Why converting cutting speed to RPM matters
Cutting speed, expressed in surface feet per minute, describes how fast the edge of the cutter should be moving through the material, but a spindle only understands RPM. Since surface speed at the cutting edge depends on bit diameter as well as rotation speed, the same RPM produces a very different surface speed on a quarter-inch bit than it does on a one-inch bit.
How the number is calculated
Spindle speed equals the cutting speed in surface feet per minute, multiplied by 3.82, divided by the bit diameter in inches. That conversion factor comes from converting feet to inches and accounting for the circumference relationship between RPM and surface speed for a rotating tool.
Practical tips
Many CNC routers, especially smaller hobby and prosumer machines, run a fixed-speed spindle or router with only a handful of discrete speed settings rather than fully variable RPM. In that case, use this calculation to find the closest available speed setting to your target rather than expecting an exact match, and adjust feed rate afterward to keep chip load correct at whatever RPM the machine actually lands on.