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.
Fundamentals
Cutting speed is the instantaneous peripheral speed of the cutting edge relative to the workpiece — one of the three cutting parameters.
For a rotary tool, $v=\pi D n$, $D$ diameter, $n$ speed (r/min), $v$ in m/min. Raising $v$ boosts output but wears the tool faster.
History
Scientific metal cutting was opened by Taylor (1907, the Taylor law v·T^n=C), making cutting data optimisable.
Engineering applications
Used to choose cutting parameters for turning, milling, drilling and grinding, balancing tool life and output.
Glossary
| Speed $v$ | Edge-to-work peripheral speed (m/min). |
| Spindle $n$ | Revolutions per minute (r/min). |
| Diameter $D$ | Workpiece/tool diameter (mm). |
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.
Parameters
Inputs
| Parameter | Symbol | Unit | Default |
|---|---|---|---|
| Diameter D (mm) | D | mm | 50 |
| Spindle RPM n (rpm) | n | rpm | 500 |
| Cutting speed v (m/min) | v | m/min | 0 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Cutting speed v | v | m/min |
| Spindle RPM n | n | rpm |
Applications
- Cutting parameters and speed
- Gear measurement (3-wire/base tangent)
- Blanking and deep-drawing process
FAQ
What formula does this tool use?
This tool computes per ISO / AGMA / ASME standard formulas: v = π D n / 1000 (m/min); n = 1000 v /(π D) (rpm)
How accurate are the results?
Results match input precision, based on SI units and common engineering approximations; for critical duty re-check with a safety factor.
Where is it used?
Cutting parameters and speed