What is the formula behind this tool?

Surface speed equals pi times diameter times RPM divided by 12. Rearranged for spindle speed it becomes RPM equals SFM times 12 divided by pi times diameter, which simplifies to the familiar shop constant 3.82 times SFM over diameter.

Is diameter the cutter or the part?

On a mill or drill it is the tool diameter. On a lathe it is the diameter of the workpiece being turned, because the surface speed is measured at the cutting edge regardless of which part spins.

Why does a smaller cutter need a higher RPM?

Surface speed is fixed by the material and tooling, but a small diameter travels a shorter distance per revolution. To reach the same surface feet per minute the spindle must spin faster, which is why tiny end mills run at very high RPM.

Where do the SFM values in the table come from?

They are representative starting speeds for high-speed-steel and carbide tooling in common materials. Always defer to your tool manufacturer's chart, then dial in by sound, chip color, and finish on the actual machine.

Does this account for coolant or rigidity?

No. The formula gives an ideal speed from geometry alone. Flood coolant, machine rigidity, depth of cut, and tool runout all shift the practical speed, so treat the result as a calculated starting point.

What is the RPM / SFM Calculator?

Convert surface feet per minute (SFM) to spindle RPM or back for any cutter or workpiece diameter using the standard machining formula RPM equals 3.82 times SFM divided by diameter. Includes HSS and carbide cutting-speed references for common materials. It runs free in your browser on Gera Tools, with nothing uploaded.

RPM / SFM Calculator

Name: RPM / SFM Calculator
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

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Surface speed, not spindle RPM, is what actually determines tool life and finish — but machines are set in RPM. This calculator converts between the two for any diameter so you can take a manufacturer’s recommended surface speed and turn it into the spindle setting your machine needs, or check what surface speed an existing RPM is producing.

How it works

The relationship is purely geometric:

SFM = (pi × D × RPM) / 12      (D in inches)
RPM = (SFM × 12) / (pi × D) = (3.82 × SFM) / D

The constant 3.82 is simply 12 divided by pi, the standard shop shortcut. Because the 12 converts inches to feet, the result is true surface feet per minute at the cutting edge. On a lathe, D is the workpiece diameter; on a mill or drill press, D is the tool diameter.

Worked examples

End mill in aluminum: a 0.5-inch carbide end mill targeting 800 SFM needs 800 × 3.82 / 0.5 = 6,112 RPM. Drop to a 0.25-inch cutter at the same surface speed and the required RPM doubles to about 12,224 — a small drill simply must spin faster to maintain the same cutting speed.

Lathe turning steel: a 2-inch diameter steel shaft with an HSS tool targeting 80 SFM needs 80 × 3.82 / 2 = 153 RPM. Many small lathes can barely go that slow, which is why facing large steel blanks at low RPM is perfectly correct — the surface speed is fine even though the spindle crawls.

Checking an existing setup: if your mill is set to 3,000 RPM with a 1-inch face mill, the surface speed is (3.14159 × 1 × 3000) / 12 = 785 SFM. That number tells you instantly whether you are in the right range for the material you are cutting.

Approximate starting SFM by material

These are general starting points for planning; always check your tool manufacturer’s data and adjust based on results:

Material	HSS (approximate SFM)	Carbide (approximate SFM)
Aluminum alloys	200–400	600–1,000+
Mild steel	60–100	300–600
Stainless steel	30–60	150–350
Cast iron	50–80	200–400
Brass	150–300	500–800
Titanium	20–40	100–200

Use the table as a starting point, then trust your senses: blue chips mean too much speed, a rubbing, burnished cut with poor finish often means too little.