How this instrument works
Deflection is how far a beam sags at its center when a load pushes down on it. For a beam simply supported at both ends with a single point load applied at midspan — a common textbook case and a reasonable approximation for many real point loads — the maximum deflection follows a well-known closed-form formula from mechanics of materials: delta = P x L³ / (48 x E x I). The load P and span L drive the sag directly; the material's stiffness E and the cross-section's moment of inertia I resist it.
Moment of inertia (I) depends on the shape of the cross-section, not just its area — for a plain rectangular section it's I = b x d³/12, where b is width and d is depth. Because depth is cubed, a beam that's twice as deep resists deflection eight times as effectively as one twice as wide, which is why joists and beams are almost always installed with their long dimension standing vertically rather than lying flat.
This is a preliminary engineering estimate for planning purposes only. Before cutting lumber, ordering steel, or finalizing a real structure, have the design checked by a licensed structural engineer or reviewed against your local building department's requirements — actual code-compliant sizing applies additional adjustment factors this simplified formula does not. This calculator also reports the span-to-deflection ratio (L/deflection) as a reference number only — it does not compare that ratio against a specific code limit, since acceptable deflection varies by application (L/360 is a common floor criterion, L/240 a common roof-with-ceiling criterion, but your governing code may specify something else).
- Select the beam material (lumber, steel, or aluminum) to set its modulus of elasticity, E.
- Enter the center point load in pounds-force.
- Enter the span between supports in feet.
- Enter the section width and depth in inches (actual, not nominal, dimensions for lumber).
- Read the deflection at center span and the span-to-deflection ratio for reference against your project's deflection limit.
A single 2x10 Douglas Fir-Larch joist under a 200 lb point load
A single 2x10 joist (actual dimensions 1.5 in x 9.25 in) spans 8 ft between supports and carries a 200 lbf point load at its center. Douglas Fir-Larch lumber has a reference modulus of elasticity of about 1,600,000 psi. Moment of inertia: I = 1.5 x 9.25³ / 12 = 98.9316 in⁴. Converting the 8 ft span to inches (96 in) and applying the formula: delta = 200 x 96³ / (48 x 1,600,000 x 98.9316) = 0.0233 in — a small, realistic deflection for a light point load on a stiff joist.
That works out to a span-to-deflection ratio of roughly 4,122:1 — comfortably stiffer than the common L/360 floor guideline (which would allow up to about 0.267 in of deflection over this span). Swap the same 2x4 in section into a 29,000,000 psi steel bar instead of 1,600,000 psi lumber under a heavier 1,000 lbf load, and the deflection drops to about 0.116 in over a 10 ft span — illustrating how dramatically material stiffness changes real-world sag. This is a preliminary engineering estimate for planning purposes only. Before cutting lumber, ordering steel, or finalizing a real structure, have the design checked by a licensed structural engineer or reviewed against your local building department's requirements — actual code-compliant sizing applies additional adjustment factors this simplified formula does not.
Questions
Is this deflection number code-compliant for my project?
Not on its own. This calculator computes raw deflection from a standard mechanics-of-materials formula, but it doesn't check that result against a specific building-code deflection limit (which varies by application — L/360 for floors and L/240 for roofs with a ceiling are common, but your local code may differ). Treat this as a preliminary estimate and have a licensed structural engineer or your building department confirm the final design.
Why does beam depth matter so much more than width?
Moment of inertia for a rectangular section is proportional to width times depth cubed (I = bd³/12). Because depth is cubed and width isn't, doubling a beam's depth increases its stiffness eightfold, while doubling its width only doubles it — which is why lumber and steel beams are installed standing on edge rather than lying flat.
What's the difference between this and the beam-load calculator?
This calculator finds how far a given beam sags under a given load (a serviceability check). The beam-load calculator instead finds the maximum uniform load a beam can carry before its bending stress hits an allowable limit (a strength check). A real design needs both checks — and the governing case is whichever gives the smaller allowable span or load.
Should I use actual or nominal lumber dimensions?
Always use actual (dressed) dimensions — a nominal 2x10, for example, actually measures about 1.5 in by 9.25 in after milling and drying. Using nominal dimensions in this formula will noticeably understate the real deflection because the actual section is smaller than its name suggests.