How to Calculate Rafter Length for a 6/12 Pitch
With a 12-foot horizontal run, a 6/12 pitch creates a 6-foot rise and a geometric common-rafter line of about 13.42 feet before overhang and cut adjustments.
Rafter length formula
For a roof with horizontal run r and pitch rise p per 12 units, first calculate the rise, then use the Pythagorean theorem:
rise = run × pitch rise ÷ 12
rafter length = √(run² + rise²)
For other pitches or runs, use the Rafter Calculator →.
What a 6/12 pitch means
A 6/12 roof rises 6 units vertically for every 12 units of horizontal run. The ratio is therefore 0.5.
rise = run x 6 / 12
Worked example with a 12-foot run
For a 12-foot horizontal run:
rise = 12 x 6 / 12 = 6 ft
The run and rise form the two legs of a right triangle. The rafter line is the hypotenuse:
rafter = sqrt(run² + rise²)
sqrt(12² + 6²) = sqrt(180) = about 13.42 ft
Rafter multiplier for a 6/12 roof
For each foot of horizontal run, a 6/12 pitch produces about 1.118 feet of sloped rafter line. That same relationship can be used for any run that shares the pitch.
rafter multiplier = sqrt(1 + 0.5²) = about 1.118
What must be added or adjusted in real framing?
The geometric line length is not automatically the final cut length. Overhang, ridge thickness, birdsmouth geometry, fascia details and exactly where the run measurement starts and ends can all affect the actual board.
Structural member sizing is also a separate question. A length calculator does not select lumber size, species, grade, spacing or allowable span.
Calculate another pitch or run
Use the Rafter Calculator to enter your own run, pitch and optional overhang. Use the Roof Pitch Calculator when you know rise and run but need the pitch, angle or slope percentage.
Related roofing tools
Browse the Roofing Calculators hub for pitch, rafter and shingle planning. For material quantity, use the Shingle Calculator; for a budget based on your own local rates, use the Roofing Cost Calculator.
Compare the same pitch across three different runs
A 6/12 pitch keeps the same slope multiplier (approximately 1.118), but the geometric rafter line gets longer as the horizontal run increases. The following values are calculated from the right-triangle formula before overhangs, ridge deductions or birdsmouth adjustments.
| Horizontal run | Rise | Slope length |
|---|---|---|
| 8 ft | 4 ft | 8.94 ft |
| 10 ft | 5 ft | 11.18 ft |
| 12 ft | 6 ft | 13.42 ft |
The result is a line length for estimation, not a safe lumber span or an installation cut list. In particular, a building width must not automatically be used as rafter run; on a simple gable roof, horizontal run is generally measured from the wall/seat reference toward the ridge and can require ridge-thickness adjustment. Use construction drawings and an appropriate structural specification for the actual framing.
Start with horizontal run, not the full roof width
Homeowners often know a building is 24 feet wide and enter 24 feet as the rafter run. On a simple symmetrical gable with the ridge centered between two equal bearing lines, that would double the horizontal run. The conceptual run for either side is about half the distance: 24 ÷ 2 = 12 feet. At 6/12 pitch, that produces a 6-foot rise and the 13.42-foot sloping line calculated above. Using 24 feet as the run would instead produce a 12-foot rise and a 26.83-foot line: a very different roof.
That half-width shortcut is only an illustration. Real plans can have an off-center ridge, different wall or seat reference points, ridge thickness, asymmetric roof planes and other details. Measure the horizontal distance on the appropriate drawing, rather than assuming every gable is a perfect triangle. If you have only a tape measurement made along the sloping surface, it is not the horizontal run and should not be entered as such.
For quick geometry checks, open the Roof Pitch Calculator first if the rise-to-run ratio is uncertain, then use the Rafter Calculator for the right roof plane.
Worked scenario: what an 18-inch horizontal overhang changes
Suppose your simplified 6/12 rafter drawing shows a 12-foot horizontal run from its chosen ridge reference to the wall reference. You want to understand what happens when the sloping line continues to the fascia with a horizontal projection of another 18 inches. Eighteen inches equals 1.5 feet, so the illustrative total horizontal projection becomes 13.5 feet. With a slope multiplier of √1.25 = 1.118034, the geometrical slope line to that new point is approximately 13.5 × 1.118034 = 15.09 feet.
| Additional horizontal projection | Combined horizontal run | Straight slope line |
|---|---|---|
| 0 in | 12.0 ft | 13.42 ft |
| 12 in | 13.0 ft | 14.53 ft |
| 18 in | 13.5 ft | 15.09 ft |
| 24 in | 14.0 ft | 15.65 ft |
These figures illustrate geometry only. An overhang dimension measured along the sloping rafter would not be added as a horizontal projection. Nor does the line automatically include the correct ridge allowance, wall seat, birdsmouth, tail cut, fascia or other drawing-specific adjustments. Do not use this table as a final cut list or a reason to choose a stock length without an approved framing detail.
Why the longest line is not a board-shopping answer
Even when your geometric result is 15.09 feet, buying an apparently long-enough board is not the entire calculation. A usable member must accommodate the actual location of plumb cuts, seat or birdsmouth geometry, the tail profile, any connection detail and waste from cutting. The selected timber also needs the specified species, grade, section, spans, spacing and structural design. Length alone says nothing about whether the board can safely carry loads.
A practical homeowner approach is to separate three documents. The measurement sketch records horizontal run, pitch and overhang reference points; the geometry estimate states the slope line with units and rounding; and the framing specification or cut schedule comes from the approved plans and qualified framing professional. That way, a cost comparison is not mistaken for a structural instruction. If suppliers offer different stock lengths, compare them against that approved schedule rather than rounding a calculator result up and assuming every cut will fit.
Five checks before trusting a result
- Check the roof shape. This right-triangle example is for a common rafter in one simple pitched plane, not a hip, valley, jack or complex roof junction.
- Label the horizontal run. Mark where the measurement starts and ends on the drawing; never substitute the whole building width without checking ridge position and bearing references.
- Keep pitch and units consistent. A 6/12 rise-to-run ratio equals 0.5 whether you use inches or feet; avoid mixing a 12-inch pitch denominator with a run entered as inches in one step and feet in another.
- Keep overhang separate. Note whether its dimension is horizontal or measured along the slope; applying the wrong convention can distort the estimated tail length.
- Validate against the framing plan. Calculated slope length is a planning number. Final member sizing, support requirements, cuts and construction safety belong to approved plans and competent professionals.
As a sanity check, if you double a horizontal run at unchanged 6/12 pitch, the geometric rafter line also doubles. If your new result does not behave that way, inspect your unit conversions and formula before using it in a material estimate.