Theoretical values for estimating only. Confirm against the mill certificate or a stamped calculation before ordering or fabricating.
A beam almost never fails by strength — it fails by being too springy to use. Deflection, not stress, decides the depth of most floor beams, and it is the check that gets forgotten.
The four load cases covered
Simply supported under uniform load: δ = 5wL⁴/384EI. Simply supported with a central point load: δ = PL³/48EI. Cantilever with an end point load: δ = PL³/3EI. Cantilever under uniform load: δ = wL⁴/8EI.
Serviceability limits
L/360 is the usual limit for floors carrying plaster or brittle finishes, L/240 where cracking is not a concern, and L/480 or tighter for crane rails and precision machinery.
Units and the trap in them
The formula only works if the units are consistent. This calculator takes span in metres, load in kN or kN/m, E in GPa and I in cm⁴, and converts internally to newtons and millimetres.
Deflection is not the whole check
Bending stress, shear, web buckling, lateral torsional restraint and the connection design all still have to be verified. This is a sizing tool, not a substitute for a stamped calculation.
Frequently asked questions
What is the maximum allowable deflection for a beam?
Usually span/360 for floors with brittle finishes, span/240 for general floors and span/480 for crane rails or precision equipment.
How do I calculate deflection of a simply supported beam?
For a uniform load use δ = 5wL⁴/(384EI); for a central point load use δ = PL³/(48EI). Keep units consistent — newtons and millimetres work directly.
Does a bigger I value always reduce deflection?
Yes, deflection is inversely proportional to the second moment of area, so doubling I halves the deflection for the same span and load.
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