A gable roof is one triangle repeated. A hip roof is that triangle plus a diagonal, and the diagonal is where the math changes. The hip rafter runs from the corner of the building to the end of the ridge, cutting across the corner at 45 degrees in plan, so its horizontal run is longer than the common rafter’s run by a factor of the square root of two. The length follows from the same Pythagorean idea, with one extra step: the horizontal leg is the diagonal of the run, not the run itself. This guide works through the hip rafter, the valley rafter, and the jack rafters with real numbers, so you can cut a hip roof from the same span and pitch you would use for a gable. Start with the common rafter length from the rafter calculator, because every hip length is built on it.
The Hip Rafter Formula
The hip rafter length is the square root of two times the run squared plus the rise squared. The two times the run squared is the diagonal: the hip rafter covers the run in both directions at once, across the corner, so its horizontal distance is the run times the square root of two. The rise is the same as the common rafter’s rise, because the hip meets the same ridge at the same height. Take the 28 ft span at 6/12 pitch from the pillar examples: the run is 14 ft, the rise is 7 ft, two times 196 is 392, plus 49 is 441, and the square root of 441 is exactly 21 ft. The common rafter on that roof is 15 ft 7 13/16 in, so the hip is more than 5 ft longer, and it needs a longer board: a 22 ft board with the tail, where the common rafter takes an 18 ft board.
Two more examples show the range. On a 24 ft span at 8/12 pitch, the run is 12 ft and the rise is 8 ft, so the hip is the square root of 288 plus 64, which is the square root of 352, or 18 ft 9 1/8 in, against a common rafter of 14 ft 5 1/16 in. On a 20 ft span at 5/12 pitch, the run is 10 ft and the rise is 4.17 ft, so the hip is the square root of 200 plus 17.36, which is 14 ft 8 15/16 in, against a common rafter of 10 ft 10 in. The hip is always about 1.30 to 1.36 times the common rafter length, and the ratio depends on the pitch: it is highest on low pitches, where the diagonal run dominates, and lowest on steep pitches, where the rise dominates. If the hip length comes out shorter than the common length, the arithmetic is wrong: check the run first, because the diagonal step is the one most often skipped.
| Span / pitch | Run | Rise | Common rafter | Hip rafter |
|---|---|---|---|---|
| 28 ft / 6/12 | 14 ft | 7 ft | 15 ft 7 13/16 in | 21 ft |
| 24 ft / 8/12 | 12 ft | 8 ft | 14 ft 5 1/16 in | 18 ft 9 1/8 in |
| 20 ft / 5/12 | 10 ft | 4.17 ft | 10 ft 10 in | 14 ft 8 15/16 in |
Valley Rafters Use the Same Length
A valley rafter is the hip rafter’s mirror image. Where a hip rafter runs from an outside corner up to the ridge, a valley rafter runs from an inside corner down to the wall, where two roof slopes meet in a valley. The plan angle is the same 45 degrees, the run is the same diagonal, and the rise is the same, so the length formula is identical: the square root of two times the run squared plus the rise squared. On the 28 ft span at 6/12 pitch, the valley rafter is also 21 ft. The difference is not the lumber but the water: a valley collects the water from both slopes, so it needs valley flashing under the shingles and a straight, true line, because a wavy valley shows from the ground and leaks at the laps. Cut the valley rafter to the same length as the hip, but spend the extra time on the flashing and the shingle layout in the valley itself.
Jack Rafters Step Down From the Hip
The jack rafters are the short rafters that frame into the hip rafter instead of running to the ridge. Each one is a common rafter shortened in proportion to its distance from the corner. The rule is simple: a jack rafter at a distance d from the corner along the plate has a run of d and a rise of d times the pitch over 12, so its length is the square root of d squared plus the rise squared. On the 28 ft span at 6/12 pitch, the jacks step down in 3.5 ft increments if they are spaced 16 in apart in plan, but the easy way to see the pattern is at whole-foot distances: a jack 3.5 ft from the corner is 3 ft 10 15/16 in long, a jack 7 ft from the corner is 7 ft 9 15/16 in, and a jack 10.5 ft from the corner is 11 ft 8 7/8 in. Each jack is the common rafter scaled by the fraction of the run it covers: the 7 ft jack is exactly half the common rafter, because 7 ft is half the 14 ft run.
