# Hip Roof Calculator – Hip Rafter Length – Framing Calculator

Nathan Clark | 🗓️Modified: March 3, 2024 | ⏳Time to read:4 min

In construction, particularly in roofing, understanding rafter lengths and hip rafters is crucial for designing and building structurally sound and aesthetically pleasing structures.

Rafters are structural components that support the roof and transfer its load to the walls of the building.

Hip rafters, specifically, are rafters that run diagonally from the ridge of the roof to the corners of the building, connecting the ends of common rafters.

In this comprehensive guide, we delve into the calculation of common rafter length and hip rafter length using a dedicated calculator.

We’ll cover the mathematical principles behind these calculations, the variables involved, and the significance of accurate rafter measurements in construction projects.

## Hip Rafter Length Calculator

Building Width ft in n
d
Overhangin n
d
Ridgeboard Thickness in n
d
Roof Pitch: 12

#### Results:

 Common Rafter Length ft in Common Rafter Length in Inches in Hip Rafter Length ft in Hip Rafter Length in Inches in

The hip rafter length calculator is a specialized tool designed to facilitate this process, particularly for complex roof designs featuring hip rafters. By inputting key parameters such as building width, overhang, ridge board thickness, and slope ratio, users can quickly obtain precise measurements for both common rafters and hip rafters.

### Functionality:

The hip rafter length calculator is a versatile tool that streamlines the calculation process for common rafters and hip rafters. Its functionality revolves around four essential parameters:

1. Building Width: This parameter represents the horizontal span between the outside sheathing of the building's walls. It serves as the foundational dimension for determining rafter lengths.
2. Overhang: The overhang measurement indicates the distance from the outside sheathing to the sub-fascia, extending beyond the edge of the building. It accounts for the eaves of the roof and plays a crucial role in rafter length calculations.
3. Ridge Board Thickness: The ridge board, positioned at the peak of the roof, is a structural component that connects the upper ends of the rafters. Its thickness impacts the overall height of the roof and influences rafter lengths.
4. Slope Ratio: The slope ratio, expressed as the amount of rise per foot of run, defines the steepness of the roof. It directly affects the length and angle of the rafters, including both common rafters and hip rafters.

## Calculation of Rafter Lengths

The calculation of rafter lengths involves several key variables, including the building width, overhang, ridge board thickness, and slope ratio. Each of these variables contributes to determining the length of both common rafters and hip rafters. Let's break down the calculation process:

1. Building Width: This refers to the distance between the outside sheathing of the walls on either side of the building. It serves as the horizontal span that the rafters will cover.
2. Overhang: The overhang is the distance from the outside sheathing to the sub-fascia, extending beyond the edge of the building. It adds extra length to the rafters to accommodate the roof's eaves and provide protection from the elements.
3. Ridge Board Thickness: The ridge board is a horizontal beam that runs along the peak of the roof, connecting the upper ends of the rafters. Its thickness affects the overall height of the roof and consequently, the length of the rafters.
4. Slope Ratio: The slope ratio, also known as the pitch or rise per foot of run, determines the steepness of the roof. It represents the amount of vertical rise for every horizontal foot of run. The slope ratio is typically expressed in inches, indicating the rise per foot of horizontal run.

## Common Rafter Length Calculation

The common rafter extends from the ridge board to the top plate of the exterior wall. Its length is influenced by the building width, overhang, ridge board thickness, and slope ratio. The calculation involves trigonometric principles, particularly the Pythagorean theorem and the tangent function, to determine the hypotenuse of a right triangle formed by the rafter and the roof's slope. The formula for calculating the common rafter length is as follows:

Common Rafter Length = Building Width^2 + Overhang^2 + Ridge Board Thickness × Slope Ratio

## Hip Rafter Length Calculation

Hip rafters run diagonally from the ridge board to the corners of the building, intersecting with the common rafters. Their length depends on the common rafter length and the geometry of the roof. The calculation of hip rafter length involves trigonometric principles, including the sine and cosine functions, to determine the length of the hypotenuse of a right triangle formed by the hip rafter and the slope of the roof. The formula for calculating the hip rafter length is as follows:

Hip Rafter Length = (Common Rafter Length × cos(Slope Angle))^2 + (Building Width × sin(Slope Angle))^2

## Importance of Accurate Rafter Measurements

Accurate measurements of rafter lengths, including common rafters and hip rafters, are essential for several reasons:

