Worked examples
Metric. A Ø40 mm shaft is turned at 180 m/min. RPM = 180 × 1000 / (π × 40) = 180 000 / 125.66 = 1,432 RPM. If the lathe has steps at 1,250 and 1,600, take 1,250: staying slightly below keeps you inside the speed you chose.
Imperial. A ½ in end mill at 100 SFM: RPM = 100 × 12 / (π × 0.5) = 1,200 / 1.5708 = 764 RPM. With 4 flutes at 0.002 in per tooth the feed is 764 × 4 × 0.002 = 6.1 in/min.
What is surface speed?
Surface speed is how fast the cutting edge moves past the material, regardless of the size of the tool. A small drill and a large one must turn at very different RPM to reach the same cutting speed: RPM falls as diameter grows. Cutting speed is metres per minute (vc) in metric shops and surface feet per minute (SFM) in imperial ones; 1 SFM = 0.3048 m/min.
Turning, drilling and milling
- Turning: D is the diameter of the workpiece at the cut. When facing, D shrinks toward the centre and the RPM would have to rise; the control does this with constant surface speed (CSS, G96) up to a spindle limit.
- Drilling: D is the drill diameter. Feed is usually per revolution, so use 1 tooth and the feed per revolution as chip load.
- Milling: D is the cutter diameter. Feed is per tooth; multiply by the number of flutes. With a ball-end mill at shallow depth the effective diameter is smaller than the nominal one.
Frequently asked questions
How do I calculate RPM from SFM?
RPM = SFM × 12 / (π × D), with D in inches – about SFM × 3.82 / D. For 100 SFM and a 0.5 in cutter that is 100 × 12 / (π × 0.5) = 764 RPM.
How do I calculate RPM from m/min?
RPM = vc × 1000 / (π × D), with vc in metres per minute and D in millimetres. At 180 m/min on a Ø40 mm shaft: 180 000 / (π × 40) = 1,432 RPM.
What is the difference between SFM and m/min?
Both measure how fast the cutting edge moves past the material. 1 SFM is 0.3048 m/min, so 100 SFM is 30.48 m/min.
How do I calculate feed rate for a milling cutter?
Feed rate = RPM × number of teeth × chip load per tooth. A four-flute cutter at 2,000 RPM and 0.05 mm per tooth feeds at 2,000 × 4 × 0.05 = 400 mm/min.
Which cutting speed should I use?
That depends on the material, the tool and its coating, the cooling and the machine, and is published by tool manufacturers. This calculator turns the speed you choose into RPM; it does not recommend one.
More free machinist calculators
- Inch to mm – Convert inches to millimetres and back, fractions like 1 3/8 included. Exact factor 25.4, with a chart of every 1/64 inch.
- Taper – Taper ratio, half angle and taper per foot from the large and small diameter and the length, or the small diameter from the angle.
- Bolt circle – X and Y coordinates of evenly spaced holes on a bolt circle, with the hole spacing, start angle and centre offset. Copy the table into your program.
- Sine bar – Gauge block height for a sine bar angle, or the angle from a known stack, for 5 in, 10 in, 100 mm, 200 mm or any other bar length.
- Metal removal rate – Metal removal rate in cm³/min or in³/min from depth, width and feed – milling and turning, metric and imperial, with the formulas.
- Drill point depth – Length of a drill's point cone from diameter and point angle, and the total depth needed for a full-diameter hole to depth.
- Right triangle – Hypotenuse and angles from two legs, or the legs from the hypotenuse and an angle – for chamfers, dovetails, tapers and hole positions.
- Machining time – Cutting time from length, feed and spindle speed – turning with feed per revolution, milling with feed rate and number of passes.
- Decimal to fraction – Turn a decimal inch or a millimetre value into the nearest fraction – 8ths to 128ths – with the error in millimetres.
- Degrees to DMS – Convert decimal degrees to degrees, minutes and seconds and back, with the angle in radians.
- SFM to m/min – Convert surface feet per minute to metres per minute and back, and inches per minute to mm per minute, with the exact factors.
- TPI to pitch – Convert a thread pitch in millimetres to threads per inch (TPI) and back, for matching metric and inch threads.
- Cpk calculator – Paste measurements from Excel, enter USL and LSL and get Cp, Cpk, Pp and Ppk. Says plainly when 25 values are too few for an index.
- Tolerance stack-up – Add up the tolerances of a chain of parts: closing gap, worst case and statistical RSS for up to eight dimensions. Free, in your browser.
- Fit clearance – Enter hole and shaft limits and get minimum and maximum clearance and the kind of fit – clearance, transition or interference.
- Chip thinning – Feed per tooth to program when the radial width of cut is below half the cutter diameter, so the real chip thickness stays right.
- Ball-nose stepover – Scallop height left by a ball-nose cutter from the stepover, or the stepover for a wanted scallop height, on a flat surface.
- Surface finish – Theoretical Rt and estimated Ra of a turned surface from the feed per revolution and the tool nose radius.
- Torque and power – Torque from power and speed in newton-metres or pound-feet, and power from torque and speed. The formulas with worked examples.
- Spur gear – Pitch and outside diameter, centre distance, ratio and circular pitch of a pair of external spur gears from the module and the tooth numbers.
Making parts for a customer who wants paperwork?
Automotive and aerospace customers ask for proof that the parts match the drawing. See first article inspection (FAI), PPAP explained and the true position calculator.