Calculate maximum deflection for simply supported beams under central point loads. Deflection is one of many serviceability checks—always verify stress, stability, shear, and all code requirements with a professional.
Last updated: March 2026
Steel: ~29M psi (200k MPa) | Wood: ~1.5M psi (10k MPa)
Deflection measures how much a beam bends under load and is a critical serviceability limit state in structural design. While strength checks ensure a beam won't fail, deflection controls whether the structure performs acceptably in use—excessive sagging can damage finishes, misalign doors and windows, and cause discomfort. The primary parameters influencing deflection are the applied load magnitude and distribution, the beam span length (deflection grows with the cube of span), the material stiffness (Modulus of Elasticity, E), and the cross-section's area moment of inertia (I). Small changes in section geometry often have large effects on deflection because I scales with height to the third or fourth power for common shapes.
Engineers use closed-form formulas for simple support conditions and point loads, but real structures frequently require superposition, distributed loads, or numerical analysis (finite element methods) for accurate results. Building codes and design guides set serviceability limits—commonly L/360 for floors and L/240 for roofs—so designers can check both safety and comfort. Use this calculator as an educational and quick-check tool; for design-critical elements, validate results with professional analysis and consider factors like long-term creep in timber, temperature effects in long spans, and combined load cases.
Follow these steps to calculate beam deflection for a simply supported beam:
A steel beam: 1000 lb load, 120" span, E=29M psi, I=100 in⁴:
Disclaimer: This calculator provides simplified structural estimates for educational purposes only. It assumes a simply supported beam with a central point load and does not account for all real-world structural factors such as shear stress, local buckling, combined loading, or dynamic effects. Do not use this tool as a substitute for professional engineering analysis. Always consult a qualified structural engineer for design and all safety-critical decisions. Improper structural design can lead to collapse and injury.
For residential floor beams, the building code typically limits deflection to L/360, meaning the beam cannot sag more than its span length divided by 360. A 10-foot (120-inch) beam would have a maximum deflection of 0.33 inches.
For rectangular beams, I = (Width × Height³) / 12. For standard steel I-beams and W-beams, manufacturers provide 'I' values in steel tables. Your structural plans should list I for each beam.
Absolutely. Steel (E ≈ 29M psi) is much stiffer than wood (E ≈ 1.5M psi). A steel beam deflects less than a wood beam under the same load. Higher E = less deflection.
This formula assumes only the point load. For accurate analysis, you should also add the beam's self-weight as a distributed load. Professional engineers use more complex methods for mixed loading.
Excessive deflection causes sagging, cracking in drywall, misaligned doors, plumbing problems, and structural concerns. That's why building codes enforce strict limits using the L/240 to L/360 ratios.
Options include: (1) use a stiffer material (steel vs. wood), (2) increase the moment of inertia (taller I-beam), (3) reduce the span length (add supports), or (4) reduce the applied load.
This calculator assumes a center point load. For distributed loads (uniform or varying), different closed-form formulas apply—use superposition or a distributed-load calculator to compute deflection accurately.
Materials like wood and concrete exhibit creep, causing additional deflection over time. For long-span or sustained loads, include creep effects or consult a structural engineer for time-dependent analysis.
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