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.
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
FAQ
Does tool deflection formula apply the same way to end mills and boring bars? The underlying beam-deflection relationship is similar, but boring bars are typically unsupported on one end in a bore with even less rigidity than an end mill of similar length and diameter.
How much deflection is considered acceptable? It depends on the tolerance being held. For most general milling, deflection well under half the part’s tolerance band is a reasonable target, since deflection compounds with other error sources like runout.
Run it instantly with the Tool Deflection calculator in Cutting & Tooling.