Pitched Roof Calculator
Use this calculator to determine key dimensions for your pitched roof project, including rafter length, roof pitch, number of rafters, and total roof surface area. Accurate measurements are crucial for material ordering and structural integrity.
Understanding Pitched Roof Calculations
A pitched roof, characterized by its sloping surfaces, is a common and durable roofing style. Calculating its dimensions accurately is fundamental for proper construction, material estimation, and ensuring structural stability. This calculator helps you determine critical measurements for a standard gable roof.
Key Terms Explained:
- Building Width: The total horizontal distance across the building, from outside wall to outside wall. For a gable roof, the 'run' (half-span) is derived from this.
- Roof Rise: The vertical distance from the top of the wall plate (where the rafter rests) to the peak of the roof (the ridge). This, along with the run, defines the roof's slope.
- Eave Overhang: The horizontal distance the roof extends beyond the exterior wall. Overhangs protect walls from rain and provide shade.
- Roof Length: The horizontal length of the building along the ridge line. This is used to calculate the total number of rafters and the roof's surface area.
- Rafter Spacing: The center-to-center distance between individual rafters. Common spacings are 16 or 24 inches, dictated by local building codes and structural requirements.
How the Calculations Work:
The calculator uses fundamental geometry to derive the roof's dimensions:
- Run: This is simply half of the building's width. It forms one leg of a right-angled triangle.
- Structural Rafter Length: This is the hypotenuse of the right-angled triangle formed by the 'run' and 'rise'. The Pythagorean theorem (a² + b² = c²) is used:
sqrt(Run² + Rise²). This is the length of the rafter from the wall plate to the ridge.
- Total Rafter Length: To get the actual cutting length for a rafter, the eave overhang is added to the structural rafter length. This accounts for the portion of the rafter that extends beyond the wall.
- Roof Pitch (Angle): The angle of the roof's slope is calculated using trigonometry:
atan(Rise / Run). The result is converted from radians to degrees.
- Number of Rafters: This is determined by dividing the roof length by the rafter spacing (converted to feet) and adding one for the end rafter. This is then multiplied by two for both sides of a gable roof.
- Total Roof Surface Area: The area of one roof slope is calculated by multiplying the total rafter length (including overhang) by the roof length. This is then multiplied by two for both slopes of a gable roof. This area is crucial for estimating roofing materials like shingles, underlayment, and decking.
Example Calculation:
Let's consider a building with the following dimensions:
- Building Width: 24 feet
- Roof Rise: 6 feet
- Eave Overhang: 1.5 feet
- Roof Length: 36 feet
- Rafter Spacing: 16 inches (1.33 feet)
Based on these inputs, the calculator would provide:
- Run: 24 ft / 2 = 12 feet
- Structural Rafter Length: sqrt(12² + 6²) = sqrt(144 + 36) = sqrt(180) ≈ 13.42 feet
- Total Rafter Length (for cutting): 13.42 ft + 1.5 ft = 14.92 feet
- Roof Pitch: atan(6 / 12) = atan(0.5) ≈ 26.57 degrees
- Number of Rafters per side: ceil(36 ft / 1.33 ft) + 1 = ceil(27.07) + 1 = 28 + 1 = 29 rafters
- Total Rafters: 29 * 2 = 58 rafters
- Total Roof Surface Area: (14.92 ft * 36 ft) * 2 = 537.12 sq ft * 2 = 1074.24 square feet
These calculations provide the essential figures needed to plan and execute your pitched roof construction effectively.
