Home · Calculators

Beam deflection

Constant EI. No shear deflection.

CaseSimply supported, UDLCantilever, point load at tip

Span L (m)

UDL w (kN/m)

Tip load P (kN)

E (kN/mm²)

I (m⁴)

CalculateReset

Method

Simply supported: δ = 5wL⁴/384EI. Worked case: 8 kN/m, 6 m, E 210 kN/mm², I 0.0001 m⁴ is 6.43 mm. Cantilever tip: δ = PL³/3EI.

Not a span/250 check and not a section design.

Logic: how this figure is built.

What the deflection is, and is not

The simply supported case is 5wL⁴/384EI. The worked beam, 8 kN/m on 6 m with E 210 kN/mm² and I 0.0001 m⁴, deflects 6.43 mm. The cantilever tip case is PL³/3EI. Both assume constant E and I, and a load of the shape named on the form.

Span is to the fourth power. A span read as 6.6 m instead of 6 m raises the simply supported deflection by about 47%. That is why the span should be the centre-to-centre or the clear span you actually mean, written in metres, before the number is compared with a limit.

A span/250 rule is a serviceability limit from a specification or a code clause. This page does not apply it. A deflection of 6.43 mm on 6 m is span/933. That comparison is arithmetic you can do after the page. It is not a pass.

Use the figure to see whether a modelled beam is in the right order before a section check. Camber, shear deflection, cracking and a non-uniform section are not in the formula.

• Related: reactions
• structural logic

Last checked 3 October 2026. See the common-calculations note and the disclaimer.