Hip Roof Calculator

This hip roof calculator lays out the hip rafters and jack rafters for an equal-pitch hip roof on a rectangular building. Enter the pitch, the building width and length and your rafter spacing, and it returns the hip rafter length, the hip plumb, seat and cheek cut angles, the jack rafter common difference, every jack rafter length from shortest to longest, the ridge length, a dimensioned plan diagram and a printable cut list. It is scoped to equal-pitch hips on a rectangle: unequal pitches, L-shaped and T-shaped roofs, valleys and turrets are out of scope. Every figure comes from the numbers you enter, so each one can be checked by hand.

Hip rafter length (each of 4)

17.906 ft

17 ft 10.88 in · body 17.906 ft after 1.125 in shortening measured back along the rafter edge

Hip plumb cut: 19.47°
Hip cheek cut: 45°
Hip run (plan): 16.971 ft
Total rise: 6.000 ft
Ridge length (theoretical): 16.00 ft
Jack common difference: 17.889 in
Jack rafters: 64
Jack plumb cut: 26.57°

Before you cut: the ridge length above is the theoretical length (building length minus width). The ridge board itself is normally cut longer than that at each end — ridge growth — so the hips have something to bear on where they land. Set that allowance from your own framing detail.

Reference figure: the common rafter on this roof measures 13.416 ft over a 12.00 ft run — shown only because the jack common difference is derived from it. For the full common rafter layout, including the birdsmouth, heel height and rafter count, use the rafter calculator.

Plan diagram

Cut list — hip and jack rafters
Tag	Member	Qty	Cut length	Buy	Notes
H1	Hip rafter	4	17.91 ft214.9 in	18 ft stock	Plumb cut 19.5° · seat cut 70.5° · double cheek cut 45° each side
J1	Jack rafter 1	8	1.39 ft16.7 in	8 ft stock	Run 16" · plumb cut 26.6° · single cheek cut 45°
J2	Jack rafter 2	8	2.88 ft34.6 in	8 ft stock	Run 32" · plumb cut 26.6° · single cheek cut 45°
J3	Jack rafter 3	8	4.37 ft52.5 in	8 ft stock	Run 48" · plumb cut 26.6° · single cheek cut 45°
J4	Jack rafter 4	8	5.86 ft70.4 in	8 ft stock	Run 64" · plumb cut 26.6° · single cheek cut 45°
J5	Jack rafter 5	8	7.35 ft88.3 in	8 ft stock	Run 80" · plumb cut 26.6° · single cheek cut 45°
J6	Jack rafter 6	8	8.85 ft106.1 in	10 ft stock	Run 96" · plumb cut 26.6° · single cheek cut 45°
J7	Jack rafter 7	8	10.34 ft124.0 in	12 ft stock	Run 112" · plumb cut 26.6° · single cheek cut 45°
J8	Jack rafter 8	8	11.83 ft141.9 in	12 ft stock	Run 128" · plumb cut 26.6° · single cheek cut 45°
Total pieces		68	494.63 ft	one board each	Rafters are not spliceable — buy one board per piece, cut to length
Jack rafter quantities are per roof: each length is repeated across all 8 jack sets (4 corners × 2 roof planes).

About this hip roof calculator

Use this calculator when you are framing a hip roof — a garage, an extension, a shed or a whole house — and you need the hip rafter length, the jack rafter schedule and the cut angles before you start cutting. It covers equal-pitch hips on a rectangular plan, which is the common case. Everything is derived from the pitch and the two building dimensions you enter, so each figure stays checkable by hand.

This page is scoped to the hips and the jacks. For a full common rafter layout — birdsmouth, heel height, rafter count along the ridge — use the rafter calculator, which is where that job belongs. If you only know the roof angle in degrees or as a percentage and need it as an X:12 pitch first, convert it with the roof pitch calculator. For other layout jobs, see all construction calculators.

How to use the hip roof calculator

1
Enter the roof pitch
Give the pitch as the rise per 12 inches of run — a 6:12 roof rises 6 inches for every 12 inches of horizontal run. All four planes of an equal-pitch hip roof use the same pitch. If you only know the roof angle in degrees or as a percentage, convert it first with the roof pitch calculator.
2
Enter the building width and length
Measure the building outside the wall plates. Width is the shorter side — the hips run in at 45 degrees from each corner, so the ridge ends up shorter than the building by exactly the building width. Length must be at least the width; when they are equal there is no ridge at all and the roof becomes a four-sided pyramid.
3
Set the ridge board and hip stock thickness
The hip is shortened at the ridge by half the 45-degree thickness of the ridge board, and each jack rafter is shortened at the hip by half the 45-degree thickness of the hip stock. Enter the real dressed thickness of your lumber — a nominal 2x ridge is 1.5 inches, not 2.
4
Set the overhang and the rafter spacing
Overhang is the horizontal eave projection measured square to the wall, not the sloped length. At the corner the hip travels diagonally, so its overhang is longer than a jack rafter overhang for the same eave. Spacing is on-center along the wall plate and sets the jack rafter common difference.
5
Read the cut list and check the hip length
The cut list gives the hip rafters first, then every jack rafter from shortest to longest with its quantity, cut length and cut angles. Check the hip length before you buy: a hip runs diagonally and is far longer than a common rafter on the same roof, so it can exceed the longest stock lumber you can buy.

Frequently asked questions

How do you calculate hip rafter length?

