Beam Deflection Calculator

This calculator finds the maximum deflection of a simply supported beam carrying a single point load at its centre, one of the most common cases in structural engineering. When a load is placed on a beam, the beam bends, and how much it sags in the middle is its deflection. Controlling deflection matters as much as controlling strength: a floor joist or a shelf that is strong enough not to break can still flex unacceptably, causing bouncy floors, cracked finishes or doors that jam. Engineers therefore check deflection against limits as a routine part of design. For a simply supported beam, one that rests on a support at each end, with a point load in the middle, the maximum deflection occurs directly under the load and follows a clear formula involving the load, the span cubed, and the beam's stiffness. Stiffness combines the material, through its modulus of elasticity, and the shape of the cross-section, through its second moment of area. This tool computes it. You enter the load, the span between supports, the modulus of elasticity of the material, and the second moment of area of the cross-section, and the calculator returns the maximum deflection, the maximum bending moment, and the reaction at each support. The results update as you type, so you can see how a deeper section or a shorter span dramatically reduces sag, since deflection depends on the cube of the span. Use it for engineering studies, for checking a beam or joist, or to understand how stiffness works. Note that deflection grows with the cube of the span, so halving the span cuts deflection to one eighth, which is why long spans need much deeper beams. This is an educational estimate; real designs must follow the building code and proper engineering.

Simply supported beam, central point load: deflection = P L³ / (48 E I). Deflection grows with the cube of the span. An educational estimate; follow the building code.