Rafter Calculator

Follow these steps to find the length of a common rafter and the angles you need to mark on the board.

1. Enter the roof span in feet. This is the full width of the building from outside wall to outside wall, measured across the direction the rafters run.
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. Enter the eave overhang in inches. This is the horizontal distance the rafter extends past the wall plate. Enter 0 for no overhang.
4. Read the results. The rafter length, run, rise, plumb cut angle and seat cut angle update instantly, with a short note on the length.

The result is a theoretical length measured along the top edge of the rafter. Allow for the ridge board, the birdsmouth and the saw kerf when you cut real lumber.

A rafter is a sloped framing member that runs from the top of an exterior wall up to the ridge of a roof. Rafters carry the roof sheathing, the roofing material and the loads placed on them, such as snow and wind, and pass those loads down to the walls. In a conventionally framed roof, pairs of rafters meet at a ridge board or ridge beam and are spaced evenly along the length of the building.

Several rafter types appear on a typical roof. Common rafters run straight from the wall plate to the ridge, and they are the type this calculator sizes. Hip and valley rafters run diagonally where roof planes meet, and they are longer than common rafters for the same run. Jack rafters are short members that fill in between a hip or valley and the wall or ridge.

Knowing the exact rafter length matters because every board is cut to a layout. A rafter that is too short leaves a gap at the ridge or a short overhang. A rafter that is too long wastes lumber and may need recutting. Getting the length and the two cut angles right before you cut saves time and material.

A roof section forms a right triangle. The run is the horizontal side, the rise is the vertical side and the rafter is the sloped side, called the hypotenuse. The pitch tells you how steep the slope is, so it links the rise to the run. The calculator finds the run and rise, then uses the Pythagorean theorem to find the sloped length and adds the overhang.

Step by step:

• The run is half the span, because the ridge sits at the center of a symmetrical gable roof.
• The rise is the run multiplied by the pitch divided by 12. A 6/12 pitch rises 6 in for every 12 in of run, so the rise is half the run.
• The sloped length comes from the square root of run squared plus rise squared.
• The overhang is converted from inches to feet and added to the sloped length.
• The plumb cut angle is the arctangent of the pitch divided by 12. The seat cut angle is 90 degrees minus the plumb cut angle.

Assumptions: a symmetrical gable roof, a common rafter, a level wall plate and an overhang measured horizontally. The calculator reports a length along the top edge of the rafter and does not subtract the ridge board thickness.

A building 20 ft wide with a 6/12 roof pitch and a 12 in eave overhang:

1. Run: 20 / 2 = 10 ft
2. Rise: 10 x (6 / 12) = 5 ft
3. Sloped length before the overhang: the square root of (10 x 10 + 5 x 5) = the square root of 125 = 11.18 ft
4. Overhang: 12 in / 12 = 1.00 ft
5. Rafter length: 11.18 + 1.00 = 12.18 ft
6. Plumb cut angle: arctan(6 / 12) = arctan(0.5) = 26.6 degrees
7. Seat cut angle: 90 – 26.6 = 63.4 degrees

The rafter needs about 12.18 ft of length, so you would start with a board of at least 13 ft or longer stock sized to your supplier lengths. Always check the result against a full-size layout before cutting the first rafter.

Roof Span

The span sets the run, and the rafter grows in direct proportion to it. Doubling the span doubles the run, the rise and the sloped length for the same pitch.

Roof Pitch

A steeper pitch raises the rise and lengthens the rafter for the same span. At 12/12 the rise equals the run and the sloped length is about 1.41 times the run. At 3/12 the sloped length is only about 1.03 times the run.

Eave Overhang

The overhang is added to the length. This calculator treats the overhang you enter as a horizontal distance but adds it directly, so it gives a slightly short result for a long overhang on a steep roof. Treat the figure as a planning length and confirm it on a layout.

Ridge Board Thickness

When rafters meet at a ridge board, half the ridge thickness is usually deducted from each rafter. The calculator does not make this deduction, so subtract it yourself when your design uses a ridge board.

