End Mill Deflection & Stickout Calculator
An end mill bends like a cantilever: deflection grows with the cube of the stickout and falls with the fourth power of the diameter. Model it as shank plus flutes, with the flutes acting like a bar of about 0.8×D. A Ø12 mm carbide end mill at 48 mm stickout, finishing 12 × 0.6 mm in steel, deflects about 22 µm.
End Mill Deflection & Stickout Calculator (Two-Segment Cantilever)
Deflection where the cut is made, from δ = F/(3E)·[(a³ − af³)/Ishank + af³/Iflute] with the load arm a = L − ap/2 with the fluted section as an equivalent diameter, plus the radial force from your cut and the effect of 20% less stickout. What to enter: stickout L = holder face to tool tip; Lf = flute length; ap = depth of cut along the tool; ae = width of cut (stepover); fz = feed per tooth; Fr only if you know the radial force.
The two-segment equation is δ = F/(3E) × [(a³ − af³)/Ishank + af³/Iflute] with I = π·d⁴/64. The cutting force acts at the middle of the engaged flute, so the load arm is a = L − ap/2 (48 − 6 = 42 mm in the example) and the fluted part of that arm is af = Lf − ap/2 (20 mm). The stress at the holder face uses the same arm: σ = F·a·(dshank/2)/Ishank = 463 × 42 × 6 / 1,018 = 115 MPa; it is the standard moment-area result for a stepped beam found in Machinery's Handbook (Industrial Press).
Why Does Stickout Matter So Much?
The beam equation has the length cubed. Cutting the stickout of the example tool from 48 mm to 36 mm lowers the deflection from 21.6 µm to 9.7 µm — far more than the 25% you shortened it. That is why the first fix for a tapered wall or a chattering finish pass is always to choke the tool up in the holder, and why the calculator shows the result for 20% less stickout next to your setup. Generic cantilever beam calculators give the same physics for a plain bar, but they miss that most of the deflection happens in the fluted part of the tool.
How Do Flutes Change the Stiffness?
Grinding flutes removes material where it matters most for bending. Models of end-mill compliance replace the fluted length with an equivalent solid diameter: about 0.70·D for two flutes, 0.80·D for four and 0.84·D for six. Because stiffness goes with the fourth power, a 4-flute section at 0.8·D keeps only 41% of the stiffness of a solid bar of the same size. The calculator treats the shank and the flutes as two beams in series, so a short flute on a long shank (or a necked tool) is handled correctly instead of assuming the whole length is fluted.
| Flutes | Equivalent Diameter | Bending Stiffness vs Solid | Carbide Deflection | HSS Deflection |
|---|---|---|---|---|
| 2 flutes | 0.70·D | 24% | 16.3 µm | 46.5 µm |
| 3 flutes | 0.75·D | 32% | 15.0 µm | 42.8 µm |
| 4 flutes | 0.80·D | 41% | 14.0 µm | 40.1 µm |
| 5 flutes | 0.82·D | 45% | 13.7 µm | 39.2 µm |
| 6 flutes | 0.84·D | 50% | 13.4 µm | 38.4 µm |
Carbide or HSS?
Solid carbide has a Young's modulus of about 600 GPa, roughly three times that of high-speed steel at 210 GPa (modulus values come from tensile and bend testing such as ISO 6892-1 (tensile testing of metals); forces and stresses here are in SI units per NIST SI units). In the example, the HSS tool deflects 62 µm against 22 µm for carbide under the same load. That stiffness — not only heat resistance — is why long-reach finishing is done in carbide, and why a carbide boring bar beats steel; compare with our boring bar deflection calculator.
| Tool | Stickout 2×D | 3×D | 4×D | 5×D |
|---|---|---|---|---|
| Ø6 mm (4-flute carbide) | 2.2 µm | 6.0 µm | 13.2 µm | 26.1 µm |
| Ø8 mm (4-flute carbide) | 2.7 µm | 7.6 µm | 16.5 µm | 32.3 µm |
| Ø10 mm (4-flute carbide) | 3.2 µm | 8.7 µm | 19.1 µm | 37.6 µm |
| Ø12 mm (4-flute carbide) | 3.6 µm | 9.7 µm | 21.6 µm | 42.7 µm |
| Ø16 mm (4-flute carbide) | 4.4 µm | 12.1 µm | 26.8 µm | 52.7 µm |
| Ø20 mm (4-flute carbide) | 5.2 µm | 14.4 µm | 31.6 µm | 62.1 µm |
Where Does the Cutting Force Come From?
If you do not enter a force, the calculator estimates it from your cut. The maximum chip thickness for a light radial engagement is h = 2·fz·√(ae/D·(1 − ae/D)) (see our chip thinning calculator), the tangential force is Ft = kc1.1 · h1−mc · ap with the specific cutting force of the material, and the radial force is taken as 40% of it. The load is applied at the middle of the engaged length, where the wall error is produced. For a stiffer number, measure the spindle load or use the tool maker's force data and type it into the force field.
How Much Deflection Is Acceptable?
- Below 10 µm — fine for finishing most ±0.025 mm features.
- 10–25 µm — semi-finish: leave stock and take a spring pass, or shorten the tool.
- Above 25 µm — roughing only; expect tapered walls, chatter and a risk of breaking small tools.
Pair this with the MRR and spindle power calculator to see whether the cut is limited by the machine or by the tool, and with the ER collet chart to keep the runout and the stickout under control.
Cite this page
ToolSpecVault Engineering Data Team. (2026, October 28). End Mill Deflection & Stickout Calculator. ToolSpecVault. https://toolspecvault.com/end-mill-deflection-stickout-cantilever-beam-calculator/