Hip Roof Calculator

This hip roof calculator gives ridge length, common and hip rafter lengths, the jack rafter common difference, the hip backing bevel angle and total sloped roof area.

By CalcBuilt Editorial TeamUpdated September 9, 2026Formulas checked against manufacturer specs, see how we calculate.

Quick answer: On an equal-pitch hip roof the ridge runs the building length minus the building width. A 40 x 28 ft hip at 6/12 with 1 ft overhangs has a 12 ft ridge, 16.7 ft common rafters and 22.41 ft hip rafters.

Your measurements

Gable end: pitch is the rise over a 12 in run; the factor from that pitch turns footprint into roof area.

Building lengthftThe longer side, outside of plate to outside of plate. On an equal-pitch hip the ridge is this dimension minus the width, so the two have to be measured on the same plates.Building widthftThe shorter side. Half of it is the common rafter run, and all four slopes are set by it once the pitch is fixed.Roof pitchAll four planes are the same pitch here, which is what makes the hips run at 45 degrees in plan. An unequal-pitch hip needs a different layout and the hip no longer bisects the corner.OverhangftHorizontal projection of the eave past the plate, measured level, not along the rafter. It lengthens every rafter but does not change the ridge.Ridge board thicknessin1.5 in for a 2x ridge, 1.75 in for LVL. Half comes off the common run, and the hip loses half the 45 degree thickness, which is 1.414 times as much in plan.Rafter spacingSets the common difference between jack rafters. The difference is the spacing times the pitch factor, which is why a framing square lists it for 16 and 24 in centers.

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Results

Ridge length: 12 ft; Length minus width on an equal-pitch hip, because each hip runs in at 45 degrees and lands 14 ft from the end
Common rafter: 16.7 ft; Run of 13.94 ft after half the ridge, x 1.118, plus 1.12 ft of tail. At 6/12 that is 13.42 in of rafter per 12 in of run, and the ridge sits 7 ft above the plate
Hip rafter: 22.41 ft; The hip covers 16.97 in of plan run for every 12 in the common covers, so it grows 18 in per 12 in of common run. Back the top edge 18.4 degrees each side, or drop the hip by the same amount
Jack rafter common difference: 17.89 in; Spacing x 1.118 at 16 in centers. The longest jack is 15.21 ft and each one after it drops by that difference; 10 jacks per side of each hip, 80 total
Total roof area: 1,409 sq ft; 906 sq ft on the two long slopes and 503 sq ft on the two hip ends, measured over 42 ft x 30 ft with the overhangs
Planning estimate: Verify on site; Layout geometry only. Rafter and hip sizes come from IRC Table R802.4.1 and the AWC span tables by species, grade, spacing and load, and a licensed pro and the local inspector govern the framing

Hip Roof formula

Ridge length = Length - Width   (equal pitch, hips at 45 degrees in plan)
Common rafter = (Width / 2 - ridge / 24) x sqrt(1 + (rise / 12)²) + Overhang x the same factor
Hip rafter = Width / 2 x sqrt(2 + (rise / 12)²), less the ridge shortening, plus Overhang x the same factor
Jack difference = Spacing x sqrt(1 + (rise / 12)²);  Backing bevel = atan((rise / 12) / sqrt(2 + (rise / 12)²))

Worked example

A 44 x 26 ft house at 8/12 with 1.5 ft overhangs, a 1.5 in ridge and jacks at 24 in centers. The ridge is 44 - 26 = 18 ft. The common run is 13 - 0.0625 = 12.94 ft, and the 8/12 factor is 1.2019, so the common rafter is 15.55 ft to the plate plus 1.80 ft of tail, or 17.35 ft.

The hip factor is sqrt(2 + 0.4444) = 1.5634, so the hip is 13 x 1.5634 = 20.32 ft, less 0.10 ft of ridge shortening, plus 2.35 ft of tail, for 22.57 ft. The backing bevel is atan(0.6667 / 1.5634) = 23.1 degrees. Jacks step by 24 x 1.2019 = 28.84 in, six per side of each hip, 48 in all. The roof covers 47 x 29 x 1.2019 = 1,638 sq ft, of which 505 sq ft is the two hip ends.

