Rafter Dimensions Calculator

Total Span (ft):

Roof Pitch (X in 12):

Rafter Overhang (in):

Rafter Spacing (in):

Rafter Depth (in):

Rafter Width (in):

Wall Plate Width (in):

Live Load (psf):

Dead Load (psf):

Wood Species/Grade: Douglas Fir-Larch No. 2 Southern Pine No. 2 Hem-Fir No. 2

Deflection Limit: L/240 (Common) L/360 (Stricter)

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Consider a deeper rafter or smaller wall plate.)"; } if (birdsmouthHeelCutDepthIn >= rafterDepthIn) { birdsmouthWarning = " (Error: Heel cut depth exceeds rafter depth. Rafter will fail.)"; } // — Load & Strength Calculations — var Fb, E; // Allowable Bending Stress (psi), Modulus of Elasticity (psi) if (woodSpecies == "Southern Pine No. 2") { Fb = 1450; E = 1600000; } else if (woodSpecies == "Douglas Fir-Larch No. 2") { Fb = 1450; E = 1700000; } else if (woodSpecies == "Hem-Fir No. 2") { Fb = 1000; E = 1300000; } else { // Default to a conservative value if somehow an unknown option is selected Fb = 1000; E = 1300000; } var deflectionFactor; if (deflectionLimit == "L/240") { deflectionFactor = 240; } else if (deflectionLimit == "L/360") { deflectionFactor = 360; } else { // Default deflectionFactor = 240; } // Actual Rafter Properties (assuming rectangular section) var actualSx = (rafterWidthIn * Math.pow(rafterDepthIn, 2)) / 6; // Section Modulus (in^3) var actualI = (rafterWidthIn * Math.pow(rafterDepthIn, 3)) / 12; // Moment of Inertia (in^4) // Load Calculations var totalLoadPsf = liveLoadPsf + deadLoadPsf; var tributaryWidthFt = rafterSpacingIn / 12; var uniformLoadPlf = totalLoadPsf * tributaryWidthFt; // Pounds per linear foot var uniformLoadPli = uniformLoadPlf / 12; // Pounds per linear inch // Bending Moment (M) – using horizontal run for effective span var effectiveSpanBendingIn = rafterRunFt * 12; var maxBendingMomentInLb = (uniformLoadPli * Math.pow(effectiveSpanBendingIn, 2)) / 8; // For simply supported beam // Required Section Modulus (Sx_req) var requiredSx = maxBendingMomentInLb / Fb; // Deflection Calculation – using actual rafter length for effective span var effectiveSpanDeflectionIn = rafterLengthFt * 12; var allowableDeflectionIn = effectiveSpanDeflectionIn / deflectionFactor; // Required Moment of Inertia (I_req) // Rearranging delta = (5 * w * L^4) / (384 * E * I) to solve for I var requiredI = (5 * uniformLoadPli * Math.pow(effectiveSpanDeflectionIn, 4)) / (384 * E * allowableDeflectionIn); // Pass/Fail Checks var bendingCheck = (actualSx >= requiredSx) ? "PASS" : "FAIL"; var deflectionCheck = (actualI >= requiredI) ? "PASS" : "FAIL"; // — Display Results — var resultsHtml = "

Calculation Results:

"; resultsHtml += "Rafter Run: " + rafterRunFt.toFixed(2) + " ft"; resultsHtml += "Rafter Rise: " + rafterRiseFt.toFixed(2) + " ft"; resultsHtml += "Rafter Length (Ridge to Wall Plate): " + rafterLengthFt.toFixed(2) + " ft"; resultsHtml += "Total Rafter Length (including overhang): " + totalRafterLengthFt.toFixed(2) + " ft"; resultsHtml += "Roof Angle: " + (angleRad * 180 / Math.PI).toFixed(2) + " degrees"; resultsHtml += "Birdsmouth Seat Cut Length: " + birdsmouthSeatCutLengthIn.toFixed(2) + " in"; resultsHtml += "Birdsmouth Heel Cut Depth: " + birdsmouthHeelCutDepthIn.toFixed(2) + " in" + birdsmouthWarning + ""; resultsHtml += "

"; resultsHtml += "Actual Rafter Section Modulus (Sx): " + actualSx.toFixed(2) + " in³"; resultsHtml += "Required Section Modulus (Sx): " + requiredSx.toFixed(2) + " in³"; resultsHtml += "Bending Check: " + bendingCheck + ""; resultsHtml += "

"; resultsHtml += "Actual Rafter Moment of Inertia (I): " + actualI.toFixed(2) + " in⁴"; resultsHtml += "Required Moment of Inertia (I): " + requiredI.toFixed(2) + " in⁴"; resultsHtml += "Deflection Check (" + deflectionLimit + "): " + deflectionCheck + ""; resultDiv.innerHTML = resultsHtml; }

Understanding Rafter Dimensions for Roof Framing

Rafters are crucial structural components of a roof, forming the framework that supports the roof deck and all associated loads. Properly sizing and cutting rafters is essential for the safety, stability, and longevity of any building. This calculator helps you determine key rafter dimensions and provides a preliminary check for bending and deflection based on common engineering principles.

