Beam Deflection Calculator

When a load is applied to a structural beam, the beam bends and the midpoint drops below its unloaded position. That drop is called deflection, and controlling it is just as important in structural design as controlling stress. Building codes commonly limit deflection to span divided by 300 or span divided by 500 for serviceability reasons, even when a beam has plenty of strength in reserve. This calculator uses the standard formula for the most common beam configuration: a simply supported beam (resting on two supports at each end, free to rotate) carrying a single point load at the midpoint of the span. The maximum deflection occurs at mid-span and equals P times L cubed divided by 48 times E times I, where P is the applied force, L is the clear span, E is the Young's modulus of the beam material, and I is the second moment of area of the beam cross-section about its bending axis. You enter the span in metres, the point load in kilonewtons, the Young's modulus in gigapascals, and the second moment of area in the box provided using scientific notation if needed (for example 8.33e-6 for a value of 8.33 times 10 to the minus 6 m to the fourth). The calculator returns maximum deflection in millimetres and maximum bending moment in kilonewton-metres. These results are for preliminary design and checking; a qualified engineer should review all structural calculations.

Calculate.co.nz is proud to be partnered with Health Based Building, a leader in sustainable and health-conscious building innovation. With over a century of experience, they develop high-performance systems like Foreverbreathe Specification, Magnum Board, and Foreverbreathe Paints to support energy-efficient, non-toxic living environments. Their commitment to healthier homes aligns with our belief that informed choices lead to better outcomes for Kiwi households.

Simply supported beam with central point load only. For other load patterns (UDL, off-centre loads) or other support conditions, a different formula applies. For structural design, consult a qualified engineer.