Why does a cantilever deflect so much more than a simply-supported beam?

A cantilever is held at only one end, so the same load and span give 16 times the midspan deflection of a simply-supported beam (the 48 in the denominator becomes 3). Cantilevers therefore need far stiffer sections for the same span.

What units should I use?

Use a consistent SI set: load in newtons, span and beam length in metres, modulus in pascals (entered here in GPa and converted), and moment of inertia in metres to the fourth. The result then comes out in metres, which the calculator also shows in millimetres.

Does this include the beam’s self-weight?

No. The formulas cover a single concentrated point load only. Self-weight acts as a distributed load with different deflection equations, so add it separately if it is significant for your member.

How do I reduce deflection?

Deflection drops with stiffer material (higher E) or a larger moment of inertia (deeper or wider section), and it rises sharply with span because of the L³ term. Shortening the span or deepening the section is usually the most effective fix.

Beam Deflection Calculator

Point Load (P)

Beam Length / Span (L)

Young's Modulus (E)

GPa

Moment of Inertia (I)

m⁴

Maximum Deflection8.3333 mm

Deflection (m)0.00833333 m

Load CaseCenter point load

Under load, a beam bends and the amount it sags is its deflection, a key serviceability check in structural and mechanical design. This calculator computes the maximum elastic deflection for two classic single-point-load cases: a simply-supported beam loaded at its centre, and a cantilever loaded at its free end. Provide the load, span, material stiffness, and cross-section moment of inertia and it returns the peak deflection in millimetres and metres.

Formula

Simply supported: δ = P·L³/(48·E·I) Cantilever: δ = P·L³/(3·E·I)

δ: Maximum deflection (metres)
P: Applied point load (newtons)
L: Beam span or length (metres)
E: Young's modulus of the material (pascals)
I: Second moment of area of the cross-section (m⁴)

How it works

Choose the load case: simply supported with a centre point load, or cantilever with an end point load.
Enter the point load P in newtons, the span or length L in metres, Young’s modulus E in gigapascals, and the second moment of area I in metres to the fourth.
For simply supported it applies δ = P·L³/(48·E·I); for a cantilever it applies δ = P·L³/(3·E·I), then reports the maximum deflection.

Worked example

A simply-supported steel beam spans 4 m with a 10 kN load at midspan. E = 200 GPa, I = 8×10⁻⁶ m⁴.

Convert modulus: E = 200 GPa = 200×10⁹ Pa.
Numerator: P·L³ = 10000 × 4³ = 10000 × 64 = 640,000.
Denominator: 48·E·I = 48 × 200e9 × 8e-6 = 76,800,000.
δ = 640,000 / 76,800,000 = 0.008333 m.

The beam deflects about 8.33 mm (0.008333 m) at midspan.

Frequently asked questions

Why does a cantilever deflect so much more than a simply-supported beam?: A cantilever is held at only one end, so the same load and span give 16 times the midspan deflection of a simply-supported beam (the 48 in the denominator becomes 3). Cantilevers therefore need far stiffer sections for the same span.
What units should I use?: Use a consistent SI set: load in newtons, span and beam length in metres, modulus in pascals (entered here in GPa and converted), and moment of inertia in metres to the fourth. The result then comes out in metres, which the calculator also shows in millimetres.
Does this include the beam’s self-weight?: No. The formulas cover a single concentrated point load only. Self-weight acts as a distributed load with different deflection equations, so add it separately if it is significant for your member.
How do I reduce deflection?: Deflection drops with stiffer material (higher E) or a larger moment of inertia (deeper or wider section), and it rises sharply with span because of the L³ term. Shortening the span or deepening the section is usually the most effective fix.

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