Beam Deflection Calculator

The Beam Deflection Calculator finds maximum vertical deflection for common simply supported and cantilever beams. Select a load case, enter span, elastic modulus $E$, moment of inertia $I$, and applied load. Results include deflection value and an $L/\delta$ serviceability ratio.

Common deflection formulas

Simply supported, center point load:

$$\delta_{max} = \frac{PL^3}{48EI}$$

Simply supported, uniform load over full span:

$$\delta_{max} = \frac{5wL^4}{384EI}$$

Cantilever, point load at free end:

$$\delta_{max} = \frac{PL^3}{3EI}$$

Where $P$ is point load, $w$ is load per unit length, $L$ is span, $E$ is modulus of elasticity, and $I$ is area moment of inertia.

Serviceability limits

Structural design checks strength and deflection. Common live-load limits include $L/360$ for floors with brittle finishes and $L/240$ for roofs. Compare your $L/\delta$ ratio to the limit required by your project.

Frequently Asked Questions

What is beam deflection?

Deflection is how much a beam bends downward under load. Excessive deflection can crack finishes and feel bouncy even when stress is within strength limits.

What units should I use for E and I?

Keep units consistent. In metric, use $E$ in GPa and $I$ in m⁴ with span in meters and load in kN. In imperial, use psi, in⁴, feet, and pounds.

How do I reduce beam deflection?

Increase depth (raises $I$ dramatically), use stiffer material (higher $E$), shorten span, add intermediate supports, or reduce load.

What is the difference between simply supported and cantilever?

A simply supported beam is pinned at both ends and free to rotate. A cantilever is fixed at one end with the other end free. Cantilevers deflect much more for the same load and span.

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Beam Deflection Calculator