Cutting speed — the surface speed at the cutting edge — is the number a tool manufacturer gives you for a material; spindle RPM is what you dial into the machine. They are linked by the diameter: N = 1000·Vc / (π·D). Because cutting speed is a rim speed, the same Vc needs a high RPM on a small tool and a low RPM on a big one. Getting this conversion right is the first step of any speeds-and-feeds calculation, and the difference between a clean cut and a burnt edge or a broken tool.
Reviewed: June 20, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: the surface-speed relation Vc = π·D·N.
The cutting speed equations
Cutting speed is the circumference (π × D) times the RPM, scaled to the unit. Solve for RPM by dividing the cutting speed by the circumference; solve for cutting speed by multiplying. The factor of 1000 in the metric form just converts millimetres to metres so Vc comes out in m/min. The imperial version uses 12 to convert inches to feet, but the physics — rim speed equals circumference times rotational speed — is identical.
Worked example — turning a bar
Scenario: You're turning a 50 mm diameter bar and the tool maker recommends a cutting speed of 100 m/min. What spindle RPM do you set?
Set about 637 RPM. As the bar is turned down to 25 mm, holding the same 100 m/min cutting speed means doubling the spindle to ~1273 RPM — which is why constant-surface-speed (CSS) mode on a CNC lathe ramps the RPM up as the diameter shrinks. On a 100 mm part the same cutting speed needs only ~318 RPM. Pick the cutting speed from the material; the calculator gives the RPM for whatever diameter you're working.
Frequently Asked Questions
N = 1000·Vc/(π·D). 100 m/min on 50 mm → 637 RPM. Imperial: RPM = SFM×12/(π·D in inches).
The rim speed at the cutting edge, set by tool and material. Quoted in m/min or SFM.
1 m/min ≈ 3.281 SFM. So 100 m/min ≈ 328 SFM.
Smaller circumference, so higher RPM for the same surface speed. Halve D → double RPM.
From the tool maker's chart for your material and tool (carbide vs HSS, aluminium vs steel).