Hip Roof Calculator

Welcome to the Hip Roof Calculator! This tool helps you quickly determine the key dimensions and material requirements for a hip roof design. Whether you’re a builder, architect, or homeowner planning a construction project, the calculator makes it easy to estimate rafter lengths, ridge board dimensions, roof pitch, and total roof area.

All you need are a few inputs—such as the building span, length, overhang, roof pitch, and rafter spacing—and the calculator will do the rest. You can start using it immediately, or keep reading to understand the formulas behind the calculations, explore parameter details, and walk through a step-by-step example.

Understanding the Formula

The hip roof design involves several important calculations:

Core Rafter Calculations
Total Run of Common Rafter = (Building Span ÷ 2) + Overhang
Total Roof Rise = Total Run of Common Rafter × (Roof Pitch Rise ÷ 12)
Common Rafter Length = √((Total Run of Common Rafter)² + (Total Roof Rise)²)

Total Run of Hip Rafter = Total Run of Common Rafter × √2
Hip Rafter Length = √((Total Run of Hip Rafter)² + (Total Roof Rise)²)

Jack Rafter Calculations
Jack rafters shorten progressively from the hip rafter to the corner.
Jack Rafter Length Increment = √((Rafter Spacing)² + ((Roof Pitch Rise ÷ 12) × Rafter Spacing)²)
Length of Jack Rafter #n = n × Jack Rafter Length Increment

Ridge and Area Calculations
Ridge Board Length = Building Length − Building Span
Roof Angle (degrees) = arctan(Roof Pitch Rise ÷ 12)
Total Roof Area = ((Building Length + 2 × Overhang) × (Building Span + 2 × Overhang)) ÷ cos(Roof Angle)

Put simply, these formulas calculate how long your rafters need to be, how steep the roof will sit, and how much total surface area it covers.

Parameters Explained

Building Span
The width of the building from one exterior wall to the opposite wall.

Building Length
The overall length of the building parallel to the ridge line.

Overhang
The distance the roof extends beyond the walls, usually for weather protection and aesthetics.

Roof Pitch Rise
The vertical rise in inches for every 12 inches of horizontal run. For example, a 6/12 pitch rises 6 inches for every foot of run.

Rafter Spacing
The distance between rafters, usually measured in inches or centimeters.

Common Rafter
The standard rafter running from the top plate of the wall to the ridge.

Hip Rafter
A diagonal rafter running from the building corner to the ridge, carrying loads from intersecting jack rafters.

Jack Rafters
Shorter rafters that connect the wall plate to the hip rafter, filling in the slope.

Ridge Board
The horizontal board at the roof peak where rafters meet.

How to Use the Hip Roof Calculator — Step-by-Step Example

Let’s work through a simple example.

• Building Span = 20 ft
• Building Length = 30 ft
• Overhang = 2 ft
• Roof Pitch Rise = 6 (6/12 pitch)
• Rafter Spacing = 24 in (2 ft)

Step 1: Common Rafter Run
(20 ÷ 2) + 2 = 12 ft

Step 2: Total Roof Rise
12 × (6 ÷ 12) = 6 ft

Step 3: Common Rafter Length
√(12² + 6²) = √(144 + 36) = √180 ≈ 13.42 ft

Step 4: Hip Rafter Run and Length
Hip Run = 12 × √2 ≈ 16.97 ft
Hip Rafter Length = √(16.97² + 6²) ≈ 18 ft

Step 5: Ridge Board Length
30 − 20 = 10 ft

Step 6: Roof Angle
arctan(6 ÷ 12) = arctan(0.5) ≈ 26.6°

Step 7: Roof Area
((30 + 4) × (20 + 4)) ÷ cos(26.6°) = (34 × 24) ÷ 0.894 ≈ 913 ft²

Final Result: In this case, you’d need common rafters about 13.42 ft long, hip rafters about 18 ft long, a ridge board of 10 ft, and the roof area is around 913 ft².

Additional Information

Here are some common roof pitch values and their approximate angles:

Roof Pitch	Angle (degrees)
4/12	18.4°
6/12	26.6°
8/12	33.7°
12/12	45.0°

This can help you quickly visualize how steep your roof design will be.

FAQs