.calculator-container {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
max-width: 700px;
margin: 20px auto;
padding: 25px;
border: 1px solid #e0e0e0;
border-radius: 10px;
background-color: #ffffff;
box-shadow: 0 4px 12px rgba(0, 0, 0, 0.08);
}
.calculator-container h2 {
text-align: center;
color: #333;
margin-bottom: 20px;
font-size: 28px;
}
.calculator-container h3 {
color: #444;
margin-top: 30px;
margin-bottom: 15px;
font-size: 22px;
}
.calculator-container h4 {
color: #555;
margin-top: 25px;
margin-bottom: 10px;
font-size: 18px;
}
.calculator-container p {
line-height: 1.6;
color: #666;
margin-bottom: 10px;
}
.calculator-form .form-group {
margin-bottom: 15px;
display: flex;
flex-direction: column;
}
.calculator-form label {
margin-bottom: 8px;
font-weight: bold;
color: #555;
font-size: 15px;
}
.calculator-form input[type="number"] {
padding: 12px;
border: 1px solid #ccc;
border-radius: 6px;
font-size: 16px;
width: 100%;
box-sizing: border-box;
transition: border-color 0.3s ease;
}
.calculator-form input[type="number"]:focus {
border-color: #007bff;
outline: none;
box-shadow: 0 0 5px rgba(0, 123, 255, 0.3);
}
.calculator-form button {
background-color: #007bff;
color: white;
padding: 14px 25px;
border: none;
border-radius: 6px;
cursor: pointer;
font-size: 18px;
margin-top: 20px;
width: 100%;
transition: background-color 0.3s ease, transform 0.2s ease;
}
.calculator-form button:hover {
background-color: #0056b3;
transform: translateY(-2px);
}
.calculator-result {
margin-top: 30px;
padding: 20px;
border: 1px solid #d4edda;
border-radius: 8px;
background-color: #e9f7ef;
color: #155724;
font-size: 17px;
line-height: 1.8;
}
.calculator-result strong {
color: #0a3622;
}
.calculator-result p {
margin-bottom: 8px;
}
.calculator-article {
margin-top: 40px;
padding-top: 20px;
border-top: 1px solid #eee;
}
.calculator-article ul {
list-style-type: disc;
margin-left: 20px;
padding-left: 0;
color: #666;
}
.calculator-article ul li {
margin-bottom: 8px;
line-height: 1.6;
}
.calculator-article code {
background-color: #f0f0f0;
padding: 2px 5px;
border-radius: 4px;
font-family: 'Courier New', Courier, monospace;
color: #c7254e;
}
function calculatePitchedRoof() {
var buildingWidth = parseFloat(document.getElementById("buildingWidth").value);
var roofRise = parseFloat(document.getElementById("roofRise").value);
var eaveOverhang = parseFloat(document.getElementById("eaveOverhang").value);
var roofLength = parseFloat(document.getElementById("roofLength").value);
var rafterSpacingInches = parseFloat(document.getElementById("rafterSpacing").value);
// Input validation
if (isNaN(buildingWidth) || buildingWidth <= 0) {
document.getElementById("result").innerHTML = "Please enter a valid Building Width (must be a positive number).";
return;
}
if (isNaN(roofRise) || roofRise <= 0) {
document.getElementById("result").innerHTML = "Please enter a valid Roof Rise (must be a positive number).";
return;
}
if (isNaN(eaveOverhang) || eaveOverhang < 0) {
document.getElementById("result").innerHTML = "Please enter a valid Eave Overhang (can be 0 or a positive number).";
return;
}
if (isNaN(roofLength) || roofLength <= 0) {
document.getElementById("result").innerHTML = "Please enter a valid Roof Length (must be a positive number).";
return;
}
if (isNaN(rafterSpacingInches) || rafterSpacingInches <= 0) {
document.getElementById("result").innerHTML = "Please enter a valid Rafter Spacing (in inches, must be a positive number).";
return;
}
// Convert rafter spacing to feet
var rafterSpacingFeet = rafterSpacingInches / 12;
// 1. Run (Half-span)
var run = buildingWidth / 2;
// 2. Structural Rafter Length (from wall plate to ridge)
var structuralRafterLength = Math.sqrt(Math.pow(run, 2) + Math.pow(roofRise, 2));
// 3. Total Rafter Length (for cutting, including overhang)
var totalRafterLength = structuralRafterLength + eaveOverhang;
// 4. Roof Pitch (Angle in degrees)
var roofPitchRadians = Math.atan(roofRise / run);
var roofPitchDegrees = roofPitchRadians * (180 / Math.PI);
// 5. Number of Rafters per side
// We need to ensure enough rafters, so use Math.ceil and add 1 for the end rafter.
var numRaftersPerSide = Math.ceil(roofLength / rafterSpacingFeet) + 1;
// 6. Total Rafters (for a simple gable roof)
var totalRafters = numRaftersPerSide * 2;
// 7. One Side Surface Area (including overhang)
var oneSideSurfaceArea = totalRafterLength * roofLength;
// 8. Total Roof Surface Area (for both sides of a gable roof)
var totalRoofSurfaceArea = oneSideSurfaceArea * 2;
// Display results
var resultHtml = "
Calculated Roof Dimensions:
";
resultHtml += "
Run (Half-span): " + run.toFixed(2) + " feet";
resultHtml += "
Structural Rafter Length: " + structuralRafterLength.toFixed(2) + " feet (from wall plate to ridge)";
resultHtml += "
Total Rafter Length (for cutting): " + totalRafterLength.toFixed(2) + " feet";
resultHtml += "
Roof Pitch: " + roofPitchDegrees.toFixed(2) + " degrees";
resultHtml += "
Total Number of Rafters: " + Math.round(totalRafters) + " (for a gable roof)";
resultHtml += "
Total Roof Surface Area: " + totalRoofSurfaceArea.toFixed(2) + " square feet";
document.getElementById("result").innerHTML = resultHtml;
}