Hip Rafter Calculator

Use this hip rafter calculator to find the length of a hip rafter on a regular, equal-pitch hip roof. Enter the common rafter run and the roof pitch, add an eave overhang if the rafters extend past the wall, and the calculator returns the total hip rafter length along with the hip line length, hip run, rise and common rafter length.

It also gives the roof pitch angle and hip plumb-cut angle, and an advanced section adds the seat cut, cheek (side-cut) and backing angles, the jack rafter length increase per spacing and a jack rafter length table. You can work in imperial feet and inches or in metric. The formulas, a worked example, a hip length factor table and an explanation of each angle follow below.

What Is a Hip Rafter?

A hip rafter is the sloping framing member that runs from an outside corner of the building up to the ridge, forming the external angle where two roof planes meet. On a regular hip roof, both planes have the same pitch, so the hip sits at 45° to the walls in plan view.

Because the hip travels diagonally across the plan, its horizontal run is longer than the common rafter run, yet it climbs the same total rise. That is why a hip rafter is longer and less steep than the common rafters on the same roof. Its length depends on two things: the hip's horizontal run and the vertical rise set by the roof pitch.

How to Use the Hip Rafter Calculator

1. Choose your units. Imperial takes feet and inches; metric takes metres for the run and overhang and millimetres for the advanced inputs.
2. Enter the common rafter run. This is the level distance from the wall plate to the ridge, measured square to the wall.
3. Enter the roof pitch as rise per 12 units of run, or pick a preset from 2:12 to 12:12. A 6:12 pitch rises 6 inches for every 12 inches of run.
4. Enter the eave overhang if needed. This is the horizontal overhang measured square to the wall, the same way as the common run, not the length measured along the hip. The calculator converts it along the hip diagonal for you. Enter 0 for no overhang.
5. Select Calculate to see the hip rafter length and supporting measurements.
6. Open Advanced Framing Calculations for the seat, cheek and backing angles. Enter a jack rafter spacing to get the jack length increase and jack table, then select Calculate again.

Hip Rafter Formulas

Every result comes from the common rafter run and pitch. In these formulas, Pitch is the rise per 12 units of run.

Common Rafter Rise and Length

Rise = Run × (Pitch ÷ 12)

Common Rafter Length = √(Run² + Rise²)

The rise is shared by the common rafters and the hip, since both reach the same ridge height.

Hip Horizontal Run

Hip Run = Common Run × √2

On a regular hip, the hip is the diagonal of a square whose sides equal the common run, so its plan length is the run multiplied by √2 (about 1.4142). A 12-foot common run gives a hip run of about 16.97 feet. This is also where the framing-square figure of 16.97 comes from: a hip travels 16.97 inches of run for every 12 inches of common run.

Hip Line Length

Hip Line Length = √(Hip Run² + Rise²)

Substituting the hip run and rise gives a single expression:

Hip Line Length = Run × √[2 + (Pitch ÷ 12)²]

This is the theoretical line length from the outside corner of the wall plate to the ridge, before any overhang or ridge deduction.

Total Hip Length With Overhang

Total Hip Length = (Run + Eave Overhang) × √[2 + (Pitch ÷ 12)²]

Because the eave overhang is measured square to the wall, adding it to the common run and applying the same hip factor gives the hip's full length, including the tail. This total is the main Hip Rafter Length result.

Hip Rafter Calculation Example

Take a regular hip roof with a 12 ft common rafter run, a 6:12 pitch and a 1 ft eave overhang.

1. Rise = 12 × (6 ÷ 12) = 6 ft
2. Hip run = 12 × √2 ≈ 16.97 ft (16 ft 11 5/8 in)
3. Hip line length = √(16.97² + 6²) = 12 × √(2 + 0.25) = 12 × 1.5 = 18 ft
4. Total hip length = (12 + 1) × 1.5 = 19.5 ft (19 ft 6 in)
5. Common rafter length = √(12² + 6²) ≈ 13.42 ft (13 ft 5 in)

The calculator reports a hip rafter length of 19 ft 6 in including the overhang, with a hip line length of 18 ft 0 in. Imperial results are rounded to the nearest 1/16 inch.

