Beam Deflection Calculator

Beam deflection is the displacement of a beam under load. A beam may be strong enough not to break but still deflect too much for serviceability, alignment, comfort, or appearance. Structural design therefore checks both strength and stiffness.

Deflection depends on load magnitude, span, support conditions, material stiffness, and cross-section geometry. The elastic modulus E describes material resistance to strain. The second moment of area I describes how the cross-section's material is distributed relative to the bending axis. Together, EI is flexural rigidity.

The same beam and load can deflect very differently depending on supports. A simply supported beam can rotate at its ends. A cantilever is fixed at one end and free at the other, making it much more flexible for the same span and load. Fixed-end beams restrain rotation and can reduce midspan deflection.

Boundary conditions are not bookkeeping; they are physical constraints. A connection assumed fixed in calculation but built as flexible in the field will not behave as predicted. Accurate deflection estimates start with honest support modeling.

Deflection often grows dramatically with span. Many common beam formulas include span to the third or fourth power. Doubling span can increase deflection far more than doubling the load. This is why small increases in unsupported length can make a design feel surprisingly soft.

Increasing section depth is usually an efficient way to improve stiffness because it raises the second moment of area. Material choice helps too, but geometry often dominates. A deeper beam of the same material can be much stiffer without requiring a proportional increase in weight.

Basic beam deflection formulas assume linear elastic behavior, small deflections, idealized loads, and simple supports. Real structures may include shear deformation, connection slip, composite action, cracking, creep, residual stress, and dynamic effects. Codes also set serviceability limits based on use case.

A formula result is useful for early sizing and sanity checks, but final structural decisions require appropriate codes, load combinations, material standards, and professional judgment. Deflection is about whether a structure works well, not only whether it survives.