Beam Span Calculator
Find the maximum deflection-governed span for a beam, joist, or LVL from its modulus of elasticity, moment of inertia, and load — solving the standard deflection formula for span.
How this calculator works
A beam that’s too long for its stiffness will sag more than a chosen deflection limit allows, even if it’s in no danger of breaking. This calculator starts from the standard deflection formula and solves it backward — instead of asking how much a given span deflects, it asks how long a span can be before deflection hits your limit.
It needs the beam material’s modulus of elasticity (E), the section’s moment of inertia (I), the uniform load, and a deflection ratio such as L/360.
Formula: For a simply supported beam under uniform load, deflection = 5wL⁴ ÷ (384EI). Solving for L at a target deflection limit of span ÷ ratio gives the maximum span: L = cube root of (384 × E × I ÷ (5 × ratio × w)), with w converted to pounds per inch.
Worked example
E = 1,600,000 psi (typical Douglas fir-larch), I = 300 in⁴, load = 40 lb/ft, deflection limit L/360:
- Maximum span ≈ 26.10 ft
Notes
This covers deflection-governed span only. The actual code-approved span is whichever is shorter — deflection or bending strength (moment capacity). Real span tables, such as AWC span tables or LVL manufacturer literature, account for both, plus the exact design values for the species and grade involved.
This calculator lets you check the deflection side of that math with your own numbers, for LVL, glulam, sawn lumber, or steel — just supply that material’s E and your section’s I, which you can get from the Moment of Inertia Calculator.
How to use
Enter the modulus of elasticity for your beam material, the moment of inertia for your section, the uniform load per foot, and your deflection ratio (commonly 360 for floor joists). The calculator returns the maximum span before that deflection limit is exceeded — check it against the Beam Load Capacity Calculator’s bending-strength result and use the shorter of the two.
This is a planning estimate using standard mechanics formulas, not a substitute for engineering design. Confirm actual member sizing and code compliance with a licensed structural engineer.
Frequently asked questions
What does 'deflection-governed span' mean?
It means the maximum span at which a beam's sag stays within a chosen deflection limit, such as L/360. A beam's real maximum span is the shorter of two limits — deflection and bending strength — so a deflection-governed number is only half the check. The other half is the bending-strength (moment capacity) limit.
What is the L/360 ratio used for?
L/360 is a common deflection limit for floor joists under live load, meaning deflection can't exceed the span divided by 360. Other ratios apply to other situations — L/240 is common for roof members, for example. The ratio you use should match your local building code and the member's application, not just floor joists by default.
Can I use this for steel beams, not just wood?
Yes. The deflection formula it solves works for any material, since it uses the material's modulus of elasticity (E) and the section's moment of inertia (I) as inputs. Use steel's E value and the section's I from a steel shape chart, or from the Moment of Inertia Calculator for a custom section.
Why is my calculated span longer than what's in a published span table?
Published span tables (like AWC or LVL manufacturer tables) account for both deflection and bending strength, and list whichever produces the shorter span. This calculator checks deflection only, so if bending strength is the controlling factor for your beam, the real safe span will be shorter than what this tool returns.
Estimates only. Verify quantities with your supplier before purchasing.