Beam Deflection Calculator (Simply Supported, Cantilever, Fixed)
Maximum deflection, bending moment, bending stress and shear force for simply supported, cantilever and fixed-fixed beams carrying a central point load, an off-centre point load or a uniformly distributed load. Results use the standard tabulated beam coefficients, so they can be checked straight against a serviceability limit such as L/250 or L/360.
How to use this calculator
- Pick the beam and loading case: simply supported, cantilever or fixed at both ends, together with a point load or a uniformly distributed load.
- Enter the span, the load, and the section stiffness: Young's modulus for the material and the second moment of area for the section.
- Enter the distance from the neutral axis to the extreme fibre, half the depth for a symmetric section, to get the bending stress M x c / I.
- Read the maximum deflection, the span to deflection ratio, the bending moment, the bending stress and the shear force.
Frequently asked questions
What is the formula for the deflection of a simply supported beam?
For a central point load P over a span L the maximum deflection at mid span is P L^3 / (48 E I). For a uniformly distributed load w it is 5 w L^4 / (384 E I), also at mid span. E is Young's modulus and I the second moment of area about the bending axis.
How much beam deflection is acceptable?
Common serviceability limits are L/250 for general structures, L/360 for floors and machine beds, and L/500 to L/1000 for precision machine tool structures. These are design decisions, not code values, so the limit for your application is the one to design against.
Why does a cantilever deflect so much more than a simply supported beam?
For the same span, load and section, an end-loaded cantilever uses the coefficient 1/3 against 1/48 for a simply supported beam with a central load, so it deflects sixteen times as much. The cantilever also carries the full moment at the support rather than a quarter of it at mid span.