Calculator

Deflection under point load or distributed load

Euler-Bernoulli beam theory: one point load or one full-span uniformly distributed load. For a point load, a is the distance to the left support (simply supported) or to the fixed end (cantilever).

Load typeBeam typeCross-sectionSpan / length L (mm)Load position a (mm)Point load F (N)MaterialBending axisAllowable deflection (mm, optional)Width b (mm)Height h (mm)

A beam bends about the axis it's actually loaded on — usually the strong axis (e.g. a plate standing on edge). The weak axis is the conservative/buckling-style behavior. Pick the axis that matches the real orientation.

Deflection at the load δ(a): 0,93 mm
Maximum deflection δ_max: 0,93 mm
Position x (δ_max): 500 mm
Moment M_max: 125.000 N·mm
Support reaction A: 250 N
Support reaction B: 250 N
σ_max: 46,9 N/mm²
Moment of inertia I: 53.333 mm⁴
L / δ_max: ≈ 1.075

This load sits at the location of maximum deflection (centred for simply supported, or at the tip for a cantilever), so δ(a) and δ_max coincide here.

Check this section/material for buckling →

PHYSICS MODEL

Assumptions: Linear-elastic, small deflections. One single load per calculation — either one point load or one full-span uniformly distributed load — no combinations or multiple separate loads (superposition). Support reactions are included. Not a substitute for a strength calculation per EN 1993-1-1 on critical structures.

Source details

Euler-Bernoulli beam theory, one point load or one full-span UDL (Roark)

Checked 2026-09-17

Technical diagram · dimensions in mm · schematic, not to scale

Allowable deflection guidelines

Generic rules of thumb — check the applicable standard for the specific application. Enter your own project-specific allowable deflection above if you have one.

Ratio	Typical use
L / 180	Light, non-critical structures
L / 250	General building structures (EN 1993 guideline)
L / 360	Floors under point load, vibration-sensitive
L / 750	Crane runways, precision machinery

Source: Engineering ToolBox — Beam deflection and stress

Loading calculation model…

Questions

Where is distance a measured from?+

For simply supported, from the left support. For cantilever, from the fixed end. a must be between 0 and L.

Why show a maximum next to δ at the load?+

For an off-center load, the largest deflection isn't under the load itself, but a bit further along the longer part of the span.

Why only two end conditions?+

Pinned-pinned and fixed-free are statically determinate: direct formulas. Fixed-fixed and fixed-pinned are statically indeterminate and aren't (yet) in this calculator.

Does this replace EN 1993-1-1?+

No. Linear-elastic beam theory, small deflections, no partial safety factors. For critical structures, use the standard or an FEM check.