounds trivial, and on one rafter it is. The problem is that it is systematic: every common rafter in the roof is long by the same amount, so the ridge sits high, the birdsmouths do not seat, and the error shows up as a consistent gap that looks like bad cutting rather than bad arithmetic. Deducting it once at the start is far easier than diagnosing it on the roof.
A worked check you can repeat on paper
A 24 foot span at 6/12 with a 12 inch overhang and a 1.5 inch ridge. The run is 12 feet, less 0.0625 feet for half the ridge, giving 11.9375. The common multiplier is the square root of 180 over 12, which is 1.11803, so the rafter from ridge to seat is 13.35 feet. The overhang adds 1 foot of run times the same multiplier, 1.118 feet, for a total cut length of 14.46 feet. The plumb cut is the arctangent of 6 over 12, which is 26.565 degrees, and the seat cut is its complement, 63.435. The hip is the 12 foot run times 1.5, exactly 18 feet.
Mistakes that catch people out
Forgetting the ridge deduction. Systematic, and it affects every rafter equally. Fix: enter the ridge thickness and let it come off the run.
Measuring the overhang horizontally and adding it directly. The overhang runs along the slope, so it gets the multiplier too. Fix: enter it as a horizontal projection; the tool converts it.
Using the common multiplier on a hip. The hip runs diagonally and is longer. Fix: separate multipliers, with the 1.5 check at 6/12.
Cutting all jacks the same. Jacks shorten by a fixed step, the spacing times the common multiplier. Fix: the cut list gives each one.
How this was checked
The geometry was verified against exact values rather than approximations: the hip multiplier at 6/12 is exactly 1.5, a 12/12 pitch gives exactly 45 degrees of plumb cut and a common rafter of run times the square root of 2, and the seat cut always sums with the plumb cut to 90 degrees. The worked example above was confirmed line by line, including the 0.0625 foot ridge deduction and the 1.118 foot sloped overhang.
Related Calculators and Reference
Covering the roof these rafters carry is the Roof Squares Calculator, which uses the same pitch multiplier. Stair stringers are the same triangle solved for a different purpose, in the Stair Stringer Calculator, and the raw geometry is the Triangle Solver.