Skip to main content
Calculator Answers

Rafter Calculator

Blake Boege
Written by Blake Boege · Founder, Calculator Answers

A rafter calculator is a carpentry construction tool used to determine the dimensions of roof framing members. Based on the geometry of a gable roof, it treats the horizontal half-span (including any overhang) and the vertical rise as the two perpendicular sides of a right triangle. The calculator applies the Pythagorean theorem to determine the precise diagonal length of the rafter board. It also calculates the vertical rise from the wall plate to the ridge and converts the pitch into an exact angle in degrees. Carpenters and builders use this calculator to estimate lumber quantities and mark cuts.

Calculate rafter length, roof rise, and pitch angles for residential roof framing. Supports common pitches (e.g. 4/12, 6/12, 12/12) and custom profiles.

See also: Roof Pitch Calculator, Stair Calculator, and Board Foot Calculator.

Quick Answer

Estimate roof rafter dimensions. Enter the building width, roof pitch, and overhang to calculate total rafter length, vertical rise, and pitch angle.

Rafter Projections

ESTIMATED RAFTER LENGTH

14 ft 6.4 in

Pitch: 6/12 · Angle: 26.6°

Building Width24 ft 0 in (288 in)
Main Span Run12 ft
Overhang Run12 in
Total Span Run13 ft
Vertical Rise to Ridge6 ft
Total Rise (inc. Overhang)6 ft 6 in
Roof Pitch6/12
Rafter Angle26.6°
Was this helpful?

Examples

24 ft building, 6/12 pitch, no overhang

Run = 12 ft · Rise = 6 ft · Rafter Length = sqrt(12² + 6²) = 13.42 ft (13 ft 5 in)

24 ft building, 6/12 pitch, 12 in overhang

Total Run = 13 ft · Total Rise = 6.5 ft · Rafter Length = sqrt(13² + 6.5²) = 14.53 ft (14 ft 6.4 in)

30 ft building, 4/12 pitch, 18 in overhang

Total Run = 16.5 ft · Total Rise = 5.5 ft · Rafter Length = sqrt(16.5² + 5.5²) = 17.39 ft (17 ft 4.7 in)

How it works

The calculator uses the building width, roof pitch, and overhang to determine the horizontal run and vertical rise of the rafter, then applies the Pythagorean theorem.

Rafter Length Formula

Rafter Length = sqrt(Run² + Rise²)

Run and Rise Equations

  • Run = (Building Width / 2) + Overhang
  • Rise = Run × (Pitch / 12)

Anatomy of a Roof Frame

Framing a gable roof requires understanding several terms:

  • Ridge Board: The horizontal beam at the peak of the roof where the top ends of the rafters meet.
  • Wall Plate: The top horizontal framing member of the wall where the bottom of the rafter rests.
  • Bird's Mouth Cut: A triangular notch cut into the rafter so that it fits flat against the top wall plate.
  • Plumb Cut: The vertical cut at the top of the rafter that rests against the ridge board.

Practical Carpentry Considerations

When ordering lumber, always round up the calculated rafter length to the nearest standard board length (typically even lengths like 14, 16, or 18 feet). Additionally, remember that the calculator gives the line length from the ridge to the tail. In practice, you must subtract half of the thickness of the ridge board (typically 3/4 inch for a standard 2x ridge board) from the top plumb cut to ensure a tight fit.

Related tools

Check out our other construction and home design estimators, such as the Tile Calculator for flooring plans, and the Stair Calculator to compute riser and run dimensions.

Related Calculators

More tools from Home

Roof Pitch CalculatorCalculate roof pitch from rise and run. Returns pitch in the U.S. x/12 convention, angle in degrees, slope percent, and the roof-surface multiplier for converting plan area to actual sloped roof area.Stair CalculatorPlan stair risers and treads from total rise and preferred riser height. Returns the riser count, actual riser height, total run, and an estimated stair angle.Board Foot CalculatorCalculate board feet for lumber from thickness, width, length, and quantity, with an optional cost estimate from a price per board foot.Paint CalculatorEstimate the gallons of paint needed for a room or wall. Subtracts doors and windows, applies coats, and rounds up to a whole gallon order.

Frequently asked questions

Rafter length is calculated using the Pythagorean theorem (A² + B² = C²) by modeling the half-span of the building and the roof rise as the two legs of a right triangle. The rafter length is the hypotenuse of this triangle. If you have an overhang, the run and rise of the overhang are added to the equation.

Roof pitch is a measure of the steepness of a roof, expressed as the number of inches of vertical rise for every 12 inches of horizontal run. For example, a 6/12 pitch means the roof rises 6 inches vertically for every 12 inches it extends horizontally.

The overhang extends the rafter beyond the exterior walls of the building. The calculator extends the horizontal run by the overhang width and projects the additional diagonal length required to maintain the same roof pitch angle.

The roof span is the total width of the building from the outside of one wall plate to the outside of the opposite wall plate. The run is the horizontal distance that the rafter covers from the wall plate to the ridge beam, which is exactly half of the span (excluding overhang).

To convert pitch to an angle in degrees, divide the rise by 12 to get the slope ratio, take the inverse tangent (arctangent) of that ratio, and convert the result from radians to degrees.

Most residential homes use a pitch between 4/12 and 9/12. Pitches below 4/12 are considered low slope (requiring special roofing materials), while pitches above 9/12 are considered steep slope.