Spindle Speed

\[N=\frac{1000V_c}{\pi D}\]

Variables

Nspindle speed (rev/min)

Vccutting speed (m/min)

Dworkpiece or tool diameter (mm)

Description

What is this formula?

Spindle Speed calculates the rotational speed required to achieve a specified cutting speed for a given tool or workpiece diameter. It is one of the most frequently used machining calculations in turning, milling, drilling, and CNC programming.

When to use it

Use this formula when selecting machine settings, programming CNC equipment, choosing cutting conditions, or converting recommended cutting speeds into spindle RPM values.

Example

A carbide turning tool is recommended to operate at a cutting speed of 180 m/min while machining a shaft with a diameter of 75 mm.

Data:

Vc = 180 m/min

D = 75 mm

Formula:

N = (1000 × Vc) / (π × D)

Substitution:

N = (1000 × 180) / (π × 75)

Result:

N = 763.94 rev/min

The spindle should operate at approximately 764 RPM.

Applications

CNC programming

Turning operations

Milling operations

Drilling operations

Machining parameter selection

Tool setup calculations

Note

This equation assumes a constant cutting diameter. In some machining operations, such as facing or contour machining, the effective cutting diameter changes continuously, causing the actual cutting speed to vary unless spindle speed is adjusted dynamically.