Rafter Calculator

From horizontal run and vertical rise, instantly compute the rafter cut length, angle, slope (%), and pitch (rise/12).

Result

Enter run and rise, then click Calculate.

What this tool does

The rafter length calculator uses the Pythagorean formula (√(run²+rise²)) to find the base rafter length from the horizontal span (run) and vertical height (rise), then adds the eave overhang corrected for slope (eave × sec θ) to give the full cut length. Angle, slope percentage, pitch-in-12, and area correction factor (sec θ = 1/cos θ) are shown simultaneously, making the results immediately useful for material ordering and roof area conversion.

Who uses this

Lumber ordering: multiply cut length by rafter count to calculate total board footage needed
Light-frame roof design: find accurate rafter length including eave overhang
Roof area conversion: use sec θ to convert horizontal projection area to actual sloped area
Cut angle reference: read upper plumb-cut and lower bird's-mouth cut angles directly from the result
Pitch notation conversion: see slope %, angle in degrees, and x/12 rise all at once

How to use (3 steps)

1Enter the horizontal run — the horizontal distance from the ridge to the top of the exterior wall plate. For a gable roof with a 6 m east-west span, the run for each side is 3 m (half the total width).
2Enter the rise — the vertical height from the top plate to the ridge. For example, run 3,000 mm and rise 900 mm gives a 30% slope and a 3.6/12 pitch.
3Enter the eave overhang length in mm if applicable. The calculator adds the slope-corrected eave diagonal (eave × sec θ) to give the total cut length. Leave it at 0 if you only need the base rafter length.

Formula & basis

Base rafter length = √(run² + rise²) Angle θ = atan(rise / run) Slope (%) = (rise / run) × 100 Pitch (x/12) = (rise / run) × 12 Area correction factor (sec θ) = 1 / cos θ → multiply projected area by sec θ to get actual sloped area Eave diagonal = eave overhang (mm) × sec θ Total cut length = base rafter length + eave diagonal Example: run=3,000 mm · rise=900 mm · eave=500 mm Base = √(9,000,000 + 810,000) = 3,132 mm θ = atan(0.30) = 16.7°, sec θ = 1.044 Eave diagonal = 500 × 1.044 = 522 mm Total cut length = 3,132 + 522 = 3,654 mm

Worked examples

Example 1: run 3,000 mm · rise 900 mm · eave 500 mm (30% slope)

Base rafter = √(3,000²+900²) = 3,132 mm. Angle 16.7°. sec θ = 1.044. Eave diagonal = 522 mm. Total cut length = 3,654 mm. Area correction 1.044 → multiply projected floor area by 1.044 to get actual roof area.

Example 2: run 4,000 mm · rise 2,000 mm · eave 600 mm (6/12 pitch)

Base rafter = √(16,000,000+4,000,000) = 4,472 mm. Angle 26.6°. sec θ = 1.118. Eave diagonal = 671 mm. Total cut length = 5,143 mm. At 6/12 the actual roof area is about 11.8% larger than the projected area.

Example 3: run 2,500 mm · rise 1,250 mm · no eave (45°)

Base rafter = √(6,250,000+1,562,500) = 2,795 mm. Angle 26.6°. With 0 mm eave, total cut length equals base length = 2,795 mm. Area correction factor 1.118. Useful when only the plain rafter length is needed.

Frequently asked questions

Where exactly is the 'run' measured?

The run is the horizontal distance from the ridge (peak) to the top of the exterior wall's top plate. For a symmetrical gable roof with a 6 m total width, each side has a run of 3 m. The eave overhang beyond the wall is entered separately.

Where is the area correction factor (sec θ) used?

Multiply the horizontal projected area by sec θ to get the actual sloped roof area. For example, sec θ = 1.118 means 100 m² projected becomes 111.8 m² actual — the figure needed for shingle or tile quantity takeoffs, waterproofing, and solar panel layout.

What does the x/12 pitch notation mean?

It is the North American light-frame convention: the number of inches of vertical rise per 12 inches of horizontal run. A 4/12 pitch rises 4 inches for every 12 horizontal inches. This calculator converts rise/run × 12 automatically.

Why is the eave not simply added to the rafter length?

The eave overhang is measured horizontally, but the rafter runs along the slope. To convert a horizontal eave distance to a sloped rafter distance you must multiply by sec θ (= 1/cos θ). Example: 500 mm horizontal eave at 16.7° becomes 500 × 1.044 = 522 mm along the rafter.

How do I use the cut angle in the workshop?

The angle result (°) is the cut angle for both ends of the rafter. Use it as the bevel setting on a circular saw or miter saw for the upper plumb cut (at the ridge) and the lower bird's-mouth seat cut (at the wall plate).

Can this calculator find the structural span limit of a rafter?

No — this tool handles geometry only (length and angle). To check whether a rafter size can safely span a given distance under bending stress and deflection criteria, use the separate Span Calculator, which applies NDS allowable stress design.

Cautions

•This calculator covers rafter geometry only. Structural adequacy (allowable span, deflection, member size) requires the Span Calculator and review by a licensed structural engineer.
•The run is measured to the top plate, not including the eave. Entering eave length in the run field will double-count the overhang.
•Results assume a simple gable or shed roof with a single straight slope. For hip roofs or complex geometries, calculate each face separately.
•In practice, rafter length may need a small adjustment (1–2 mm) to account for ridge board thickness at the peak.
•Always have a licensed structural professional review calculations before construction.