The jack rafters meet the hip rafter with a compound cut, which is two angles at once: the plumb angle of the pitch and the side angle of the 45-degree plan. That cut is the hardest on a hip roof, and it is where a pattern jack earns its keep. Cut one jack, test it against the hip, and use it to mark the rest, because the jacks on one hip are all the same shape at different lengths. The common rafter on the same roof is the reference for the jack angles: the plumb cut on the jack is the same angle as the plumb cut on the common rafter, and only the length and the side cut change. The common rafter vs jack rafter post explains the two members side by side, including which one carries the load and which one is nailed to the hip.
Ordering Lumber for a Hip Roof
A hip roof needs more lumber and more kinds of lumber than a gable roof on the same building. Count the pieces before you order: four hip rafters, two sets of jack rafters stepping down each hip, the common rafters on the ridge between the hips, and a ridge board that is shorter than the building, because the hips take up the ends. The hip rafters are the longest boards on the job: 21 ft plus the tail on the 28 ft span roof, so a 22 ft board, and longer on a wider building. The jacks are short boards, and offcuts from the common rafters often cover the shortest jacks, which saves lumber if the cutting order is planned. Work out the common rafter length first with the rafter calculator, then the hip length from the formula above, then the jack lengths from their distances, and order the boards by length, longest first. A hip roof also takes longer to frame than a gable roof, because every hip and jack is a cut that a gable roof does not have, so the labor quote should be higher, and a quote that prices a hip roof like a gable roof has missed the hips.
Related reading: rafter calculator, plus our guides on common rafter vs jack rafter and how to calculate rafter length, and the roofing calculators hub.
Building a Hip Roof?
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Frequently Asked Questions
How do you calculate hip rafter length?
A hip rafter is the hypotenuse of a triangle whose horizontal leg is the diagonal of the run: the square root of two times the run squared plus the rise squared. On a 28 ft span at 6/12 pitch, the run is 14 ft and the rise is 7 ft, so the hip rafter is the square root of 392 plus 49, which is exactly 21 ft from ridge to plate, against 15 ft 7 13/16 in for the common rafter.
How long is a hip rafter compared to a common rafter?
Always longer, because it runs diagonally across the corner. On a 24 ft span at 8/12 pitch, the common rafter is 14 ft 5 1/16 in and the hip rafter is 18 ft 9 1/8 in. On a 20 ft span at 5/12 pitch, the common rafter is 10 ft 10 in and the hip rafter is 14 ft 8 15/16 in. The ratio depends on the pitch: on the roofs worked through here it runs about 1.30 to 1.36 times the common length.
What is the difference between a hip rafter and a valley rafter?
The length formula is the same, but the position is opposite. A hip rafter runs from the outside corner of the building up to the ridge, on the outside of the roof. A valley rafter runs from the inside corner where two roof slopes meet down to the wall, on the inside of the roof. Both are diagonal members with the same diagonal length on the same pitch and run. The valley carries water, so its flashing matters more, but the lumber math is identical.
How do you calculate jack rafter length?
A jack rafter is a common rafter shortened in proportion to its distance from the corner. On a 28 ft span at 6/12 pitch, a jack rafter 7 ft from the corner has a 7 ft run and a 3.5 ft rise, so it is 7 ft 9 15/16 in long. A jack 3.5 ft from the corner is 3 ft 10 15/16 in, and a jack 10.5 ft from the corner is 11 ft 8 7/8 in. Each jack is shorter than the one before it by the same step, so once you know the step, the whole set follows.
Do hip roofs need more lumber than gable roofs?
Yes. A hip roof has four hip rafters, two sets of jack rafters, and a shorter ridge, where a gable roof has only common rafters and a full-length ridge. The hip rafters are longer boards, the jacks are many short boards, and the cutting takes longer. The trade is wind resistance and looks: a hip roof has no gable end for the wind to catch, which is why it is common on homes that face Lake Michigan storms, and many homeowners prefer the way it looks.
Zayn Robert is a content specialist focused on roofing, construction, and home improvement topics. He creates easy-to-understand guides that help homeowners learn about roof measurements, materials, maintenance, and repair decisions. His work combines detailed research with practical insights from roofing professionals at Zuniga Roofing Inc.