123 123Calculator

Beam Deflection Calculator

This beam deflection calculator will help you determine the maximum beam deflection of simply-supported or cantilever beams subjected to simple load configurations.

Pounds per foot for a uniform load, or total pounds for a point load.
Clear
Deflection0.4491 inL/321 — passes L/240 but fails L/360
L/360 limit0.4 inthe usual limit for a floor
L/240 limit0.6 inthe usual limit for a roof or ceiling
Bending stress1,731.1 psiagainst an allowable 1,200 psi for Douglas fir–larch
Stress checkoverstressed144.3% of allowable
Maximum moment86,400 lb·in7,200 lb·ft
Second moment of area (I)230.84 in⁴b d³ ÷ 12
Section modulus (S)49.911 in³b d² ÷ 6
Total load4,800 lb
Reaction at each end2,400 lbwhat the supports must carry
Beam section3.5 × 9.25 insingle ply
If the depth grew one inch0.3301 instiffness goes with depth cubed

The formula

δ = 5wL⁴ ÷ (384EI) for a uniform load; PL³ ÷ (48EI) for a central point load

Depth cubed

A beam’s stiffness goes with the cube of its depth and only linearly with its width. Turning a 2×10 on edge instead of flat multiplies its stiffness by about 30; doubling it up side-by-side merely halves the deflection. If a beam is too bouncy, go deeper.

Deflection usually governs before strength in timber. The L/360 limit — a 12-foot span may sag 0.4 inches — is not about safety but about plaster cracking and floors feeling springy. A beam can pass every stress check and still be unacceptable.

This is a check on a simply supported beam with an idealised load, using nominal moduli. It is not a design: real work needs the graded material’s published values, adjustments for duration, moisture, size and repetitive use, plus shear and bearing checks. Have anything structural designed.