Quick reference

Per foot of common run, plus the backing bevel and jack difference at 16 in centers
Pitch	Common per ft of run	Hip per ft of run	Backing bevel	Jack difference
3/12	12.37 in	17.23 in	9.9 deg	16.49 in
4/12	12.65 in	17.44 in	12.9 deg	16.87 in
5/12	12.99 in	17.69 in	15.8 deg	17.32 in
6/12	13.42 in	18.00 in	18.4 deg	17.89 in
8/12	14.42 in	18.76 in	23.1 deg	19.23 in
10/12	15.62 in	19.70 in	26.9 deg	20.83 in
12/12	16.97 in	20.78 in	30.0 deg	22.63 in

Why the hip runs 17 inches to the common rafter's 12

On a hip roof where all four planes are the same pitch, each hip bisects its corner and runs at 45 degrees in plan. That means while a common rafter travels 12 in of horizontal run, the hip beside it travels 12 x 1.414, or 16.97 in, which every framing square rounds to 17. The rise over that distance is the same as the common rafter's rise, so the hip is a flatter-looking member that is nonetheless longer. Its length per foot of common run is sqrt(2 + (rise/12)²) feet: at 6/12 that is exactly 1.5, or 18.00 in per foot, against the common rafter's 13.42 in.

The same 45 degree geometry sets the ridge. Each hip starts at a corner and reaches the ridge when it has come in half the building width, so the ridge is short at both ends by half the width, twice: length minus width. A 40 x 28 ft house has a 12 ft ridge. A square building has no ridge at all, just four hips meeting at a point, which is a pyramid hip. Overhang lengthens every rafter but changes nothing about the ridge, because the ridge point is fixed by the wall plates.

Laying out hips and jacks on the deck

Cut one common rafter, test it at both ends of the building, then gang cut the rest. The hip gets a double cheek cut at the ridge so it fits into the corner between the last common rafters, and the shortening is half the ridge thickness measured on the 45, which is 1.414 times the straight deduction. Then either back the hip, beveling both top edges so the two roof planes land flat, or drop it: lower the seat cut so the top corners fall below the plane instead. Backing is cleaner where the sheathing has to bear evenly, and dropping is faster.

Jacks are the easy part once the common difference is known. Each jack sits one spacing closer to the corner than the last, so each is shorter by the spacing times the pitch factor: 17-7/8 in at 16 in centers on a 6/12 roof. The longest jack is one difference shorter than the common. Every jack takes a 45 degree cheek cut where it meets the hip, and the cheeks alternate hands, so cut them in mirrored pairs and stack them by length. Number the stacks before you carry them up, because a jack in the wrong bay is a wasted board.

What this calculator leaves out

Member sizing, which comes from IRC Table R802.4.1 and the AWC span tables by species, grade, spacing and snow load. Unequal-pitch hips, where the hip no longer bisects the corner and the whole layout changes. Irregular and bastard hips, dormers, valleys where a wing meets the main roof, and the hip set on a truss roof, which the fabricator designs. Sheathing, subfascia, ceiling joists, collar ties, hurricane ties, ridge vent, and the extra waste a hip roof carries: cut shingles at four hip lines typically push waste to 15 to 20 percent against 10 on a plain gable.

Code limits that apply

IRC R802.3checked
Below 3:12 the ridge, hips and valleys are designed as beams, not nailed up as boards
If you miss it: A hip board on a 2:12 roof sags at the corner and the ceiling below cracks along the hip line
IRC R802.3 depth
Ridge and hip at least as deep as the plumb cut of the rafters bearing on them
If you miss it: A 2x8 hip under 2x8 jacks leaves the cheek cuts hanging past the board and the inspector sees it from the hatch
IRC Table R802.4.1
Rafter span by species, grade, spacing and load, taken on the horizontal run
If you miss it: Jacks sized from their cut length come out a size light and the long slopes dish between hip and ridge
IRC R802.5.2
Rafter ties at the plate, or a ridge and hips designed as beams on posts
If you miss it: A vaulted hip with no ties spreads the walls and the hip corners drop; the fix is posts under each hip
IRC R802.7.1
End notch at most a quarter of the member depth, 1-13/16 in on a 2x8
If you miss it: A deep compound seat cut on a hip splits along the grain and the whole member is re-cut
IRC R802.11
Rafter to plate connection sized for uplift, with ties past toenail capacity
If you miss it: Hip corners lift first in high wind, and toenails alone at the corner jacks get written up at framing

