4:12 Roof Pitch Calculator: Rise, Run and Rafter Length

This 4:12 roof pitch calculator works out the angle, slope, and theoretical rafter length for a roof that rises 4 inches for every 12 inches of horizontal run. Enter the horizontal run and the calculator returns the rafter length, roof angle, and rise, helping homeowners and builders check basic layout measurements.

Formula

A roof pitch of 4:12 means the roof rises 4 inches vertically for each 12 inches of horizontal distance. The calculator treats the entered run as the horizontal distance from the roof edge to the ridge, measured along a level line—not along the sloping roof surface.

Rafter length = run × √[1 + (rise ÷ 12)²]. The rise input is in inches per 12 inches of run, and the run and answer are in feet. This is the Pythagorean theorem: the horizontal run and total vertical rise form the two legs of a right triangle, while the rafter is its hypotenuse.

Roof angle = arctan(rise ÷ 12). The angle is measured in degrees above horizontal. Total rise = run × rise ÷ 12, with the entered run and result in feet; the rise-per-12 ratio makes the units cancel correctly.

This calculator’s default values describe a 4:12 pitch over a 12-foot horizontal run. The rafter length is a geometric length, not a complete cut list: it does not account for an eave overhang, ridge-board thickness, seat cuts, or other framing details.

Worked Example

Using the calculator’s defaults: horizontal run = 12 ft and rise per 12 inches of run = 4 in.

Rafter length: 12 × √[1 + (4 ÷ 12)²] = 12 × √(1 + 0.111111…) = 12 × 1.054092… = 12.6491… ft, or 12.65 ft.

Roof angle: arctan(4 ÷ 12) = arctan(⅓) = 18.4349…°, or 18.43°.

Total rise: 12 × 4 ÷ 12 = 4.00 ft. These are the calculator’s rounded results for the displayed defaults.

How to Use the Result

For a 4:12 roof, each foot of horizontal run produces 4 inches of rise. That is a 1:3 rise-to-run ratio, an angle of about 18.43 degrees, and a rafter-length multiplier of about 1.0541. For example, a 10-foot run gives a theoretical rafter length of about 10.54 feet before framing allowances.

On a symmetrical gable roof, the run is generally half the building’s outside width only when the ridge is centered and the measurement is taken from the relevant eave line to the ridge’s vertical projection. A 24-foot-wide building with a centered ridge therefore has a nominal 12-foot run. Actual framing dimensions can differ depending on wall and ridge details.

To convert the results, multiply feet by 12 for inches, or by 0.3048 for metres. The default 12-foot run is 3.6576 m, the 4-foot rise is 1.2192 m, and the calculated 12.65-foot rafter is about 3.86 m. Keep all inputs in the units specified; enter the pitch rise as inches per 12 inches, not as a decimal such as 0.333.

How to Choose

First establish what measurement you actually have. If you know the building width, determine whether it is the full span or the half-span run; entering the full width for a centered gable roof would roughly double the calculated rafter length and rise. If you already measured the sloping rafter, this calculator is not the right way to infer the horizontal run unless you rearrange the geometry separately.

Check the pitch convention before using a value from a plan or measurement. A 4:12 pitch is rise over horizontal run, not roof angle and not a ratio of rafter length to width. Keep the 4-inch rise-per-12-inch-run figure in the pitch field, and enter the horizontal run in feet.

Finally, decide whether a geometric estimate is enough. This tool is useful for estimating stock length or checking a simple roof layout, but a build-ready rafter measurement must also reflect the overhang, ridge-board or ridge-beam arrangement, birdsmouth and plumb cuts, and the specific framing plan. Do not use the rounded result as a final cut dimension without checking those details.

When to Use a 4:12 Pitch

Use a 4:12 calculator when the roof pitch is known and you need a quick geometric check of rise, angle, or rafter length. It can help compare a plan measurement with a simple triangle calculation or estimate the length of the main sloping member before additional framing allowances are considered.

Roof pitch alone does not establish whether a roof covering is appropriate. Material requirements depend on the product, installation method, underlayment, climate exposure, and applicable construction requirements. Check the chosen product’s installation instructions and the project documents rather than treating the pitch calculation as approval for a particular covering.

Frequently Asked Questions

What does a 4:12 roof pitch mean?
It means the roof rises 4 inches vertically for every 12 inches of horizontal run. The same slope can be expressed as one-third, or about 18.43 degrees above horizontal.

Is the run the full width of the roof?
Usually not for a symmetrical gable roof. The run is the horizontal distance from the eave to the ridge’s vertical projection, typically half the building span when the ridge is centered.

Does the result include the roof overhang?
No. The calculation uses only the horizontal run you enter. Add the overhang’s horizontal projection to the run if you are estimating the full geometric slope to the eave tip, then account separately for cuts and framing details.

How long is a rafter on a 4:12 roof?
It depends on the horizontal run. At a 12-foot run, the theoretical rafter length is 12.65 feet; at other runs, multiply the run by approximately 1.0541.

Can I enter metric measurements?
The calculator’s run field is in feet and its pitch field is inches per 12 inches. Convert metric measurements first, or convert the displayed results afterward; 1 ft equals 0.3048 m and 1 in equals 25.4 mm.

Is the calculated length ready for cutting?
No. It is the theoretical length along the roof slope. A cut dimension needs allowances and deductions for the overhang, ridge, seat cut, and the specified framing layout.

Final Thoughts

A 4:12 roof has a consistent slope: 4 inches of rise per foot of horizontal run. Use the calculator to check the basic triangle, then verify the actual span, overhang, and framing cuts against the project plan before measuring or cutting lumber.

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in run | Horizontal run | ft | 12 | 0
in rise | Rise per 12 inches of run | in | 4 | 0
out rafter | Rafter length | ft | run * sqrt(1 + (rise / 12)^2) | 2
out angle | Roof angle | degrees | atand(rise / 12) | 2
out totalrise | Total rise | ft | run * rise / 12 | 2