Cantilever Beam Deflection Calculator
Calculate cantilever beam displacement and support bending moments for mechanical brackets, balcony beams, diving boards, and structural overhangs.
How it works
Under classical beam bending mechanics, the maximum deflection occurs at the unsupported tip and is proportional to the cube of beam length ($L^3$).
Formula
δ_max = (F L^3 / 3 E I), M_max = F × L
Computes elastic beam bending deflection proportional to the cube of span length and inversely proportional to flexural rigidity (E·I).
| Symbol | Variable | Unit | Description |
|---|---|---|---|
| F | Applied end force | N | |
| L | Cantilever beam length | m | |
| E | Young's Modulus of elasticity | Pa | |
| I | Area second moment of inertia | m⁴ | |
| δ_max | Maximum displacement at free end | m |
Worked example
5,000 N point load on a 2m steel beam (E = 200 GPa, I = 8.33e-5 m⁴)
- Force:
- 5,000 N
- Length:
- 2 m
- E:
- 200 GPa
- I:
- 8.33e-5 m⁴
δ_max = (5000 × 2³) / (3 × 200e9 × 8.33e-5) = 40000 / 49980000 = 0.000800 m (0.800 mm). Maximum bending moment at root = 10,000 N·m.
Limitations
Does not account for shear deformation (Timoshenko beam effects for deep, short beams) or plastic yielding beyond material yield strength.
Frequently asked questions
What is Young's Modulus (E)?
Young's Modulus measures a material's intrinsic mechanical stiffness (resistance to elastic deformation under axial tension or compression). Structural steel is typically 200–210 GPa, aluminum is ~70 GPa, and titanium is ~110 GPa.
How do I calculate the moment of inertia (I) for a rectangular beam?
For a rectangular section with width b and height h, the second moment of area about the neutral axis is I = (b × h³) / 12.
Why does length have such a dramatic impact on beam deflection?
Deflection scales with the cube of length (L³). Doubling the beam length increases its end deflection by 2³ = 8 times under the same load.
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Last reviewed: 2026-08-22.