A hip rafter runs diagonally from the corner of the building to the ridge, forming the "hip" of the roof where two roof planes meet. It's longer than a common rafter (the rafters that run perpendicular to the ridge).

Key Formula for Calculating Hip Rafter Length

The hip rafter length is calculated using the Pythagorean theorem, adapted to account for the diagonal slope of the hip rafter.

$L = H \times S$

Where:

• L = Hip rafter length (in feet or meters)
• H = Horizontal run, which is half the building width plus overhang
• S = Slope factor for the hip rafter

1. Calculate Horizontal Run

The horizontal run (H) is the sum of half the building width and the overhang:

$H = \frac{W}{2} + O$

Where:

• H = Horizontal run (in feet or meters)
• W = Building width (in feet or meters)
• O = Overhang (in feet or meters)

Example Calculation for Horizontal Run

Input Values:

• Building Width (W) = 20 ft
• Overhang (O) = 2 ft

Using the formula:

$H = \frac{20}{2} + 2 = 10 + 2 = 12 \, \text{ft}$

2. Calculate Slope Factor

The slope factor (S) for the hip rafter accounts for the diagonal slope, using the roof pitch (P):

$S = \sqrt{2 + P^2}$

Where:

• S = Slope factor
• P = Roof pitch, expressed as the rise/run ratio (e.g., 6/126/12 is 0.50.5)

Example Calculation for Slope Factor

Input Values:

• Roof Pitch (P) = 6/12 = 0.5

Using the formula:

$S = \sqrt{2 + 0.5^2} = \sqrt{2 + 0.25} = \sqrt{2.25} \approx 1.5$

3. Calculate Hip Rafter Length

Finally, the hip rafter length (L) is calculated by multiplying the horizontal run by the slope factor:

$L = H \times S$

Where:

• L = Hip rafter length (in feet or meters)
• H = Horizontal run (from Step 1)
• S = Slope factor (from Step 2)

Example Calculation for Hip Rafter Length

Input Values:

• Horizontal Run (H) = 12 ft
• Slope Factor (S) = 1.5

Using the formula:

$L = 12 \times 1.5 = 18 \, \text{ft}$

Benefits of Using the Hip Rafter Length Calculator

1. Accuracy: Eliminates errors in manual calculations, ensuring precise rafter cuts.
2. Time-Saving: Quickly calculates the hip rafter length, even for complex roof designs.
3. Versatility: Works for any roof pitch and building size.
4. Ease of Use: Perfect for contractors, architects, and DIY enthusiasts alike.