Beam Deflection Calculator
Calculate the deflection of a simply supported beam under a uniform load from its span, load, modulus of elasticity, and moment of inertia.
How this calculator works
When a beam spans between two supports and carries an even load, it doesn’t just resist breaking — it also bends a measurable amount under that load. This calculator takes the span, the uniform load, the beam material’s stiffness, and the beam’s cross-sectional shape, and returns how far the beam sags at its center.
That sag matters because building codes and common practice set limits on how much a beam is allowed to bend before it causes problems like bouncy floors or cracked drywall, even if the beam itself is strong enough not to break.
Formula: For a simply supported beam with a uniform load, deflection = (5 × w × L⁴) ÷ (384 × E × I), where w is load in lb per inch, L is span in inches, E is the modulus of elasticity in psi, and I is the moment of inertia in in⁴. A common deflection limit is L/360 for live load.
Worked example
A 12 ft span carrying a 200 lb/ft load:
- Span: 12 ft = 144 in
- Load: 200 lb/ft ≈ 16.67 lb/in
- E = 1,600,000 psi, I = 100 in⁴
- Deflection ≈ 0.583 in
- L/360 limit for this span: 144 ÷ 360 = 0.4 in
- This beam exceeds that limit and would need to be stiffer (more I) or shorter
Notes
E and I both depend on the beam’s material and cross-section, not just the load it carries. E comes from a lumber species-and-grade design-value table, since different wood species and grades are stiffer than others. I is a property of the beam’s shape, and deeper beams have much higher I than shallow ones of the same width — doubling a beam’s depth increases I roughly eightfold, which is why going deeper is such an effective way to cut deflection.
How to use
Enter the span, the uniform load per foot, the modulus of elasticity for your beam material, and the moment of inertia for your beam’s cross-section. The calculator returns the deflection at the center of the span so you can compare it against your deflection limit, such as L/360.
This is a planning estimate using standard beam-deflection mechanics, not a substitute for engineering design. Confirm actual beam size, material, and deflection limits with a structural engineer and your local building code.
Frequently asked questions
What is beam deflection?
Deflection is how far a beam bends or sags under load, measured as a distance at the point of greatest movement — usually the center of the span. Every beam deflects at least a little under load; the question is whether that movement stays within an acceptable limit. Too much deflection can cause a bouncy floor, cracked finishes, or doors that stick, even if the beam is in no danger of breaking.
What is the L/360 deflection limit?
L/360 is a common serviceability limit for live load deflection, meaning the beam should not sag more than its span length divided by 360. For a 12 ft (144 in) span, that works out to 0.4 in. It is a comfort and cosmetic limit, not a strength limit — a beam can pass a strength check and still fail L/360 if it is too flexible.
What are E and I in the deflection formula?
E is the modulus of elasticity, a measure of how stiff the beam material is, in pounds per square inch. I is the moment of inertia, a measure of how the beam's cross-section resists bending, in inches to the fourth power. Both come from tables — E from a lumber or steel design-value chart, and I from the beam's depth and width or a steel shape chart.
How do I reduce excessive beam deflection?
The two levers are stiffness (E) and shape (I), since load and span are usually fixed by the design. Switching to a stiffer material raises E, while using a deeper or wider beam raises I — and because I grows with the cube of depth, even a modest increase in beam depth can cut deflection substantially. Shortening the span also helps, since deflection grows with the fourth power of span length.
Estimates only. Verify quantities with your supplier before purchasing.