A hip rafter runs diagonally across the plan, so its horizontal run is the diagonal of a square whose side is the common rafter run — that is the common run multiplied by the square root of 2. The hip length is then the hypotenuse of that diagonal run and the total rise. For a 24 ft wide building at 6:12 the common run is 12 ft, the total rise is 6 ft, the hip run is 16.97 ft and the hip rafter measures exactly 18.00 ft to the ridge before shortening.

Why is 17 the magic number for hip rafters?

For every 12 inches of common rafter run, a hip or valley rafter travels 12 times the square root of 2, which is 16.97 inches. Carpenters round that to 17 and use the 17 inch mark on the framing square blade instead of the 12 inch mark. This calculator uses the exact value of 16.97 rather than 17, which is about 0.17 percent shorter — roughly one third of an inch over 12 ft of common run.

Can I use a common rafter calculator for a hip rafter?

No. A common rafter runs square to the wall and a hip runs diagonally, so for the same pitch and the same building the hip is much longer. On a 24 ft wide building at 6:12 the common rafter is 13.42 ft and the hip is 18.00 ft — using the common rafter figure would leave every hip 4.58 ft short, which is 25 percent of the piece. Use the rafter calculator for common rafters and this page for hips and jacks.

What is the common difference for jack rafters?

Jack rafters sit on the wall plate at your on-center spacing and each one is longer than the last by a fixed amount called the common difference. It equals the rafter unit length for your pitch multiplied by the spacing divided by 12. At 6:12 the unit length is 13.42 inches, so at 16 inches on-center the common difference is 17.89 inches. Cut the shortest jack, then add the common difference for each one after it.

How long is the ridge on a hip roof?

On an equal-pitch hip roof over a rectangle, the hips run in from each corner at 45 degrees by exactly the common run, so the ridge is shorter than the building by the full building width. A 40 ft long by 24 ft wide building has a 16 ft ridge. When the length equals the width the ridge length is zero and all four hips meet at a single point, giving a pyramid hip roof.

How many jack rafters does a hip roof need?

Each corner has jack rafters on both adjoining roof planes, so an equal-pitch hip roof has eight sets of jacks. Each set holds one jack per spacing interval across the common run, minus the last position, which is filled by a full-length rafter at the end of the ridge. A 24 ft wide building at 16 inches on-center gives eight jacks per set and 64 jacks in total.

What cuts does a hip rafter need?

A hip needs a plumb cut at the ridge, a seat cut where it crosses the wall plate corner, and a double cheek cut at the top so it fits between the two common rafters at the end of the ridge. On an equal-pitch hip the cheek cuts are 45 degrees on each side. The hip plumb cut is shallower than the common rafter plumb cut because the hip covers more horizontal distance for the same rise.

Is the ridge board cut to the ridge length shown?

No — the ridge length shown is the theoretical length, the building length minus the building width. The ridge board itself is normally cut a little longer at each end, which framers call ridge growth, so that the hips have something to bear on where they land against it. How much to add depends on your ridge and hip stock and how you detail the joint, so set that allowance yourself rather than cutting the ridge to the theoretical figure.

What happens on a square building with no ridge?

When the length equals the width the ridge length is zero and all four hips meet at a single peak, which is a pyramid hip roof. There is no ridge board to shorten against, so this calculator deducts no ridge shortening in that case and gives the full centerline length to the peak. How the four hips are joined at the peak varies — usually two run through and two butt into them — so make your own deduction for that joint before cutting.

Does this calculator handle unequal pitches or L-shaped roofs?

No. It covers equal-pitch hip roofs on a rectangular plan only. Unequal-pitch hips, bastard hips, L-shaped and T-shaped roofs with valleys, dormers and turrets all change the hip run ratio and the cheek cut angles, so they need a different layout. Do not apply these numbers to those roofs.

Does the calculator include hip backing or dropping?

No. The hip lengths here are centerline lengths. In practice the top edge of a hip is either backed — bevelled on both sides so the roof planes break cleanly over it — or dropped slightly so the sheathing lies flat. Both are small adjustments made at the saw and neither changes the hip length, but you do need to allow for one of them.

Hip roof terms glossary

Hip rafter: The rafter that runs diagonally from an outside corner of the building up to the end of the ridge, forming the external angle where two roof planes meet.
Jack rafter: A shortened rafter that runs from the wall plate to a hip rafter instead of to the ridge. Jacks get progressively longer as they move away from the corner.
Common difference: The fixed increase in length between one jack rafter and the next, set by the pitch and the on-center spacing.
Common run: The horizontal distance from the outside of the wall plate to the centerline of the ridge — half the building width on an equal-pitch roof.
Hip run: The horizontal distance a hip rafter covers in plan. Because the hip runs diagonally it equals the common run times the square root of 2, or 16.97 inches for every 12 inches of common run.
Cheek cut: An angled side cut that lets a rafter meet another member face to face. Hips take a double cheek cut at the ridge; jacks take a single cheek cut where they land on the hip.
Plumb cut: The vertical cut at the top of a rafter. Its angle equals the slope angle of that rafter, which is shallower for a hip than for a common rafter on the same roof.
Seat cut: The horizontal cut that lets a rafter bear on the wall plate. It is the complement of the plumb cut angle.
Pyramid hip: A hip roof on a square plan. The ridge length is zero and all four hip rafters meet at a single peak.
Hip backing: Bevelling the top edge of a hip rafter on both sides so the two roof planes meet cleanly over it. The alternative is dropping the hip slightly at the seat cut.