Rafter Calculator
A 24 ft span at 6/12, with a 12 in horizontal overhang and a 1.5 in ridge, is a common rafter of 14.4646 ft. The plumb cut is 63.43°, the seat cut is 26.57°, and the rise at the ridge cut is 5.9688 ft.
Last updated . Span starts at 24 ft and the pitch box starts at 6. Overhang starts at 12 in. Ridge thickness starts at 1.5 in. Lengths can be typed in millimeters through yards.
A rafter calculator for one common rafter. The run drops half the ridge thickness, adds the horizontal overhang, then stretches by the full square root of 1 plus the slope squared. Hip and valley rafters are not in this length.
Pitch, degrees, and the area factor: roof pitch calculator. Squares of roof: roofing calculator. Studs in the wall under the plate: stud calculator.
Common rafter
The span is the outside width. Half of the ridge thickness is removed from the horizontal run. The overhang is a horizontal projection, then the slope stretches that whole run into the rafter length. Total rise stops at the ridge cut and does not include the overhang.
Results
How the common rafter length is calculated
Horizontal run = span ÷ 2 − ridge thickness ÷ 2 + overhang. All three are converted to feet first. On the opening numbers, 24 ÷ 2 − 1.5 ÷ 24 + 12 ÷ 12 = 12 − 0.0625 + 1 = 12.9375 ft. The ridge term is a horizontal deduction, the same subtraction Will Holladay describes in “Production Roof Cutting” (JLC, May 1, 1990): take the ridge thickness off the span, then divide by two. That article’s line length stops at the birdsmouth heel and leaves the tail off. This page folds the overhang into the run before the stretch, so the printed length includes the tail.
Length = horizontal run × √(1 + slope²), and the root is not rounded before the multiply. At 6/12 the slope is 0.5 and the root is √1.25. Total rise = (span ÷ 2 − ridge ÷ 2) × slope, so the tail does not add height. Seat cut = atan(slope), the angle between the rafter edge and a level line. Plumb cut = 90° − that angle, the angle between the rafter edge and a vertical line. In rise mode the number you type is that total rise, and the slope is rise ÷ (span ÷ 2 − ridge ÷ 2).
Source: Will Holladay, Production Roof Cutting, Journal of Light Construction, May 1, 1990. The run rule quoted above is from that article. This page does not size the rafter, pick a species, or read a span table. A 1.5 in ridge is the thickness sitting in the box, not a required board.
Lengths for the 24 ft span
| Case | Run | Length | Rise | Seat | Plumb |
|---|---|---|---|---|---|
| 6/12, 12 in overhang, 1.5 in ridge | 12.9375 ft | 14.4646 ft | 5.9688 ft | 26.57° | 63.43° |
| Rise mode, 6 ft at the ridge cut | 12.9375 ft | 14.4797 ft | 6.0000 ft | 26.68° | 63.32° |
| 6/12, no overhang, no ridge | 12.0000 ft | 13.4164 ft | 6.0000 ft | 26.57° | 63.43° |
Worked example
Leave 24 ft, pitch 6, overhang 12 in, and ridge 1.5 in. Rafter length reads 14.4646 ft · 173.57 in. Total rise reads 5.9688 ft · 71.63 in. Seat cut reads 26.57°. Plumb cut reads 63.43°.
Rafter length questions
How long is the common rafter on a 24 ft span at 6/12?
Leave span at 24 ft, slope on Pitch, the pitch box at 6, overhang at 12 in, and ridge thickness at 1.5 in. Rafter length reads 14.4646 ft · 173.57 in. Horizontal run reads 12.9375 ft. Total rise reads 5.9688 ft · 71.63 in. Pitch reads 6.00 / 12. Plumb cut reads 63.43°. Seat cut reads 26.57°.
Why is the length 14.4646 ft and not 14.4641 ft?
Half the span is 12 ft. Half the 1.5 in ridge is 0.75 in, which is 0.0625 ft, so the run to the ridge cut is 11.9375 ft. The 12 in overhang adds 1 ft, and the full horizontal run is 12.9375 ft. The slope is 6 ÷ 12 = 0.5. The stretch is the square root of 1.25, kept in full, and 12.9375 times that root is 14.4646 ft. A root chopped to 1.118 would give 14.4641 ft, and that is not the length line.
What do the plumb cut and the seat cut mean here?
The seat cut is the angle between the rafter edge and a level cut, atan of the slope, 26.57° on this 6/12. The plumb cut is the angle between the rafter edge and a vertical cut, 90° minus that angle, 63.43°. The two unrounded angles add to 90°. The printed 26.57 and 63.43 add to 100.00 only because each line is rounded to two decimals. This is not a speed-square pitch number.
What if I type a 6 ft total rise instead of 6/12?
Set Slope entered as to Total rise at the ridge cut and leave the rise at 6 ft. Span, overhang, and ridge stay at the opening values. Pitch reads 6.03 / 12. Rafter length reads 14.4797 ft · 173.76 in. Horizontal run stays 12.9375 ft. Total rise reads 6.0000 ft · 72.00 in. Plumb cut reads 63.32°. Seat cut reads 26.68°.
What if the overhang and the ridge are both zero?
Set overhang to 0 and ridge thickness to 0. Switch the slope back to Pitch and leave it at 6, with the span at 24 ft. Rafter length reads 13.4164 ft · 161.00 in. Horizontal run reads 12.0000 ft. Total rise reads 6.0000 ft · 72.00 in. Pitch reads 6.00 / 12. Plumb cut reads 63.43°. Seat cut reads 26.57°. That length is 12 times the square root of 1.25.
Does the total rise include the overhang?
No. Total rise uses only the run that reaches the ridge cut, 11.9375 ft on the opening example, times the slope. The overhang is added to the horizontal run before the length is stretched, and it is left out of the rise. Will Holladay’s 1990 line length also stops at the birdsmouth and leaves the tail off. This length line puts the tail on.
What if the ridge is as wide as the span?
Set the span to 2 ft and the ridge thickness to 24 in, and leave the other opening values. Every result line reads —. The note reads: Half the ridge is at least half the span, so the rafter has no horizontal run. A blank span reads: Enter a span greater than zero. A negative overhang reads: Overhang and ridge thickness cannot be negative.