Formula and Method for Speeds and Feeds Calculation
Speeds and feeds are the two core parameters that control any machining operation: how fast the cutting tool spins, and how quickly it moves through the workpiece. Cutting speed (Vc) — the surface speed at the cutting edge — combines with tool diameter to set the spindle speed: N = 1000 × Vc ÷ (π × D) in metric units (Vc in m/min, D in mm, N in RPM), or N = 12 × Vc ÷ (π × D) in imperial units (Vc in SFM, D in inches). The feed rate is how fast the table advances, driven by the feed per tooth (fz), the number of flutes (Z), and the spindle speed: Vf = fz × N × Z. This calculator also reports feed per revolution (fn = fz × Z) and an estimated metal removal rate from an optional axial depth of cut.
How the calculation works
Enter the tool diameter, number of flutes, cutting speed, and feed per tooth for your unit system. The calculator first solves for spindle speed from the surface-speed formula, then multiplies that RPM by the feed per tooth and flute count to get the linear feed rate (table feed) the machine should be programmed with. Feed per revolution simply strips the RPM term out, leaving the tool's advance per spindle rotation — useful for comparing against drilling or turning feed charts. If you supply an axial depth of cut, the tool estimates metal removal rate as Q = ap × D × Vf ÷ 1000 (cm³/min in metric, in³/min in imperial), assuming full-diameter radial engagement (a slotting pass); for partial-width cuts, scale MRR down by the actual radial engagement as a fraction of the diameter.
Common mistakes
- Confusing cutting speed with spindle speed: Vc (m/min or SFM) is a surface speed independent of tool diameter; RPM depends on diameter too, so the same Vc gives a very different RPM on a 6 mm tool versus a 25 mm tool.
- Mixing metric and imperial values: the formula constant changes (1000 for m/min and mm, 12 for SFM and inches) — entering an SFM value into a metric-labeled field (or vice versa) gives a spindle speed that is wrong by a large factor.
- Treating feed per tooth as feed rate: fz is the chip load per cutting edge; the machine's programmed feed rate (Vf) also depends on spindle speed and flute count, so doubling the flute count roughly doubles the feed rate for the same chip load.
- Ignoring radial engagement in MRR: the metal removal rate here assumes a full-width (slotting) cut; at low radial stepover the actual volume removed per minute is proportionally lower, even though RPM and feed rate stay the same.
Real-world applications
- CNC mill and router programming — converting a material's recommended cutting speed and chip load into the RPM and feed rate values a CAM program or manual G-code needs.
- Tool life and surface finish tuning — cutting speed and feed per tooth are the two levers machinists adjust first when a tool wears prematurely or leaves a poor finish.
- Roughing versus finishing pass planning — roughing favors higher metal removal rate (larger depth of cut, moderate feed), while finishing favors lower feed per tooth for a smoother surface.
- Drilling and tapping speed charts use the same Vc-to-RPM relationship, just with the drill or tap diameter in place of an end mill's cutting diameter.