Hip Rafter Length Factors by Roof Pitch

The factor √[2 + (Pitch ÷ 12)²] is the hip length per unit of common run. Multiply it by the common run to get the hip line length, or by the run plus the eave overhang for the total length. The common rafter factor is shown for comparison.

Pitch	Common rafter factor	Hip rafter factor	Roof angle	Hip slope angle
3:12	1.031	1.436	14.04°	10.02°
4:12	1.054	1.453	18.43°	13.26°
5:12	1.083	1.474	22.62°	16.42°
6:12	1.118	1.500	26.57°	19.47°
7:12	1.158	1.530	30.26°	22.42°
8:12	1.202	1.563	33.69°	25.24°
9:12	1.250	1.601	36.87°	27.94°
10:12	1.302	1.641	39.81°	30.51°
12:12	1.414	1.732	45.00°	35.26°

For example, a 10 ft common run at 8:12 gives a hip line length of 10 × 1.563 ≈ 15.63 ft.

Hip Rafter Angles

The roof pitch angle and hip plumb-cut angle appear in the main results. The seat cut, cheek and backing angles are in Advanced Framing Calculations. All values are displayed to two decimal places; the figures quoted below are for a 6:12 pitch.

Roof Pitch Angle

Roof Angle = arctan(Pitch ÷ 12)

This is the slope of the common rafters and the roof planes. A 6:12 pitch is 26.57°.

Hip Plumb-Cut Angle

Hip Plumb-Cut Angle = arctan[Pitch ÷ (12 × √2)]

This equals the hip's own slope angle, which is flatter than the roof pitch because the hip covers more run for the same rise. It is measured from a line square to the rafter edge, and it matches marking the plumb cut with a framing square set to the pitch on the tongue and 16.97 on the blade. At 6:12 it is 19.47°.

Seat Cut Angle

Seat Cut Angle = 90° − Hip Plumb-Cut Angle

The seat cut is the level cut where the hip bears on the wall plate, square to the plumb cut. At 6:12 it is 70.53°, using the same square-to-edge reference.

Cheek / Side-Cut Angle

Cheek Angle = arctan[cos(Hip Plumb-Cut Angle)]

The cheek cut is the angled cut across the top edge of the hip where it meets the ridge or the common rafters. On a flat plane it would be exactly 45°; the slope of the hip reduces it slightly. At 6:12 it is 43.31°, measured from square across the top edge.

Backing Angle

Backing Angle = arctan[sin(Hip Plumb-Cut Angle)]

The backing angle is the bevel along the top edge of the hip that lets its two top faces line up with the adjoining roof planes, measured from level in a section square to the hip. At 6:12 it is 18.43°; at 12:12 it is 30.00°. Some framers drop the hip instead of backing it, in which case this angle is not cut.

These are geometric values. Check them against your framing method, saw setup and plans before cutting.

Jack Rafter Calculations

Jack rafters run from the wall plate up to the hip, parallel to the common rafters, getting longer as they move away from the corner. Enter a jack rafter spacing in Advanced Framing Calculations, then select Calculate again, to see these results.

Jack Length Increase per Spacing

Jack Length Increase = Spacing × √[1 + (Pitch ÷ 12)²]

Each jack's run grows by one spacing interval, so its length grows by that spacing multiplied by the common rafter factor. At 6:12 with 16-inch spacing: 16 × 1.118 ≈ 17.89 inches, displayed as 1 ft 5 7/8 in. This is often called the common difference.

Jack Rafter Length Table

The table lists each jack with its distance from the corner and its approximate length. The distance is measured along the wall plate from the outside corner where the hip starts. On a regular 45° hip, a jack's run is equal to that distance, so its length is the distance multiplied by the common rafter factor. The table continues in spacing steps until the next position would reach the common run.

With a 12 ft run, 6:12 pitch and 16-inch spacing, the table lists eight jacks, from 1 ft 5 7/8 in at 16 inches from the corner up to 11 ft 11 1/8 in at 10 ft 8 in. These are theoretical centreline lengths to the hip centreline. They do not include a rafter tail, and they are not shortened for half the hip's thickness, which must be taken off at the 45° cut.

