CNC / machinist calculator
Surface Speed Calculator (SFM and RPM)
Surface speed and spindle RPM are two ways of describing the same thing: how fast the cutting edge travels. This converter turns a target surface speed into the spindle RPM you set on the machine, or works backward from a known RPM to the surface speed it produces. It handles both imperial surface feet per minute with an inch diameter and metric cutting speed in metres per minute with a millimetre diameter, so you can move between a tool catalog and your control without arithmetic.
How it works
Cutting speed is a linear speed, the distance a point on the edge sweeps in a minute. A spindle turns in revolutions per minute, so the link between them is the circumference of the cutting circle. In one revolution the edge travels pi times the diameter, which is why RPM equals twelve times the surface speed divided by pi times the diameter in inches.
The metric form is identical in spirit: the cutting speed in metres per minute equals pi times the diameter in millimetres times RPM, divided by one thousand. Because the relationship is exact and reversible, the same tool gives you RPM from a recommended speed or the achieved speed from a spindle limit, which is handy when a small drill would otherwise need an impossibly high RPM.
Use the workpiece diameter for turning on a lathe and the tool diameter for milling and drilling. That single substitution is the only thing that changes between operations.
Worked example
Turning at 100 SFM on a 1/4 in tool: RPM = 12 x 100 / (pi x 0.25) = 1,528 RPM. Halve the diameter and the RPM doubles, which is why small drills spin so fast.
Frequently asked questions
What is the difference between SFM and RPM?
SFM is the linear speed of the cutting edge in surface feet per minute and is set by the material and tool. RPM is how fast the spindle turns. For a given diameter each one fixes the other.
How do I convert SFM to RPM?
Multiply the surface speed in SFM by 12 and divide by pi times the tool diameter in inches. For example 100 SFM on a quarter-inch tool is about 1528 RPM.
What is the 3.82 rule of thumb?
RPM is often estimated as 3.82 times SFM divided by diameter. The 3.82 is just twelve divided by pi rounded off, so the rule and the exact formula agree to within a fraction of a percent.
Do I use the tool or the workpiece diameter?
Use the tool diameter for milling and drilling because the tool spins. Use the workpiece diameter for lathe turning because the part spins and the surface speed is measured at its outside diameter.
How do I work in metric cutting speed?
Switch to metric and enter the cutting speed Vc in metres per minute with the diameter in millimetres. RPM equals one thousand times Vc divided by pi times the diameter in millimetres.
Related calculators
Sources
Every formula on this page is shown and sourced. See how we verify.
These calculators are for planning and as a starting point. Recommended speeds and feeds are published starting values that vary with your specific tool, coating, machine rigidity, workholding and coolant. Always start conservative, listen to the cut, and follow your tool maker data sheet.