Beam Deflection

Beam deflection is the vertical displacement, or sag, that occurs in a beam when it is loaded, whether by the weight of a floor, roof, snow load, or occupants above it. Every beam deflects at least slightly under load, since no structural material is perfectly rigid, but building codes limit how much deflection is acceptable to prevent visible sagging, cracked finishes, and a floor that feels unstable to walk on. Deflection is checked as a separate calculation from strength, because a beam can be strong enough to avoid breaking while still deflecting more than is comfortable or code-compliant.

Deflection calculations are essential whenever a beam replaces a removed Load-Bearing wall or spans an open area such as a garage or great room. The Beam Deflection Calculator takes the beam's span, load, material properties, and cross-sectional dimensions to calculate expected sag, then compares that figure against standard limits like span divided by 360 for floors carrying live load.

Deflection is closely related to but distinct from bending stress, which measures whether internal forces in the beam material will cause it to fracture or permanently yield. The Bending Stress Calculator checks that separate failure mode, and a properly sized beam, along with the Joist system it supports, must satisfy both the deflection limit and the bending stress limit to be considered safely designed.

For a simply supported beam under a uniformly distributed load, the maximum deflection at midspan is:

δ = (5 × w × L⁴) / (384 × E × I)

Where:

• δ = maximum deflection, in inches
• w = uniformly distributed load, in pounds per inch
• L = span length, in inches
• E = modulus of elasticity of the material, in psi
• I = moment of inertia of the beam's cross-section, in inches⁴

Consider a wood beam spanning 144 inches (12 feet), carrying a uniform load of 20 lb/in, with a modulus of elasticity E = 1,600,000 psi and moment of inertia I = 300 in⁴.

δ = (5 × 20 × 144⁴) / (384 × 1,600,000 × 300)

δ = (5 × 20 × 429,981,696) / (184,320,000,000)

δ = 42,998,169,600 / 184,320,000,000 ≈ 0.233 inches

The code limit for this 144-inch span at L/360 is 144 ÷ 360 = 0.4 inches, so this beam's calculated deflection of about 0.233 inches is well within the allowable limit, which the Beam Deflection Calculator would confirm as a pass.

• Deflection and strength are separate checks. A beam must pass both the deflection limit and a bending stress check from the Bending Stress Calculator, since one does not guarantee the other.
• Deflection limits vary by application. Floors commonly use L/360 for live load, while roofs may use a more lenient L/240, reflecting the different comfort and cracking tolerances for each use.
• Beam depth matters far more than width. Because deflection is inversely proportional to the moment of inertia, which scales with depth cubed, increasing a beam's depth reduces sag much more effectively than increasing its width.
• Deflection compounds with joist spans above it. A beam supporting a long run of Joist members must be stiff enough that its own deflection doesn't add to the perceived bounce of the floor system as a whole.
• Material stiffness changes the outcome dramatically. Steel's much higher modulus of elasticity compared to wood means a steel beam of the same dimensions will deflect far less under an identical load.