Provision	Limit	If you miss it
IRC R802.3checked	Below 3:12 the ridge, hips and valleys are designed as beams, not nailed up as boards	A hip board on a 2:12 roof sags at the corner and the ceiling below cracks along the hip line
IRC R802.3 depth	Ridge and hip at least as deep as the plumb cut of the rafters bearing on them	A 2x8 hip under 2x8 jacks leaves the cheek cuts hanging past the board and the inspector sees it from the hatch
IRC Table R802.4.1	Rafter span by species, grade, spacing and load, taken on the horizontal run	Jacks sized from their cut length come out a size light and the long slopes dish between hip and ridge
IRC R802.5.2	Rafter ties at the plate, or a ridge and hips designed as beams on posts	A vaulted hip with no ties spreads the walls and the hip corners drop; the fix is posts under each hip
IRC R802.7.1	End notch at most a quarter of the member depth, 1-13/16 in on a 2x8	A deep compound seat cut on a hip splits along the grain and the whole member is re-cut
IRC R802.11	Rafter to plate connection sized for uplift, with ties past toenail capacity	Hip corners lift first in high wind, and toenails alone at the corner jacks get written up at framing

Rows marked checked produce a warning in the results when an entry crosses the limit. The others are on the plans or on site and this calculator does not test them. Local amendments can be stricter; the adopted edition and the inspector govern.

Mistakes that cost money

Laying a hip out on the common pitch: it covers 17 in of plan run per foot, so the cut lands short of the ridge.
Square plumb cuts where jacks meet the hip: jacks take a 45 degree cheek cut, and the hip a double cheek at the ridge.
Leaving the hip unbacked: bevel both top edges, or drop the hip by half its 45 degree thickness times the pitch, or the sheathing rocks.
Ordering hip stock in common rafter lengths: a hip runs about a third longer, and over 20 ft is a special order.
A 2x8 hip under 2x8 jacks: R802.3 wants the hip as deep as the jack plumb cut, so use a 2x10.
Notching a hip seat as deep as a common seat: R802.7.1 caps an end notch at a quarter of the hip depth.

Key facts

On an equal-pitch hip roof the ridge equals the building length minus the building width, because each hip runs in at 45 degrees from a corner.
A hip rafter covers 16.97 in of horizontal run, rounded to 17 in on a framing square, for every 12 in a common rafter covers.
At a 6/12 pitch a common rafter is 13.42 in per foot of run and the hip rafter is exactly 18.00 in per foot of that same common run.
The hip backing bevel is atan of (rise/12) divided by sqrt(2 + (rise/12)²), which is 18.4 degrees at 6/12 and exactly 30 degrees at 12/12.
The common difference between jack rafters is the spacing times the pitch factor: 17-7/8 in at 16 in centers on a 6/12 roof, and 26-13/16 in at 24 in centers.

Frequently asked questions

How do you calculate the ridge length on a hip roof?

Subtract the building width from the building length. On an equal-pitch hip each hip runs in at 45 degrees and reaches the ridge after half the width, once at each end, so a 40 x 28 ft house has a 12 ft ridge. A square building has no ridge, just a peak.

Why is the hip rafter run 17 inches instead of 12?

Because the hip runs diagonally at 45 degrees in plan. For every 12 in a common rafter travels toward the ridge, the hip travels 12 x 1.414, or 16.97 in, which framing squares round to 17. That is why rafter tables carry a separate hip and valley line.

How do you find jack rafter lengths?

Start from the common rafter length and subtract one common difference for each step toward the corner. The difference is the rafter spacing times the pitch factor: 16 x 1.118 = 17-7/8 in at 16 in centers on a 6/12 roof. Every jack also needs a 45 degree cheek cut at the hip.

What is the hip rafter backing angle?

It is the bevel on the top edges of the hip so both roof planes lie flat. It equals the arctangent of (rise/12) divided by sqrt(2 + (rise/12)²): 12.9 degrees at 4/12, 18.4 at 6/12 and exactly 30 at 12/12. Dropping the hip instead achieves the same thing without ripping a bevel.

Sources and references

Chapter 8 Roof-Ceiling Construction, Section R802.3 ridge, hip and valley members, 2021 IRC (ICC)
2024 Span Tables for Joists and Rafters (American Wood Council)
H2.5A hurricane tie for the rafter to top plate connection (Simpson Strong-Tie)

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