Beam Deflection Calculator 2026
Calculate maximum deflection, slope, and reaction forces for simply supported, cantilever, and fixed beams. Built for structural engineers, students, and designers.
Beam & Loading Properties
Select beam configuration, load type, and enter the structural parameters
Choose the support and loading condition that matches your beam.
Structural Results
Maximum deflection, slope, and reaction forces
Enter beam properties above and click Calculate Deflection to see maximum deflection and structural results.
Deflection Formulas for Common Beam Cases
Standard maximum deflection formulas used in structural engineering. E is Young’s modulus, I is the second moment of area, L is span, P is point load, and w is the distributed load per unit length.
| Beam Type | Loading | Max Deflection Formula | Location of Max δ |
|---|---|---|---|
| Simply Supported | Central Point Load | PL³ / (48EI) | Midspan |
| Simply Supported | Uniform Distributed Load | 5wL⁴ / (384EI) | Midspan |
| Simply Supported | Point Load at Position a | Pab(L²−a²−b²)^1.5 / (9√3 EIL) | Near load point |
| Cantilever | Point Load at Free End | PL³ / (3EI) | Free end |
| Cantilever | Uniform Distributed Load | wL⁴ / (8EI) | Free end |
| Fixed-Fixed | Central Point Load | PL³ / (192EI) | Midspan |
| Fixed-Fixed | Uniform Distributed Load | wL⁴ / (384EI) | Midspan |
Beam Deflection FAQ
Everything you need to understand structural beam analysis, from basic deflection formulas to allowable limits in building codes.
Beam deflection is the degree to which a structural element displaces under a load. When a load is applied to a beam, the beam bends and the resulting displacement at any point is called deflection. Engineers must ensure deflections stay within allowable limits to maintain structural integrity and serviceability, preventing damage to finishes and discomfort to occupants.
The formula depends on the beam type and loading. For a simply supported beam with a central point load: δ = PL³ / (48EI). For a cantilever with a tip load: δ = PL³ / (3EI). For a simply supported beam with a uniform distributed load: δ = 5wL⁴ / (384EI). In all cases, E is Young’s modulus, I is the second moment of area, L is the span, P is the point load, and w is the load per unit length.
EI is the flexural rigidity of a beam — the product of Young’s modulus (E) and the second moment of area (I). It measures the beam’s resistance to bending. A higher EI means the beam is stiffer and will deflect less under the same load. To reduce deflection you can increase E (choose a stiffer material) or increase I (use a deeper cross-section or a more efficient profile like a wide-flange section).
Standard building codes typically limit deflection to L/360 under live loads for floors and L/240 for roof beams, where L is the span. For beams supporting brittle finishes like plaster ceilings, stricter limits of L/480 may apply. These limits prevent cracking, protect finishes, and ensure occupant comfort. The Eurocode, AISC, and BS standards all specify similar serviceability criteria.
The second moment of area (I), sometimes called the moment of inertia, is a geometric property of a cross-section describing how its area is distributed relative to the neutral axis. A larger I means greater resistance to bending. For a rectangular section: I = bh³/12. Wide-flange (I-beam) profiles are designed to maximise I for a given weight by placing most material far from the neutral axis.