Jack rafter calculator

Jack rafters are the short rafters that run from the wall up to a hip (or from a valley up to the ridge). On an equal-pitch roof each one is longer than the last by the same amount — the common difference, which is the rafter spacing × the slope factor. New to this? Words explained.

The common difference

A hip runs at 45° across the corner, so a jack rafter set one spacing further from the corner also runs one spacing further before it meets the hip. Its level run grows by exactly the spacing, and its length grows by the spacing × the slope factor. That step is the common difference; the framing square prints it on the “difference in length of jacks” lines for 16 and 24 in centers.

slope factor = √(1 + (pitch ÷ 12)²)
common difference = spacing × slope factor
jack run = distance from the corner − ½ × 45° thickness of the hip
jack length = (jack run + overhang) × slope factor   (centre line)

Example: a 24 ft wide hip roof at 6/12 with jacks 16 in on center, a 1½ in hip and a 12 in overhang. The common difference is 16 × 1.118 = 17.89 in. The first jack sits 16 in from the corner; take off half the hip’s 45° thickness (1.06 in) and add the overhang, and it is 26.94 in of run — 30.12 in on the centre line and about 31 in to the long point. Eight jacks fit on each side of each hip before the run reaches the 144 in where the hip meets the ridge, so a full hip roof takes 64.

Cutting jack rafters

1. Cut a pattern. Lay out the birdsmouth and tail exactly as on a common rafter — same seat, same height above plate — so the jacks line up with the commons.
2. Mark the length along the top edge from the tail to the long point of the cheek cut — the calculator’s figure for that jack. The shortening for the hip is already taken off.
3. Cheek cut. Mark the plumb line at the common pitch and cut it with the saw at a 45° bevel. The long point is on the face away from the corner.
4. Work in pairs. At each hip the jacks on the two sides are mirror images, so cut each length in lefts and rights. Step the next pair up by the common difference.

Valley jacks and cripples

Valley jacks run from a valley up to the ridge and grow by the same common difference, starting from the inside corner. They lose half the ridge’s 45° thickness at the top and half the valley’s 45° thickness at the bottom. Cripple jacks touch neither a plate nor a ridge — they run between a hip and a valley (or two valleys) — and take the valley shortening at one end and the hip shortening at the other.

The full-length common rafters on the same roof come from the rafter length calculator.