# CNC End Mill Deflection Calculator

> Source: https://netray.co/tools/cnc-end-mill-deflection-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Predict how far a cutter bends under load, and see why shorter stickout and a larger diameter matter so much for accuracy.

## Category

manufacturing

## Industry

CNC Machining

## Audience

- CNC programmer
- Machinist
- Manufacturing engineer

## Tool

**Kind:** calculator

**Inputs:**

#### Radial cutting force on the tool

**Key:** force

**Type:** number

**Default:** 150

**Min:** 1

**Step:** 10

**Unit:** N

**Help:** Use the force component that pushes the tool sideways. A rough guide is 30 to 50 percent of the tangential force.

#### Tool diameter

**Key:** d

**Type:** number

**Default:** 10

**Min:** 1

**Step:** 0.5

**Unit:** mm

#### Stickout length (beyond the holder)

**Key:** stick

**Type:** number

**Default:** 40

**Min:** 2

**Step:** 1

**Unit:** mm

#### Tool material (Young's modulus)

**Key:** emod

**Type:** select

**Default:** 600000

**Options:**

##### Solid carbide, about 600 GPa

**Value:** 600000

##### Cobalt HSS, about 220 GPa

**Value:** 220000

##### Steel shank, about 210 GPa

**Value:** 210000

#### Flute section stiffness factor

**Key:** ff

**Type:** select

**Default:** 0.8

**Options:**

##### Fluted end mill (0.8 of diameter)

**Value:** 0.8

##### Plain shank (full diameter)

**Value:** 1

**Outputs:**

#### Effective bending diameter

**Key:** deff

**Expr:** d * ff

**Format:** decimal

**Description:** mm.

#### Second moment of area

**Key:** inertia

**Expr:** pi * pow(deff, 4) / 64

**Format:** decimal

**Description:** mm4.

#### Tip deflection

**Key:** defl_um

**Expr:** force * pow(stick, 3) / (3 * emod * inertia) * 1000

**Format:** decimal

**Primary:** true

**Description:** Micrometres at the cutter tip.

#### Tool stiffness

**Key:** stiff

**Expr:** force / defl_um

**Format:** decimal

**Description:** N per micrometre.

#### Stickout to diameter ratio

**Key:** ld

**Expr:** stick / d

**Format:** decimal

**Primary:** true

#### Deflection relative to 3 x D stickout

**Key:** rel

**Expr:** defl_um / (force * pow(3 * d, 3) / (3 * emod * inertia) * 1000)

**Format:** decimal

**Description:** Multiple of the deflection at a stickout of three diameters.

**Chart:**

#### Tip deflection (um) vs stickout (mm)

**Type:** line

**X:** stick

**From:** 10

**To:** 80

**Steps:** 30

**Series:**

- defl_um

**Disclaimer:** This models the tool as a simple cantilever beam and ignores holder and spindle compliance, run-out and the varying force along the flute. Real deflection is higher. Use it for comparing options, not for guaranteeing tolerance.

## Content

**Intro:** When a thin wall comes out tapered or a deep pocket is not square, tool deflection is often the cause. This calculator uses beam theory to show how much the cutter bends and how fast it grows with stickout.

**Sections:**

#### How to use it

**Body:** Enter the sideways force on the tool, the diameter, the stickout and the tool material. The force can come from a CAM force estimate, a dynamometer, or from the cutting power calculation by taking a fraction of the tangential force. The main result is the tip deflection in micrometres. Compare setups by changing the stickout or the diameter and watch the chart of deflection against stickout.

#### The beam formula

**Body:** A cutter held in a rigid holder behaves like a cantilever beam with a point load at the tip. Deflection is delta = F x L^3 / (3 x E x I), where I = pi x d^4 / 64 for a round section. Stickout enters as a cube and diameter as the fourth power, which is why a small change in either has a big effect. A 10 mm carbide cutter with 40 mm stickout and 150 N lateral load deflects about 26 um with an effective diameter of 8 mm for the flutes. Doubling the stickout to 80 mm increases it by a factor of eight.

**Bullets:**

- Deflection varies with L cubed.
- Deflection varies with 1 over d to the fourth power.
- Carbide is about three times stiffer than HSS.

#### Using the result

**Body:** If the deflection is a significant fraction of your tolerance, reduce stickout first, then use a larger diameter or a stiffer carbide tool, then reduce the radial and axial depth so the force falls. A common strategy for finishing walls is a light spring pass that removes the leftover. Remember that the deflection leaves material in the corner or on the wall, not an oversize cut, so thin features come out thick at the base and thin at the top when the tool leans.

#### Common mistakes

**Body:** The stickout to measure is the length from the holder face to the tool tip, not the length of cut. Another is neglecting that a long holder or a weak spindle adds to the total compliance, so the real part error exceeds the figure shown. Finally, using the nominal diameter for a fluted section overestimates stiffness by about 40 percent, which is why this tool applies a factor of 0.8 for the flute section.

**Cta:** If you track tooling and job tolerances in an ERP or quality system, we can help connect them. This calculator does not need that.

**Faq:**

#### How accurate is this?

**Answer:** It is a screening tool. The cantilever model ignores holder, spindle and fixture compliance and the way force acts along the flute, so measured errors are usually larger. Use it to rank options, such as 30 mm versus 50 mm stickout, rather than to predict exact errors.

#### What force should I enter?

**Answer:** Use the sideways, or radial, force. If you know the tangential cutting force Ft, the radial force is typically 30 to 50 percent of it for end milling. Ft can be estimated as kc multiplied by the chip cross-section area per tooth engaged.

#### Why does stickout matter more than diameter?

**Answer:** Both matter strongly. Stickout is cubed and diameter is to the fourth power, so a 20 percent increase in stickout adds about 73 percent deflection, while a 20 percent increase in diameter reduces it by about 52 percent.

#### What is a good length to diameter ratio?

**Answer:** Up to 3 times diameter is rigid for most work. Between 4 and 6 times needs reduced cuts. Beyond 8 times, use special tools such as reduced-neck or variable-pitch cutters and expect to take light passes.

## Search terms

end mill deflection calculator, tool deflection formula, cantilever beam tool deflection, end mill stickout calculator, tool deflection and part accuracy, carbide end mill stiffness, length to diameter ratio end mill, wall thickness taper from tool deflection

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