1. Structural Integrity: Properly sized rafters ensure the structural integrity and stability of the roof. Inadequate rafter lengths can lead to sagging, roof collapse, or structural failure, compromising the safety of the building and its occupants.
2. Aesthetic Appeal: Well-proportioned rafters contribute to the aesthetic appeal of the roof and the overall architectural design of the building. Precise measurements ensure uniformity and symmetry, enhancing the visual impact of the structure.
3. Material Efficiency: Optimizing rafter lengths minimizes material waste and reduces construction costs. Accurate measurements help contractors plan and order the right quantity of lumber, minimizing excess material and associated expenses.
4. Roof Performance: The length of rafters affects the roof's performance in terms of drainage, insulation, and weather resistance. Properly sized rafters facilitate effective water runoff, prevent moisture buildup, and support the installation of insulation and roofing materials.

## The Hip Rafter Length Calculator

The hip rafter length calculator simplifies the process of calculating common rafter lengths and hip rafter lengths by providing a user-friendly interface and automated calculations. It allows users to input the building width, overhang, ridge board thickness, and slope ratio, generating accurate results for both rafter types.

## How to Use the Calculator

Using the hip rafter length calculator is straightforward:

1. Input Parameters: Enter the building width in feet and inches, the overhang in inches, the ridge board thickness in inches, and the slope ratio (rise per foot of run) in inches.
2. View Results: Once the parameters are entered, the calculator computes the common rafter length and hip rafter length, displaying the results in both feet and inches for convenience.
3. Adjust Parameters: Users can adjust the input parameters as needed to explore different scenarios and variations in roof design.

### How do you calculate the length of a hip rafter?

Calculating the length of a hip rafter involves trigonometric principles and the dimensions of your roof structure. Here's a step-by-step guide:

1. Calculate the Common Rafter Length: Determine the length of a common rafter using the formula: Common Rafter Length = √(Building Width^2 + Overhang^2) + (Ridge Board Thickness × Slope Ratio).
2. Use Trigonometric Functions: Employ trigonometric functions to calculate the length of the hip rafter. The formula is: Hip Rafter Length = √((Common Rafter Length × cos(Slope Angle))^2 + (Building Width × sin(Slope Angle))^2).
3. Input the Parameters: Ensure you have the necessary parameters such as building width, overhang, ridge board thickness, and slope ratio to perform the calculations accurately.
4. Apply the Formula: Substitute the values into the formula and solve for the hip rafter length. This will provide you with the precise measurement needed for your roof design.

### What size are hip rafters?

Hip rafters come in various sizes depending on the dimensions and specifications of the roof they are supporting. The size of hip rafters is typically determined by factors such as the building width, slope of the roof, and structural requirements. It's crucial to consult building codes, engineering guidelines, and architectural plans to determine the appropriate size for your hip rafters.

### How do I calculate my hip roof?

Calculating a hip roof involves determining the dimensions, angles, and lengths of the roof's components, including hip rafters. Here's a basic outline of the process:

1. Measurements: Measure the building width, length, and height to determine the overall dimensions of the roof.
2. Determine Slope Ratio: Calculate the slope ratio, which represents the amount of rise per foot of run, using the rise and run measurements.
3. Calculate Common Rafter Length: Use the formula provided earlier to calculate the length of a common rafter.
4. Calculate Hip Rafter Length: Utilize the formula for hip rafter length to determine the diagonal length from the ridge board to the corners of the building.
5. Check for Accuracy: Ensure all measurements and calculations are accurate and consistent with building codes and structural requirements.

### What is the formula for rafter size?

The formula for calculating rafter size depends on several factors, including the span of the roof, the spacing of the rafters, the load they will support, and local building codes. However, a basic formula for determining the size of a common rafter is:

Rafter Size = (Span × Spacing × Load Factor) ÷ (Depth Factor × Species Factor × Grade Factor).

The specific values for the load factor, depth factor, species factor, and grade factor can vary based on regional building codes and engineering standards. It's essential to consult these guidelines and possibly consult with a structural engineer to determine the appropriate rafter size for your project.

### Common Rafter Length per Foot

The common rafter length per foot is a term used to express the ratio of the rafter length to the horizontal span per foot of run. It's calculated by dividing the total rafter length by the horizontal span. This ratio helps determine the pitch or slope of the roof and is crucial for ensuring proper drainage and structural integrity.