Bob Oswald replies: The only formula relating RPM to cutting speed is a calculation that determines the tip velocity. The circumference of the circle formed at the tips travels that many times per minute as indicated in RPM. The formula 3.14 x diameter (inches) x RPM will give you inches per minute at the tip of the cutter—usually not a useful number in itself.
Divide by 60 to get inches per second. Or divide by 720 to get feet per second. Or divide by 1056 to get miles per hour.
Determining best cutting speed is a different requirement. That is usually determined from math tables that depend on the cutter type and material and the type of material being cut. There’s no simple formula for that.
Steve Costain replies: A good reference can be found at www.carbidespecialties.com/cutter_performance_specs.htm.
Bruce Wedlock replies: If you are asking what RPM you need to achieve a particular cutting speed. F in feet per minute for a given cutter diameter, D in inches, the approximate formula is RPM = 2F/D.