Beam Deflection Calculator
Find deflection of a uniformly loaded beam.
Distributed load per unit length.
Results update as you type.
How it works
Beam deflection is how far a loaded beam sags from its straight position, and this beam deflection calculator finds the maximum deflection of a simply supported beam carrying an evenly distributed load. It uses the load per unit length, the span, the material's Young's modulus, and the cross-section's moment of inertia to return the mid-span sag in metres, the point where a uniformly loaded beam bends the most. This matters because floors, bridges, shelves, and machine frames must not sag beyond acceptable limits even when they are strong enough not to break. Excessive deflection cracks finishes, causes bouncy floors, and misaligns machinery, so building codes cap it as a fraction of the span. A beam deflection calculator lets you check a design against those limits before choosing a beam size or material. The formula works because deflection grows with the fourth power of the span, so length dominates the result, while a stiffer material and a deeper cross-section resist bending through the modulus and the moment of inertia in the denominator. This is why doubling a beam's span increases sag sixteenfold. Structural and mechanical engineers and students use a beam deflection calculator to size beams that stay comfortably within serviceability limits.
δ = 5 × load × length⁴ ÷ (384 × modulus × inertia)
For a simply supported beam carrying a uniform load, the maximum deflection at mid-span is five times the load times span to the fourth power, divided by 384 times the modulus times the moment of inertia. Span appears to the fourth power because deflection accumulates along the length and the bending it causes compounds. Stiffer materials and larger cross-sections, captured by modulus and inertia, resist that bending proportionally.
Source:Standard mechanical engineering
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter uniform load, beam span, young's modulus and moment of inertia.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Maximum deflection updates instantly as you type — no button to press.
Frequently asked questions
What type of beam does this calculator model?
It models a simply supported beam, one resting on a support at each end, carrying a uniformly distributed load across its full length. This is one of the most common cases in structural work, covering floor joists, shelf spans, and simple bridge decks. The maximum deflection occurs at mid-span. Different support conditions, such as a cantilever or fixed ends, use different formulas and would give different results.
Why does span have such a large effect on deflection?
Span appears to the fourth power in the deflection formula, so it dominates the result. Doubling the length of a beam while keeping everything else the same increases its deflection by a factor of sixteen. This strong dependence is why long spans need much deeper or stiffer beams, and why adding an intermediate support to shorten the effective span reduces sag so dramatically in practice.
What is the moment of inertia?
The moment of inertia, or second moment of area, measures how a cross-section's material is distributed relative to the bending axis. Placing material farther from the neutral axis, as in an I-beam, sharply increases it and resists bending far more efficiently than a solid bar of the same weight. A larger moment of inertia means less deflection, which is why structural shapes are engineered to maximise it.
What units should I use?
Enter the distributed load in newtons per metre, the span in metres, Young's modulus in pascals, and the moment of inertia in metres to the fourth power. The deflection then comes out in metres. Because structural deflections are small, the result is often a fraction of a millimetre; multiply by 1000 to read it in millimetres, the unit most commonly used when checking against code limits.
How much deflection is acceptable?
Building codes usually limit deflection to a fraction of the span, commonly the span divided by 250 or 360 depending on the element and finish. A beam can be strong enough to avoid breaking yet still sag too much for comfort or to protect brittle finishes like plaster. Always compare the calculated deflection against the relevant serviceability limit for your application rather than strength alone.