Structural Beam Calculator
A Beam That Doesn't Break Can Still Fail by Sagging
Most beams in residential and light-commercial framing are never at real risk of snapping under normal loads — they're limited by how much they're allowed to bend. Excessive deflection cracks drywall, makes floors feel bouncy, and can jam doors, which is why deflection, not raw strength, is often the governing design check for a simply-supported beam.
The Formula
This is the standard mechanics-of-materials formula for the maximum deflection (δ) at the center of a simply-supported beam carrying a uniformly distributed load. w is the load per unit length, L is the span between supports, E is the material's modulus of elasticity (a measure of stiffness), and I is the cross-section's moment of inertia (a measure of how efficiently that shape resists bending). All four values must be entered in a single consistent unit system — imperial (lb/in, in, psi, in⁴) or metric (N/m, m, Pa, m⁴) — since mixing units produces a meaningless result.
Where This Calculation Matters
- Floor joist and beam sizing — residential floor beams are commonly checked against a deflection limit like L/360 (span divided by 360) to keep floors from feeling springy.
- Header and lintel design — a beam spanning a wide window or garage door opening needs its deflection checked separately from its bending strength, since it can pass one check and fail the other.
- Material comparison — because deflection depends on both E and I, swapping a beam's material or cross-section shape (not just its size) changes deflection dramatically, which this formula makes explicit.
Worked Example
A beam spanning 120 in (10 ft) carrying a uniform load of 20 lb/in, with a modulus of elasticity of 1,600,000 psi (representative of graded structural lumber) and a moment of inertia of 100 in⁴:
| Input | Value |
|---|---|
| Load (w) | 20 lb/in |
| Span (L) | 120 in |
| Modulus of Elasticity (E) | 1,600,000 psi |
| Moment of Inertia (I) | 100 in⁴ |
| Deflection (δ) | 0.3375 in |
This calculator solves for deflection specifically; it assumes a simply-supported beam under a single uniformly distributed load, not a point load, cantilever, or continuous span.
How to Use This Calculator
- Select Imperial or Metric units.
- Enter the Load (w) per unit length of beam.
- Enter the Span (L) between supports.
- Enter the Modulus of Elasticity (E) for the beam's material.
- Enter the Moment of Inertia (I) for the beam's cross-section.
- Select Calculate to see the maximum deflection at the beam's center.
Related Calculations
Sizing the beam's cross-section itself? The I-Beam Calculator covers structural steel shapes, and the Steel Weight Calculator helps price a steel beam once it's sized.