Wood Beam Span Calculator
Allowable span estimate for a sawn-lumber beam under a uniform load — an estimate, not an engineering design.
Estimate only — this is not an engineering sign-off
This tool applies a published code equation or standard beam formula to the numbers you enter. It does not know your building, your local code amendments, your soil, your connections, or your load path. The result is a planning estimate for sizing conversations and material take-offs only.
- Every design value (loads, allowable stresses, factors) is your input — a wrong value in gives a wrong answer out.
- Allowable-stress inputs (Fb', Fv', E) must already include every NDS adjustment factor — choosing those factors is engineering judgement.
- Uniform load, simple span, fully braced only. Point loads, cantilevers, notches, connections and bearing are not checked.
- Not valid for LVL / LSL / PSL / glulam / I-joists — use the manufacturer's span tables.
- No load path, connection, lateral, uplift, bearing, notch, hole, fire, or serviceability check beyond the one stated formula.
A licensed engineer or your local building official must review and stamp the final design before you build or order structural members.
Result appears here
Fill in the fields and press Calculate.
Formula, calculation, assumptions and sources
Section modulus S = (b·plies)·d² ÷ 6; moment of inertia I = (b·plies)·d³ ÷ 12; area A = (b·plies)·d
Bending: M = w·L² ÷ 8 ≤ Fb'·S → L = √(8·Fb'·S ÷ w)
Shear: V = w·L ÷ 2 ≤ (2⁄3)·Fv'·A → L = 4·Fv'·A ÷ (3·w)
Deflection: 5·w·L⁴ ÷ (384·E·I) ≤ L ÷ k → L = ∛(384·E·I ÷ (5·w·k))
Allowable span = the smallest of the three
Run the calculation to see each step with your own numbers.
Three-ply 2x10 (1.5×9.25), DF-L, Fb' = 1,200 psi, Fv' = 180 psi, E = 1,600,000 psi, 400 plf total load, L/240.
Built-up width = 4.5 in; S = 4.5 × 9.25² ÷ 6 ≈ 64.2 in³; I ≈ 296.8 in⁴; A ≈ 41.6 in²
Bending L = √(8 × 1,200 × 64.2 ÷ (400/12)) ≈ 11.3 ft
Shear L = 4 × 180 × 41.6 ÷ (3 × 33.3) ≈ 25.0 ft; deflection L (L/240) ≈ 13.8 ft
Governing ≈ 11.3 ft (bending) — verify with an engineer
- Simply-supported single span, uniformly distributed load, load applied to the top edge, beam laterally braced against rotation and buckling (Cl = 1.0).
- You must enter ALLOWABLE (adjusted) stresses — the NDS reference value times every applicable factor (load duration CD, size CF, repetitive Cr, wet service CM, incising Ci, temperature Ct, beam stability CL). Getting these factors right is an engineering judgement.
- Built-up beams assume the plies are fastened to share load per the NDS / manufacturer; a side-loaded built-up beam needs each ply connected for its share.
- No check of bearing length, connections, notches/holes, point loads, cantilevers, uplift, or vibration. Point loads and non-uniform loads change everything.
- For engineered lumber (LVL, LSL, PSL, glulam, I-joists) use the manufacturer's span tables and software — their allowable-stress basis differs.
- Why do I have to enter the stress values myself?
- Because the allowable stress isn't a single number — it's the tabulated value for your species and grade, multiplied by factors for load duration, member size, moisture, repetitive use and stability. Those depend on your project. The NDS Supplement has the base values; an engineer applies the factors.
- Can I use this for an LVL or glulam beam?
- Use it only for solid sawn lumber. Engineered products have their own published allowable stresses and span tables — use the manufacturer's literature or software, which also handles their specific bearing and connection requirements.
Beam mechanics
Elastic bending, shear and deflection of a simply-supported beam under uniform load (M = wL²/8, V = wL/2, Δ = 5wL⁴/384EI) — standard mechanics of materials. Deflection limits per IRC Table R301.7.
Allowable stresses
AWC National Design Specification (NDS) for Wood Construction and NDS Supplement 'Design Values for Wood Construction'. Same allowable-stress-design basis as the AWC Span Calculator and the IRC / AWC WFCM span tables.
About the Wood Beam Span Calculator
The Wood Beam Span Calculator estimates how far a simply-supported sawn or built-up wood beam can span under a uniform load, checking bending, shear and deflection and reporting the smallest of the three. Every design value — the allowable stresses, the load per foot, the deflection limit — is your input from the NDS Supplement, and choosing the adjustment factors correctly is engineering judgement. It is not valid for LVL, LSL, PSL, glulam or I-joists.
What you enter
- Single-ply width b (in) — Actual width of one ply. A 2x is 1.5 in; a 1¾ in LVL is 1.75.
- Depth d (in) — Actual depth. 2x10 = 9.25 in, 2x12 = 11.25 in, LVL to order.
- Number of plies — Plies fastened to act together per the manufacturer / NDS.
- Total uniform load w (plf) — Total load the beam carries per lineal foot = tributary width × (dead + live/snow) load. lb per lineal ft.
- Allowable bending stress Fb' (psi) — NDS reference Fb × all applicable adjustment factors (CD, CF, Cr, CM, Ci…). e.g. DF-L No.2 2x10 with CD=1.0 ≈ 900×1.1 ≈ 990; enter YOUR adjusted value.
- Allowable shear stress Fv' (psi) — NDS reference Fv × adjustment factors. DF-L ≈ 180 (CD=1.0).
- Modulus of elasticity E (psi) — NDS reference E (× CM, Ci if applicable). DF-L No.2 ≈ 1,600,000; LVL ≈ 1,900,000–2,000,000.
- Deflection limit
What you get back
- Estimated allowable clear span — The smallest of the bending, shear and deflection limits. Clear span between supports.
- Bending-limited span — the exact result of the calculation.
- Shear-limited span — the exact result of the calculation.
- Deflection-limited span — the exact result of the calculation.
The formula, a worked example, the assumptions behind it and the sources are shown in full below the calculator.
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Part of the Framing calculators.