Rafter length calculator

What is a rafter length calculator?

A rafter is the sloped beam that runs from the wall plate up to the ridge and carries the roof deck. Its length is not the same as the width of the building: because the rafter climbs as it travels, it is always longer than the horizontal distance it covers. This calculator turns the two numbers a builder already knows — the run and the pitch — into the rafter length, the roof rise, and the roof angle.

The run is the horizontal distance from the outside of the wall to the point below the ridge. For a symmetrical gable roof the run is half the span, so a building 8 m wide has a 4 m run. The pitch is written as the rise per 12 units of run — a “6/12” (or 6:12) roof climbs 6 units for every 12 units it travels horizontally.

How does the calculator work?

The run, the rise, and the rafter form a right triangle: the run is the horizontal side, the rise is the vertical side, and the rafter is the hypotenuse. That makes the rafter length a direct application of the Pythagorean theorem.

Enter the run, the pitch as a rise-per-12 number, and the eave overhang (leave it at 0 if you do not want one). The calculator returns the rafter length, the rise, and the angle immediately. Both the run and the overhang can be entered in metric or imperial units, and the rafter and rise outputs can be switched between them.

Key formulas

1. Roof rise — how far the roof climbs over the run:

$$\text{rise} = \text{run} \times \frac{\text{pitch}}{12}$$

2. Rafter length — the hypotenuse of the run–rise triangle, plus the overhang:

$$\text{rafter} = \sqrt{\text{run}^2 + \text{rise}^2} + \text{overhang}$$

3. Rafter length, straight from the pitch — substituting the rise gives an equivalent one-step form:

$$\text{rafter} = \text{run} \times \sqrt{1 + \left(\frac{\text{pitch}}{12}\right)^2} + \text{overhang}$$

4. Roof angle — the inclination measured from horizontal:

$$\theta = \arctan\left(\frac{\text{pitch}}{12}\right)$$

The square-root term in formula 3 is the rafter multiplier: a single number that converts any run into a rafter length for a given pitch.

Examples

Example 1: a 4 m run at a 6/12 pitch (metric)

A gable roof on a building 8 m wide has a 4 m run. With a 6/12 pitch and no overhang:

• Rise: $\text{rise} = 4 \times \frac{6}{12} = 2$
• Rafter length: $\text{rafter} = \sqrt{4^2 + 2^2} = \sqrt{20} = 4.4721$
• Roof angle: $\theta = \arctan\left(\frac{6}{12}\right) = 26.57°$

So each rafter is about 4.47 m long.

Example 2: a 12 ft run at a 6/12 pitch (imperial)

The same pitch on a 24 ft wide building, giving a 12 ft run and no overhang:

• Rise: $\text{rise} = 12 \times \frac{6}{12} = 6$
• Rafter length: $\text{rafter} = \sqrt{12^2 + 6^2} = \sqrt{180} = 13.416$
• Roof angle: $\theta = \arctan\left(\frac{6}{12}\right) = 26.57°$

The rafter is 13.416 ft, or roughly 13 ft 5 in.

Example 3: the same roof with a 2 ft overhang

The overhang is measured along the slope and is simply added to the rafter: $\text{rafter} = \sqrt{12^2 + 6^2} + 2 = 13.416 + 2 = 15.416$

Note that the rise stays at 6 ft — an overhang lengthens the rafter but does not raise the ridge.

Common pitches and their rafter multipliers

Multiply the run by the multiplier to get the rafter length: a 12 ft run on a 6/12 roof gives $12 \times 1.1180 = 13.416$ ft, exactly as in Example 2.

Practical notes

• The run is half the span on a symmetrical gable roof. Entering the full width of the building is the single most common mistake and doubles the rafter length.
• A steeper pitch means a longer rafter for the same building, and therefore more timber and more roofing material. Going from 4/12 to 12/12 lengthens every rafter by about 34%.
• This calculator returns the theoretical rafter length measured along the slope. Real rafters still need a birdsmouth cut at the wall plate and a plumb cut at the ridge, and you should subtract half the ridge-board thickness from the run before cutting.
• The overhang here is the length added along the rafter. If you know the horizontal projection of the eave instead, multiply it by the rafter multiplier before entering it.
• The pitch is a ratio, so it is unit-free: a 6/12 roof is 6/12 whether you measure in inches, feet, or metres. Only the run, the overhang, and the resulting lengths carry units. To work the other way round — from a measured rise and run to the pitch — use the roof pitch calculator.

Frequently Asked Questions

Is the run the same as the width of the house?

No. On a symmetrical gable roof the run is half the span, because two rafters meet at the ridge in the middle. A house 24 ft wide has a 12 ft run, and each rafter covers only that half.

How long is a rafter for a 6/12 roof with a 12 ft run?

The rise is 6 ft, so the rafter is:

$$\sqrt{12^2 + 6^2} = \sqrt{180} = 13.416 \, \text{ft}.$$

Does the overhang change the roof angle or the rise?

No. The overhang continues along the same slope, so it adds length to the rafter while the angle and the rise stay exactly the same. In Example 3 the rafter grows from 13.416 ft to 15.416 ft but the rise remains 6 ft.

What pitch gives a 45° roof?

A 12/12 pitch, because the rise equals the run:

$$\arctan\left(\frac{12}{12}\right) = 45°.$$

Its rafter multiplier is $\sqrt{2} = 1.4142$, so the rafter is about 41% longer than the run.

Can I use metres instead of feet?

Yes. The run and the overhang both accept metric and imperial units, and the rafter and rise outputs can be displayed in either system. The pitch stays a plain rise-per-12 ratio in both cases — a 4 m run at 6/12 gives a 4.4721 m rafter.