Cutting Speed & RPM
Compute cutting speed from diameter and RPM, or spindle RPM from cutting speed and diameter (turning/milling).
Inputs
Formula
v = π D n / 1000 (m/min); n = 1000 v /(π D) (rpm)
Leave v blank to compute from D,n; provide v to solve n.
How to use
- Fill in Diameter D, Spindle RPM n, Cutting speed v in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Cutting speed v, Spindle RPM n in the results area.
Formula notesCutting speed v = π·D·n/1000 (D mm, n r/min, v m/min); or n = 1000·v/(π·D).
Formula · Worked Example · Knowledge
Formula
In rotary cutting, cutting speed is the surface speed of the cutting edge relative to the work:
$$v=\frac{\pi\,D\,n}{1000}\ \text{(m/min)}$$
$D$ = tool/work diameter (mm), $n$ = spindle speed (r/min). Solve for speed:
$$n=\frac{1000\,v}{\pi\,D}\ \text{(r/min)}$$
$$v=\frac{\pi\,D\,n}{1000}\ \text{(m/min)}$$
$D$ = tool/work diameter (mm), $n$ = spindle speed (r/min). Solve for speed:
$$n=\frac{1000\,v}{\pi\,D}\ \text{(r/min)}$$
Worked Example
Drilling cast iron with a $\phi25\ \text{mm}$ drill at $v=18\ \text{m/min}$:
$$n=\frac{1000\times18}{\pi\times25}=\frac{18000}{78.54}\approx299\ \text{r/min}$$
$$n=\frac{1000\times18}{\pi\times25}=\frac{18000}{78.54}\approx299\ \text{r/min}$$
Key Points
- Cutting speed is the prime factor for tool life and surface quality; pick it from a manual by tool/work pair.
- Larger diameter → higher surface speed; reduce rpm for large parts to stay in the recommended range.
- Cutting fluid cuts friction and carries heat away; MQL suits dry/near-dry cutting.