Ridge Board Thickness

The Ridge Board Thickness field is for reference only. When a value above zero is entered, the calculator shows a note but does not change any length. The hip lengths remain the theoretical line lengths to the ridge point, because the amount to deduct depends on how the hip meets the ridge and common rafters and on which point your layout measures from. Apply any shortening according to your framing method.

Imperial and Metric Inputs

Input or result	Imperial	Metric
Common rafter run	Feet and inches	Metres
Eave overhang	Feet and inches	Metres
Roof pitch	Rise per 12	Rise per 12
Ridge thickness and jack spacing	Inches	Millimetres
Length results	Feet and inches to the nearest 1/16 in	Millimetres below 1 m, metres above
Angles	Degrees	Degrees

Pitch is entered as rise per 12 in both unit systems, because the ratio has no units. Switching units clears the current result so values are not mixed.

What Is a Regular Equal-Pitch Hip Roof?

In a regular hip roof, every roof plane that meets at a hip has the same pitch, so the hip bisects the corner at 45° in plan. All of the calculator's formulas, including the √2 relationship and the 45° hip plan angle shown in the results, depend on that condition.

Roofs with unequal pitches on adjoining sides, corners that are not square, or other irregular layouts have a different hip plan angle and need a different calculation.

Common Hip Rafter Calculation Mistakes

• Using the common run as the hip run. The hip covers the diagonal, so its run is the common run × √2.
• Confusing run with rafter length. Run is level. The rafter slopes, so its line length is always longer.
• Entering the overhang measured along the hip. The calculator expects the horizontal eave overhang square to the wall. Entering the hip's own overhang would overstate the total length.
• Using the common rafter angle for hip cuts. The hip is flatter than the roof pitch, so its plumb and seat cuts use the hip slope angle.
• Forgetting deductions. Line lengths do not allow for the ridge or for half the hip thickness on jack rafters.
• Applying regular-hip geometry to an irregular roof. Unequal pitches change the hip plan angle and every result that depends on it.

Hip Rafter Calculator FAQs

Length and Run Questions

How do you calculate hip rafter length?

For a regular hip roof, multiply the common rafter run by √[2 + (Pitch ÷ 12)²]. To include the tail, add the horizontal eave overhang to the run before multiplying.

What is the hip run for a 12-foot common run?

12 × √2 ≈ 16.97 feet, or 16 ft 11 5/8 in to the nearest 1/16 inch.

How long is a hip rafter on a 6:12 roof?

At 6:12 the hip factor is exactly 1.5, so the hip line length is 1.5 times the common run. A 10 ft run gives 15 ft; a 12 ft run gives 18 ft. You still need the run to get an actual length.

Why is the hip rafter longer but flatter than the common rafter?

The hip covers about 1.414 times as much horizontal run as a common rafter while rising the same height. The extra run makes it longer and lowers its slope angle, which is why a 6:12 roof has a hip slope of about 19.47° instead of 26.57°.

Using the Calculator

How should I enter the overhang?

Enter the eave overhang as a horizontal distance measured square to the wall, the same way you measured the common run. The calculator converts it along the hip diagonal and includes it in the Hip Rafter Length result.

Does the calculator deduct for the ridge board?

No. The ridge thickness field is for reference only. All lengths are theoretical line lengths, and any shortening depends on your framing method.

Can I use metric measurements?

Yes. Select Metric to enter the run and overhang in metres and the ridge thickness and jack spacing in millimetres. The pitch stays as rise per 12.

Can I use this calculator for an irregular hip roof?

No. It assumes equal pitches and a 45° hip plan angle. Unequal-pitch or irregular hips need different geometry.

Does the calculator determine lumber size?

No. It calculates geometry only. It does not size rafters, check spans or loads, or confirm structural adequacy.

Before Cutting Hip Rafters

This hip rafter calculator is intended for regular, equal-pitch hip-roof geometry. It does not perform structural engineering, lumber sizing, load calculations, or irregular or unequal-pitch roof calculations. Treat the results as geometric measurements, and verify lengths, deductions and cuts against your framing plans, construction method and the building requirements that apply to your project.