Beam Deflection Calculator
Calculate maximum beam deflection for the four most common load cases and check it against the usual serviceability limits (L/360, L/240, L/180). Long spans are almost always governed by deflection rather than strength.
Beam deflection
Elastic deflection under service load, uncracked and untorsioned. Moment of inertia I is taken about the bending axis (Ix for normal orientation).
Deflection formulas
| Load case | Maximum deflection | Location |
|---|---|---|
| Simply supported, uniform load w | 5wL⁴ / (384EI) | Mid-span |
| Simply supported, central point load P | PL³ / (48EI) | Mid-span |
| Cantilever, uniform load w | wL⁴ / (8EI) | Free end |
| Cantilever, end point load P | PL³ / (3EI) | Free end |
A cantilever deflects far more than a simply supported beam of the same span and load — roughly 9.6× for a uniform load — which is why cantilever spans are kept short.
Frequently asked questions
How do you calculate beam deflection?
For a simply supported beam with a uniform load the maximum deflection is 5wL^4/(384EI). For a central point load it is PL^3/(48EI). E is the modulus of elasticity and I the moment of inertia of the section.
What is an acceptable deflection limit?
L/360 is common for floors with brittle finishes, L/240 for general floors and roofs, and L/180 for some roof members. Divide the span by the denominator to get the allowable deflection.
What modulus of elasticity should I use for steel?
200 GPa (200,000 MPa), equivalent to about 29,000 ksi, for all structural carbon steels. Stainless is slightly lower at about 193 GPa.
Why is my beam failing deflection but not stress?
Deflection grows with the fourth power of span while bending stress grows with the square, so long spans become deflection-controlled. You need a deeper section with a larger moment of inertia, not a stronger steel.
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