Jack Rafter Calculator

Follow these steps to find the common difference and the length of each jack rafter on one side of a hip or valley.

1. Enter the common run in feet. This is the horizontal distance from the wall plate to the ridge. On a roof with a centered ridge it equals half the building span.
2. Select the roof pitch from 3/12 to 12/12. The first number is the rise in inches for every 12 inches of run.
3. Select the on-center spacing of 12, 16 or 24 inches. This is the spacing used for the common and jack rafters.
4. Read the results. The common difference, jack count, longest jack and side cut angle update instantly. The note under the result lists each jack length from longest to shortest when the count is six or fewer.

All lengths are theoretical line lengths. Allow for the thickness of the hip or valley rafter and the birdsmouth before you cut real lumber.

A jack rafter is a shortened common rafter. It runs from the wall plate up to a hip rafter, from a valley rafter up to the ridge, or between a hip and a valley. Because it stops short of the ridge or the plate, it is shorter than a full common rafter, and each jack along a hip or valley is a little shorter than its neighbor.

Jack rafters take three common forms. A hip jack runs from the wall plate up to a hip rafter. A valley jack runs from a valley rafter up to the ridge. A cripple jack sits between a hip and a valley and touches neither the plate nor the ridge. This calculator handles the length pattern that all three share.

Knowing the pattern matters because a hip roof can need dozens of jacks. Calculating one common difference lets you cut the whole set from a single pattern rafter instead of measuring each board separately.

Every jack on one side of a hip or valley is spaced the same distance apart along the plate, and the roof slope is constant. Because of that, each jack is shorter than the previous one by the same amount, called the common difference. The common difference is the on-center spacing multiplied by the unit rafter length for the pitch.

1. Find the unit rafter length: sqrt(1 + (pitch / 12)^2). This is the rafter length for each 1 inch of run.
2. Multiply the on-center spacing in inches by the unit length to get the common difference.
3. Multiply the run in inches by the unit length to get the full common rafter length, then subtract one common difference to get the longest jack.
4. Divide the run in inches by the spacing and round down to get the number of jacks per side.
5. Find the side cut as arctan(cos(plumb angle)), where the plumb angle is arctan(pitch / 12).

Each later jack equals the previous jack minus one common difference. The calculator lists these lengths for you when the count is small.

A hip roof with a 10 ft common run, a 6/12 pitch and rafters at 16 in on center:

1. Unit rafter length: sqrt(1 + (6 / 12)^2) = sqrt(1.25) = 1.1180
2. Common difference: 16 x 1.1180 = 17.89 in, which is about 1 ft 5 7/8 in
3. Common rafter length: 120 in x 1.1180 = 134.16 in
4. Longest jack: 134.16 – 17.89 = 116.27 in, which is 9.69 ft
5. Jacks per side: floor(120 / 16) = 7
6. Side cut: arctan(cos(26.57 degrees)) = arctan(0.8944) = 41.8 degrees

The seven jacks run from 9.69 ft down in steps of 17.89 in. As a check, the Swanson Blue Book lists a common difference of 1 ft 5 7/8 in for a 6/12 pitch at 16 in on center, which matches the 17.89 in result here.

Roof Pitch

A steeper pitch lengthens the unit rafter, so the common difference grows. At 12/12 the unit length is about 1.414, while at 3/12 it is about 1.031. The same 16 in spacing therefore gives a larger step on a steep roof.

On-Center Spacing

The common difference scales directly with spacing. Moving from 16 in to 24 in multiplies the step by 1.5 and cuts the number of jacks per side, so the roof uses fewer but more widely stepped boards.

Run Length

A longer run gives a longer longest jack and more jacks per side. The count is the run in inches divided by the spacing, rounded down.

Hip Side or Valley Side

The common difference is the same for hip jacks and valley jacks at the same pitch and spacing. What differs is where each jack starts and ends, and the direction of the side cut, so mark the cheek cut on the correct face of the board.

Position of the First Jack

This calculator places the first jack one spacing in from the common rafter. If your layout starts the first jack at a different distance, the longest jack changes by the same offset multiplied by the unit length.

Cost depends on lumber size, grade and local prices, so no price is stated here. Because jacks are cut from shorter stock, a good cut list can reduce waste, so plan lengths before you order.

Hip Roof Framing

Use a jack rafter calculator on any hip roof. The hip creates triangular roof planes, and the jacks fill those planes between the plate and the hip rafter.

Valley Framing

Where two roof planes meet at an inside corner, valley jacks run from the valley rafter up to the ridge. The same common difference applies, with the longest jack nearest the plate end of the pattern.

Ordering Lumber and Cut Lists

The list of jack lengths shows which stock lengths to buy and how many pieces to cut from each. It helps you avoid ordering a full length for every jack.

Comparing Spacing Options

Switch between 12, 16 and 24 in on center to see how the count and the step change. This shows the effect on lumber use before you commit to a layout.

1. Reusing One Common Difference for Every Pitch

The common difference changes with the pitch. A 6/12 roof and an 8/12 roof at the same spacing have different steps, so recalculate whenever the pitch changes.

2. Using the Wrong On-Center Spacing

The spacing must match the layout of the common rafters. If the commons are at 16 in, the jacks must be too, or the pieces will not line up with the sheathing edges.

3. Skipping the Hip Deduction

The theoretical length runs to the center line of the hip or valley. Each jack must be shortened by half the thickness of the hip or valley rafter, measured square to its face, so subtract it before cutting.

4. Measuring Along the Slope Instead of Horizontally

The run and the spacing are horizontal distances. Measuring them along the sloped rafter gives a count and a step that are too large.

5. Cutting the Side Cut on the Wrong Face

Left and right jacks need mirrored cheek cuts. Mark a pattern for each side of the hip or valley and label them.

The arithmetic is exact for the numbers you enter, but the model is a simplified roof. Treat the results as a planning cut list and confirm them with a pattern rafter.

A jack rafter is a shortened common rafter that runs from the wall plate to a hip rafter, or from a valley rafter up to the ridge. Each jack along a hip or valley is shorter than its neighbor.

The common difference is the amount each jack is shorter than the one before it. It equals the on-center spacing times the unit rafter length for the pitch.

Multiply the on-center spacing in inches by the square root of 1 plus the pitch over 12, squared. For a 6/12 pitch at 16 in on center the result is 17.89 in.

Divide the run in inches by the on-center spacing and round down. A 10 ft run at 16 in on center gives 7 jacks per side.

The side cut, also called the cheek cut, is the angled cut that lets the jack meet a hip or valley rafter. It equals arctan(cos(plumb angle)), which is 41.8 degrees for a 6/12 pitch.

Yes. At the same pitch and spacing the step is identical. The jacks differ in where they start and end and in the direction of the side cut.

No. The lengths are theoretical line lengths. Subtract half the hip or valley thickness, measured square to its face, from each jack before cutting.

A steeper roof makes each inch of run longer along the slope. The unit rafter length grows with the pitch, and the common difference grows with it.

Yes, if the structure and local code allow it. Wider spacing makes the common difference larger and cuts the jack count. Confirm rafter size and spacing with your code or a professional.

No. The calculator runs in your browser and nothing you enter is stored or sent anywhere.

• Swanson Blue Book Cutting Jack Rafters (Swanson Tool Company).
• Rafter Tables on a Framing Square (US Army Engineer Manual EN5156).
• Hip Valley Roof Framing Example (SBE Builders framing reference).
• Lengths of Jack Rafters for Square Cornered Roofs (Classic carpentry text).