Birdsmouth Cut

The birdsmouth is a notch that lets the rafter sit on the wall plate. It does not change the overall length along the top edge, but it removes material from the bottom edge, so the depth is limited by the width of the rafter.

Wall Height and Plate Position

Rafter length is measured from the outside edge of the wall plate. If the walls are out of level or the plate is set back from the outside face, the real rafter length shifts. Measure the building after the walls are framed.

Cost depends on the lumber size and grade, the span, labor rates and the delivery of trusses, so no price is stated here. Get written quotes for both methods if you are deciding between them, and ask a framing contractor which approach suits your span and roof shape.

Planning a New Roof Frame

Use a rafter calculator before you order lumber. The length tells you which board lengths to buy and how many pieces you need to cut for each side of the roof.

Building a Shed, Garage or Porch

Small gable structures are a common use case. A quick calculation gives the rafter length and cut angles so you can build a pattern rafter and trace it for the rest.

Comparing Roof Pitches

Change the pitch from 4/12 to 8/12 and watch the length change. This shows how much extra lumber and roofing material a steeper roof needs.

Checking a Plan or Quote

If a plan or contractor lists a rafter length, compare it with your own figure. A large gap is worth a question about the overhang, the ridge allowance or the pitch used.

Setting Up Cut Angles

The plumb and seat angles help you set a speed square, a miter saw or a framing square. Use a speed square and a pattern rafter to confirm the angles before you cut the full set.

Using the Roof Length Instead of the Span

Enter the width of the building across the rafter direction. Do not enter the length of the ridge, which runs the other way.

Forgetting the Overhang

Leaving the overhang out gives a rafter that ends at the wall plate. Add the overhang you want at the eave, or enter 0 if there is none.

Mixing Pitch and Angle

A 6/12 pitch is not a 6 degree slope. It is about 26.6 degrees. Enter the pitch ratio in this tool and use the angle results for your saw settings.

Ignoring the Ridge Board

Without a deduction for half the ridge board thickness, each rafter will be a little long. Subtract it when your design uses a ridge board.

Treating the Length as a Structural Check

This tool gives geometry, not strength. A rafter that fits the length may still be too small for the span and load. Confirm the size with span tables, the local code or a qualified professional.

Measuring Rafter Length Without a Layout Check

Always cut one pattern rafter and test it in place. Walls are rarely perfectly square, and a trial fit catches errors before you cut the full set.

This calculator applies standard right-triangle geometry, so the numbers are exact for the inputs you enter. The limits come from the simplified roof model, not from the arithmetic.

Halve the building span to get the run, multiply the run by the pitch over 12 to get the rise, take the square root of run squared plus rise squared, then add the overhang. For a 20 ft span at 6/12 with a 12 in overhang the length is 12.18 ft.

The run is the horizontal distance from the outside of the wall to the center of the ridge. On a symmetrical gable roof it equals half the building span.

It means the roof rises 6 inches for every 12 inches of horizontal run. The slope angle is about 26.6 degrees.

The plumb cut is the vertical cut at the top of the rafter where it meets the ridge, and at the tail end. Its angle is the arctangent of the pitch over 12 measured from the rafter edge.

The seat cut is the horizontal cut of the birdsmouth that sits on top of the wall plate. Its angle is 90 degrees minus the plumb cut angle.

Yes. This calculator adds the overhang you enter to the sloped length, so the result runs from the ridge to the tail of the eave.

Yes, if your design uses a ridge board. Rafters are usually shortened by half the ridge thickness, and this calculator does not apply that deduction, so subtract it yourself.

No. Hip and valley rafters run diagonally and are longer than common rafters for the same run. This tool is for common rafters on a gable roof.

No. Lumber size depends on span, spacing, grade, species and loads. Use span tables from the American Wood Council, your local code or a qualified professional to choose a size.

The arithmetic is exact for the numbers you enter. Real roofs vary because of wall out-of-square, ridge board thickness and the birdsmouth, so test a pattern rafter before cutting the full set.

• IRC R802 Roof Framing Requirements (International Code Council, 2021 IRC).
• AWC Span Tables for Joists and Rafters (American Wood Council).
• Fine Homebuilding Roof Framing Geometry (Taunton Press).