Structural & Mechanical

Simple Beam Deflection Calculator

Estimate elastic deflection, bending moment and bending stress for common simple beam cases.

A 500 kg pump sits on a two-metre beam. Will the beam sag enough to affect alignment?
Preliminary screeningUse this result to screen and frame the problem—not to approve regulated or high-consequence work.
Core formulae

Beam deflection reference

Centre point loadδ_max = P L³ / 48 E I
Uniformly distributed loadδ_max = 5 w L⁴ / 384 E I
Cantilever end loadδ_max = P L³ / 3 E I
Elastic bending stressσ = M / Z
Simple arrangement sketch

Simply supported beam with central point load

Pδ_maxL
1

Choose the beam and load case

Start with the support condition and the load you actually know.

2

Tell us what section you have

You no longer need to know I and Z before using the calculator.

Properties inserted automaticallyI = 1,910 cm⁴ · Z = 191 cm³PFC preset is for bending about the strong x-x axis only.
3

Choose how to compare deflection

L/500 means the allowable movement is the span divided by 500. For a 2 m span, that is 4 mm.

Your comparison meansMaximum movement = 4 mmBased on a 2 m span and the selected L/500 comparison.
Results

Elastic beam response

Maximum deflection0.214 mm
Calculated deflection ratioL/9,349

Span divided by calculated movement.

Comparison limit4 mm

L/500

Second moment I used1,910 cm⁴
Section modulus Z used191 cm³
Maximum bending moment2.452 kN·m
Elastic bending stress12.84 MPa
Below the entered deflection comparison

Elastic deflection is 5.3% of the selected L/500 comparison.

Scope

Euler-Bernoulli elastic beam formulas only. This does not check lateral-torsional buckling, local buckling, web crippling, torsion, load distribution, support flexibility, vibration, fatigue or dynamic amplification.

Job-file record

Save the calculation, not just the number.

Copy a permalink that reloads these inputs, or download a PDF record with inputs, visible results, assumptions, a sensitivity note, date and disclaimer.

Important boundary

A calculator can show the arithmetic. It cannot establish every requirement that applies.

Confirm the actual equipment, loading, materials, condition, jurisdiction, contractual requirements, standard edition and current project documentation before using the result for design, repair, testing or lifting decisions.

Ask an engineer about this calculation →