An end mill bends like a cantilever beam fixed in the holder. The deflection formula shows why stickout and diameter dominate: length is cubed and diameter is raised to the fourth power.
δ = (F × L³) / (3 × E × I), I = πD⁴ / 64
What the variables mean
| Symbol | Meaning |
|---|---|
| δ | Deflection at the tool tip (inches) |
| F | Cutting force (pounds) |
| L | Stickout / unsupported length (inches) |
| E | Elastic modulus (carbide ~90 × 10⁶ psi, HSS ~30 × 10⁶) |
| I | Area moment of inertia (in⁴) |
| D | Tool diameter (inches) |
Worked example
Because deflection scales with L³/D⁴, doubling stickout bends the tool ~8× more, while doubling diameter stiffens it ~16×. Shorten the tool before anything else.
Run it instantly with the Tool Deflection calculator in Cutting & Tooling.