Beam Deflection Calculator: Interactive Graph & Formula

Maximum elastic deflection

0.01333 m

Load case Cantilever, end point load

Formula δmax = P L³ / (3 E I)

Deflection at 50% span 0.004167 m

Inputs

Beam and Load Case

Select one idealized beam case.

Point Load N

Downward point force; used in the point-load cases.

Uniform Load N/m

Uniform distributed load; used for the cantilever distributed-load case.

Span / Length m

Unsupported beam span or cantilever length.

Elastic Modulus Pa

Young’s modulus for the material.

Second Moment of Area m⁴

Area moment of inertia about the bending axis.

Results & Graph

Maximum elastic deflection

0.01333 m

Load case

Cantilever, end point load

Formula

δmax = P L³ / (3 E I)

Deflection at 50% span

0.004167 m

Elastic deflection shape

Graph 1 • Entered design case Domain-specific illustration generated from the active calculator inputs.

Graph 2 • Engineering outputs The center point load case reaches its peak at midspan.

Graph 3 • Calculated response Shape follows the selected support and load case.

Summary: Maximum elastic deflection: 0.01333 m.

Summary: The idealized beam model gives a maximum deflection of 0.01333 m. Confirm units are consistent: N, m, Pa, and m⁴.

⚠️ Linear-elastic, small-deflection Euler–Bernoulli beam model. This does not check stress, buckling, vibration, connections, code limits, or member suitability.

Formula & Mathematical Methodology: Beam Deflection Calculator

Cantilever point load: δmax=PL³/(3EI) center load on simple span: δmax=PL³/(48EI) cantilever UDL: δmax=wL⁴/(8EI)

: Point force
: Uniform load per unit length
: Beam length
: Elastic modulus and second moment of area

Rounding: Displayed values are rounded for readability; calculations retain full floating-point precision.

Worked Example: A 1 kN load at the end of a 2 m steel cantilever

Use E=200 GPa and I=1×10⁻⁶ m⁴.

Select the cantilever end-load case.
Use δ=PL³/(3EI) with SI units.
Compare the deflected shape and maximum displacement.

Result: The idealized elastic deflection is approximately 13.3 mm.

Frequently Asked Questions

Can I use this to size a beam?

No. It estimates deflection for idealized cases only. A qualified engineer must check strength, stability, connections, and applicable codes.

Science & Engineering • Structural Engineering Guide

How to Use the Beam Deflection Calculator: Practical Guide & Visual Analysis

Choose a beam support/loading case and enter consistent SI values for load, span, elastic modulus and section inertia. Whether you are researching beam deflection calculator, cantilever beam deflection, simply supported beam deflection, beam load deflection, this interactive tool helps you estimate elastic maximum deflection for three idealized beam and loading cases.

Interpreting the 3 Custom Visual Graphs & Key Outputs

As you adjust Beam and Load Case, Point Load, Uniform Load, Span / Length, the calculator immediately computes Primary result, Supporting calculation metrics, Three calculator-specific visualizations and updates all three domain-specific SVG charts in real time. Instead of relying on a single static figure, you can inspect the primary domain diagram, component breakdown, and multi-point trajectory curve to see how changing your inputs shifts the final result. Use the Compare (up to 3 scenarios) button to evaluate side-by-side variations before making a decision.

Real-World Benchmark & Planning Tips (Global; user-entered values, assumptions and currency)

In our benchmark scenario (A 1 kN load at the end of a 2 m steel cantilever), The idealized elastic deflection is approximately 13.3 mm. Keep in mind that linear-elastic, small-deflection Euler–Bernoulli beam theory. For related calculations in Science & Engineering, explore Concrete & Square Footage Calculator, Board Foot, Lumber Weight, Wall Stud Framing & Board-and-Batten Calculator, Roofing, Stair Stringer, Tile, Mulch/Gravel & HVAC BTU Calculator.