Key Rafter Terminology and Inputs:

Total Span: This is the horizontal distance from the outside edge of one wall plate to the outside edge of the opposite wall plate. The rafter's 'run' is typically half of this total span.
Roof Pitch (X in 12): Represents the slope of your roof. A 6/12 pitch, for example, means the roof rises 6 inches vertically for every 12 inches it extends horizontally. This angle is critical for determining rafter length and cuts.
Rafter Overhang: The portion of the rafter that extends horizontally beyond the exterior wall plate, forming the eaves. This provides protection to the walls and can be a design element.
Rafter Spacing: The on-center distance between individual rafters. Common spacings are 16 inches or 24 inches, which directly impacts the load each rafter must bear.
Rafter Depth & Width: These are the actual dimensions of the lumber used for the rafters (e.g., a "2×10" typically has an actual depth of 9.25 inches and a width of 1.5 inches). These dimensions are vital for calculating the rafter's strength and stiffness.
Wall Plate Width: The actual width of the top plate of your wall (e.g., 3.5 inches for a 2×4 wall, 5.5 inches for a 2×6 wall). This dimension is used for the birdsmouth cut.
Live Load (psf): Variable loads that a roof must support, such as snow, wind, or temporary loads from people working on the roof. Measured in pounds per square foot (psf).
Dead Load (psf): Permanent, static loads, including the weight of the roofing materials (shingles, tiles), sheathing, insulation, and the rafters themselves. Also measured in psf.
Wood Species/Grade: Different types of wood and their grades (e.g., Douglas Fir-Larch No. 2, Southern Pine No. 2) have varying structural properties like allowable bending stress (Fb) and modulus of elasticity (E). These properties are crucial for determining how much load a rafter can safely carry and how much it will deflect.
Deflection Limit: The maximum allowable sag or bending of a rafter under load, typically expressed as a fraction of its span (L/240 or L/360). L/360 is a stricter limit, often used for ceilings where plaster or drywall might crack with excessive deflection.

Understanding the Outputs:

Rafter Run: The horizontal distance from the outside of the wall plate to the center of the ridge.
Rafter Rise: The vertical distance from the top of the wall plate to the top of the ridge.
Rafter Length (Ridge to Wall Plate): The actual diagonal length of the rafter from the ridge board to the wall plate, excluding any overhang.
Total Rafter Length (including overhang): The full length of the rafter lumber needed, from the ridge cut to the end of the overhang.
Roof Angle: The angle of the roof slope in degrees, useful for setting up saws.
Birdsmouth Seat Cut Length: The horizontal portion of the birdsmouth cut that rests on the wall plate. This is typically equal to the wall plate's width.
Birdsmouth Heel Cut Depth: The vertical portion of the birdsmouth cut. This is the depth of the cut from the bottom edge of the rafter. It's important that this cut doesn't remove too much material, compromising the rafter's strength.
Section Modulus (Sx): A geometric property of the rafter's cross-section that indicates its resistance to bending. The 'Actual Sx' must be greater than or equal to the 'Required Sx' for the rafter to safely resist bending forces.
Moment of Inertia (I): Another geometric property indicating the rafter's resistance to deflection (sagging). The 'Actual I' must be greater than or equal to the 'Required I' for the rafter to meet deflection limits.
Bending Check & Deflection Check: These indicate whether the chosen rafter dimensions (depth and width) are sufficient to safely carry the specified loads without excessive bending or deflection, based on the selected wood species and deflection limit.

How to Use This Calculator:

Enter Your Roof's Dimensions: Input the total span, roof pitch, and desired rafter overhang.
Specify Rafter & Wall Plate Sizes: Provide the actual depth and width of the lumber you plan to use for your rafters, and the width of your wall's top plate.
Input Load Information: Estimate your live load (e.g., snow load for your region) and dead load (weight of roofing materials). Consult local building codes for specific requirements.
Select Wood Properties: Choose the wood species and grade you intend to use. This significantly impacts the rafter's strength.
Choose Deflection Limit: Select the appropriate deflection limit based on your project's requirements and local codes.
Click "Calculate": The calculator will provide all the geometric dimensions needed for cutting your rafters, along with structural checks for bending and deflection.

Important Considerations:

This calculator provides a helpful estimate based on simplified engineering principles for simply supported beams. However, actual structural design can be more complex, involving factors like continuous spans, multiple supports, specific connection details, and local building code variations. Always consult with a qualified structural engineer or your local building authority before finalizing your rafter design and construction plans.

The birdsmouth cut, in particular, can weaken a rafter if too much material is removed. The warning provided by the calculator regarding heel cut depth should be taken seriously. Ensure that the remaining rafter depth at the birdsmouth is adequate for structural integrity.