Hong Life CalculatorsUnderstanding the spindle speed calculator — concept and principle
This calculator converts a recommended cutting speed into spindle rpm for milling, drilling or turning. It works in metric (m/min and mm) or inch units (surface feet per minute and inches) and also shows revolutions per second, angular speed and the cutting speed and diameter in the other unit system.
How it is calculated
Metric: n = 1000 × vc ÷ (π × D), with vc in m/min and D in mm
Inch: n = 12 × SFM ÷ (π × D), with D in inches (often written 3.82 × SFM ÷ D)
Revolutions per second = n ÷ 60; ω = 2π × n ÷ 60 (rad/s)
- D is the tool diameter for milling and drilling, and the workpiece diameter being cut for turning.
- 1 ft = 0.3048 m and 1 in = 25.4 mm are exact conversions.
The principle
The cutting edge sits on a circle of diameter D. In one revolution it travels the circumference π × D, so its speed is π × D × n. The tool and material set a suitable surface speed: too fast overheats and wears the edge, too slow gives poor finish and built-up edge. Solving the speed equation for n gives the rpm. The factor 1000 converts metres to millimetres, and the factor 12 converts feet to inches. Small tools therefore need high rpm and large ones low rpm for the same cutting speed.
Worked example
Default inputs: metric, cutting speed 120 m/min, diameter 10 mm.
- Circumference = π × 10 = 31.42 mm.
- n = 1000 × 120 ÷ 31.42 = 3,820 rpm.
- Revolutions per second = 3,820 ÷ 60 = 63.66.
- ω = 2π × 63.66 = 400 rad/s.
- In inch units: 120 ÷ 0.3048 = 393.7 SFM, and 10 mm = 0.3937 in.
| Diameter: cutter (milling, drilling) or workpiece (turning) | Spindle speed n (rpm) |
|---|---|
| 2.5 | 15,279 |
| 5 | 7,639 |
| 7.5 | 5,093 |
| 10 | 3,820 |
| 12.5 | 3,056 |
| 15 | 2,546 |
| 20 | 1,910 |
How to read the result
Use the rpm as the starting setting. If it exceeds the machine's maximum, run at the maximum and accept a lower cutting speed. In turning, the diameter changes as you cut, so the rpm for the same surface speed rises as the part gets smaller; lathes with constant surface speed control adjust this automatically. The inch and metric values are shown so you can compare with tool catalogues from either system.
Common mistakes
- Using the shank diameter instead of the cutting diameter.
- Using the finished diameter of a turned part rather than the diameter being cut now.
- Mixing SFM with millimetres or m/min with inches.
- Treating catalogue speeds as fixed; they depend on coating, coolant and rigidity.
Frequently asked questions
How do I convert SFM to rpm quickly?
rpm ≈ 3.82 × SFM ÷ diameter in inches.
Why do small drills need such high rpm?
The circumference is small, so the tool must spin faster to reach the same edge speed.
Is the angular speed useful?
It is used in dynamics and power calculations, such as torque × ω for spindle power.
Does the formula change for turning?
No. Only the meaning of D changes: it is the workpiece diameter.
Sources: Standard formula: cutting speed v = πDn; 1 ft = 0.3048 m and 1 in = 25.4 mm (exact)