Rafter Length Calculator

What is a Rafter Length Calculator?

A rafter length calculator helps you determine the exact length of roof rafters needed for your construction project. Whether you are building a new home, adding a shed, or replacing an existing roof, knowing the precise rafter length ensures you cut lumber correctly and avoid material waste. This tool also estimates the number of roof trusses needed and the total project cost.

Rafter length is calculated using the Pythagorean theorem, treating the roof section as a right triangle. The rise (vertical height) and run (horizontal span) form the two legs, while the rafter itself is the hypotenuse. You can input the rise and run directly, or use the roof pitch (slope) to calculate the rafter length automatically.

Rafter Length Formula

The rafter length is calculated using the Pythagorean theorem:

$$ L = \sqrt{R^2 + r^2} $$

Where $L$ is the rafter length, $R$ is the rise (vertical height), and $r$ is the run (horizontal span). When using roof pitch, the rise is derived from the pitch ratio:

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

$$ L = \sqrt{(\text{run} \times \text{pitch})^2 + \text{run}^2} = \text{run} \times \sqrt{\text{pitch}^2 + 1} $$

How Many Trusses Do I Need?

The number of roof trusses depends on the roof length and the on-center spacing between trusses. Standard spacing is typically 24 inches. The formula is:

$$ n = \left\lceil \frac{L_r}{s} \right\rceil + 1 $$

Where $n$ is the number of trusses, $L_r$ is the roof length, and $s$ is the on-center spacing. The total cost is then the number of trusses multiplied by the price per truss, plus optional installation labor costs.

For related calculations, check the Birdsmouth Cut Calculator for rafter notch cuts, or the Roofing Calculator for complete roofing material estimates.