An insert box says 250. A machinist sets the spindle to 250 rpm and ruins a carbide insert on a 20 mm bar, or scraps it instantly on a 200 mm one. The 250 was a CUTTING SPEED — how fast the metal passes the cutting edge — and it has nothing to do with how fast the spindle turns until a diameter has had its say.

$V = \pi D N$ — read aloud V equals pi D N. $V$ is the cutting speed, the surface speed at the edge, in metres per minute. $D$ is the diameter at the cut in millimetres — the workpiece diameter when turning, the cutter diameter when milling. $N$ is the spindle speed in revolutions per minute. The bar presents its CIRCUMFERENCE to the edge once per revolution, which is where the $\pi$ comes from, and forgetting it is a factor-of-three error that looks perfectly reasonable on the page.

Which diameter goes in depends on what the machine is doing, and the trap is turning: it is the diameter of the surface BEING CUT, which shrinks with every pass, so a roughing sequence at fixed rpm runs slower and slower in surface terms. That is precisely what a CNC lathe's constant-surface-speed mode exists to fix.

Then the feed. A milling cutter is fed per TOOTH, because each tooth takes its own chip: $v_f = N z f_z$ — v-f equals N z f-z. $v_f$ is the table feed rate in millimetres per minute, the one number the machine is actually programmed in. $N$ is the spindle speed in rpm. $z$ is the number of effective cutting teeth, a plain count with no units. $f_z$ is the feed per tooth, the chip load, in millimetres per tooth — the one number the cutter's data sheet actually cares about.

A chip load too small is not the safe error. The edge stops cutting and starts rubbing, which work-hardens the surface and burns the tool faster than a heavy cut ever would. Machining is one of the few places where being timid is the expensive choice.