Roof pitch calculator

What is roof pitch?

Roof pitch describes how steep a roof is. It is the amount a roof rises vertically for a given horizontal distance it covers. In construction, pitch is most often written as a ratio against a 12-unit run, such as 4:12 or 6:12, which reads as “4 inches of rise for every 12 inches of run”. This calculator takes the rise (vertical height) and the run (horizontal distance) and returns three things: the pitch ratio, the roof angle in degrees, and the rafter length.

How does the calculator work?

The roof rise, run, and rafter form a right triangle. The rafter is the slanted top side (the hypotenuse), the run is the horizontal bottom side, and the rise is the vertical side. Knowing any two of these lets you describe the whole roof.

Enter the rise and the run, and the calculator immediately computes the pitch, the angle, and the rafter length.

Key formulas

1. Pitch (as x:12) — the rise scaled to a run of 12:

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

2. Roof angle — the inclination measured from horizontal:

$$\theta = \arctan\left(\frac{\text{rise}}{\text{run}}\right)$$

3. Rafter length — the hypotenuse of the rise–run triangle (Pythagoras):

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

Examples

Example 1: a 4:12 roof (rise 4, run 12)

• Pitch: $12 \times \frac{4}{12} = 4 \quad (4{:}12)$
• Angle: $\arctan\left(\frac{4}{12}\right) = 18.43°$
• Rafter length: $\sqrt{4^2 + 12^2} = \sqrt{160} = 12.65$

Example 2: a 6:12 roof (rise 6, run 12)

• Pitch: $12 \times \frac{6}{12} = 6 \quad (6{:}12)$
• Angle: $\arctan\left(\frac{6}{12}\right) = 26.57°$
• Rafter length: $\sqrt{6^2 + 12^2} = \sqrt{180} = 13.42$

Example 3: a 12:12 roof (rise 12, run 12)

• Pitch: $12 \times \frac{12}{12} = 12 \quad (12{:}12)$
• Angle: $\arctan\left(\frac{12}{12}\right) = 45°$
• Rafter length: $\sqrt{12^2 + 12^2} = \sqrt{288} = 16.97$

Common roof pitches

The pitch is a ratio, so it does not depend on the unit you use for the rise and run as long as both use the same unit. The rafter length, however, comes out in the unit you measured with.

Practical notes

• A roof is usually described by its pitch ratio (such as 4:12), while builders use the angle when setting saws or framing.
• Steeper roofs (higher pitch) shed water and snow faster, but use more material because the rafters are longer.
• The rafter length here is the straight rise-to-run span. Real rafters also need an overhang and a ridge/seat allowance, so add those before cutting.

Frequently Asked Questions

What does a 4:12 roof pitch mean?

It means the roof rises 4 units for every 12 units of horizontal run. The angle is:

$$\arctan\left(\frac{4}{12}\right) = 18.43°.$$

How do I convert a roof angle to a pitch?

Multiply the tangent of the angle by 12. For a 30° roof:

$$12 \times \tan(30°) = 6.93 \quad \Rightarrow \quad \approx 7{:}12.$$

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

The rise is 6 ft, so:

$$\sqrt{6^2 + 12^2} = \sqrt{180} = 13.42 \, \text{ft}.$$

Does the unit of rise and run change the pitch?

No. Because pitch is a ratio of rise to run, any consistent unit gives the same value. A 1 m rise over a 3 m run is the same 4:12 pitch as 4 in over 12 in.