Wood Beam Span Calculator

Enter Calculation

Uniform Load w (lb/ft)

Span L (ft)

Allowable Bending Stress Fb (psi)

Results

Required Section Modulus (S)

36

cubic inches (in³)

Maximum Bending Moment	3,600 lb-ft
Maximum Moment (lb-in)	43,200 lb-in

What This Calculator Does

The Wood Beam Span Calculator estimates the maximum bending moment and the required section modulus for a simply supported wood beam carrying a uniformly distributed load. These two values are the foundation of beam sizing: the moment tells you how hard the load tries to bend the beam, and the section modulus tells you how stout the cross section must be to resist that bending without exceeding the wood's allowable stress.

How to Use It

Enter the uniform load w in pounds per linear foot, the clear span L in feet, and the allowable bending stress Fb in psi for your lumber grade and species. The calculator returns the maximum bending moment (in both lb-ft and lb-in) and the required section modulus in cubic inches. Compare that required S against the published section modulus of candidate beam sizes — choose one whose S is equal to or greater than the result.

The Formula Explained

For a simply supported beam with a uniform load, the maximum moment occurs at midspan and equals \(M = wL^2 / 8\). To find the section modulus we convert this moment from lb-ft to lb-in by multiplying by 12, then divide by the allowable bending stress: \(S = M(\text{in}) / F_b\). This comes from the bending stress relation \(\sigma = M / S\) rearranged to solve for S at the allowable stress limit.

$$S = \frac{12 \cdot M_{\max}}{\text{F}_b\text{ (psi)}}, \qquad M_{\max} = \frac{\text{w (lb/ft)} \cdot \text{L (ft)}^{2}}{8}$$

The bending moment is greatest at midspan, where \(M = wL^2/8\).

A simply supported beam carrying a uniform load w over span L, with reactions at each end.

Worked Example

Suppose w = 200 lb/ft, span L = 12 ft, and Fb = 1200 psi. The moment is $$M = 200 \times 12^2 / 8 = 200 \times 144 / 8 = 3{,}600 \text{ lb-ft}.$$ Converting: \(3{,}600 \times 12 = 43{,}200\) lb-in. The required section modulus is $$S = 43{,}200 / 1{,}200 = 36 \text{ in}^3.$$ You would then pick a beam (for example a doubled or built-up member) whose section modulus is at least 36 in³.

FAQ

What load value should I use? Combine the dead load and live load tributary to the beam, expressed per linear foot of beam length.

Does this check deflection? No — it sizes for bending strength only. Long spans are often governed by deflection limits, so check that separately.

Is this for a specific span condition? Yes: it assumes a single simply supported span with a uniformly distributed load. Cantilevers, point loads, or continuous beams use different moment formulas. Always have a qualified engineer verify structural work.