Speeds and feeds
CNC turning calculators: lathe speeds and feeds
On a lathe D is the work diameter: RPM = (SFM x 12) / (pi x D); 400 SFM on 2.000 in bar is 764 RPM.
Technical review pending. Formulas and values are cited. This notice comes down after a machinist review.
Inch
RPM = (SFM x 12) / (pi x D); IPM = RPM x IPR; MRR = 12 x DOC x IPR x SFM; Ra = f^2 / (32 x r)
| Symbol | Meaning | Unit |
|---|---|---|
| SFM | Cutting speed, surface feet per minute | ft/min |
| D | Work diameter at the cut | in |
| IPR, f | Feed per revolution, inches per revolution | in/rev |
| IPM | Feed rate, inches per minute | in/min |
| DOC | Depth of cut, on the radius | in |
| MRR | Metal removal rate | in³/min |
| r | Tool nose radius | in |
| Ra | Theoretical arithmetic average roughness | in (shown in µin) |
Metric
RPM = (Vc x 1000) / (pi x D); vf = RPM x fn; Q = Vc x ap x fn; Ra = fn^2 / (32 x r)
| Symbol | Meaning | Unit |
|---|---|---|
| Vc | Cutting speed | m/min |
| D | Work diameter at the cut | mm |
| fn | Feed per revolution | mm/rev |
| vf | Feed rate | mm/min |
| ap | Depth of cut, on the radius | mm |
| Q | Metal removal rate | cm³/min |
| r | Tool nose radius | mm |
Source: Machinery's Handbook (speeds and feeds; metal removal rate; surface finish); insert makers' published data for SFM and feed.
One pass: RPM, feed, removal rate and finish
Spindle speed
RPM
RPM = (SFM x 12) / (pi x D) = (400 x 12) / (3.1416 x 2) = 764 RPM
Starting point. Feed 6.11 IPM; removal rate 1.92 in³/min; theoretical Ra 64 µin (1.63 µm).
| Value | Result | Formula with your numbers |
|---|---|---|
| Spindle speed | 764 RPM | RPM = (SFM x 12) / (pi x D) = (400 x 12) / (3.1416 x 2) = 764 RPM |
| Feed rate | 6.11 IPM (155.24 mm/min) | IPM = RPM x IPR = 764 x 0.008 = 6.11 IPM |
| Metal removal rate | 1.92 in³/min (31.46 cm³/min) | MRR = 12 x DOC x IPR x SFM = 12 x 0.05 x 0.008 x 400 = 1.92 in³/min |
| Theoretical finish, Ra | 64 µin (1.63 µm) | Ra = f^2 / (32 x r) = 0.008^2 / (32 x 0.03125) = 0.000064 in = 64 µin |
Under constant surface speed (G96 on a Fanuc-style lathe), RPM climbs as the diameter shrinks: 400 SFM at 0.250 in is 6,112 RPM. A G50 spindle cap goes ahead of G96.
Turning tools
- RPM from SFM or m/min for the work diameter comes from the spindle speed calculator.
- IPR to IPM, and inch feeds to metric, convert on the feed rate conversion calculator.
- Removal rate and horsepower for a turning pass come from the metal removal rate calculator.
- Theoretical Ra from nose radius and feed, or the feed for a target Ra, is on the surface finish calculator.
- G41 and G42 on a Fanuc-style lathe are covered in the tool nose radius compensation guide.
- The facing stock removal cycle is walked through in G72 facing cycle explained.
- A full threading program for a Fanuc lathe is in the G92 threading cycle example.
- Thread depth and infeed per pass come from the CNC threading formulas.
- Taper per foot and the compound angle come from the taper calculator.
- Lathe codes in G-code system A are in the lathe column of the G and M codes list.
- The speeds and feeds formulas are explained, with a worked cut, on the machining formulas page.
- Manual lathe tools live on the manual machining calculators hub.
How to choose a starting point
- Material first. Cutting speed and feed come from the insert maker or the Handbook for the material on the chuck.
- Carbide runs several times the HSS speed in the same material.
- On a light lathe, start at the low end of the range.
- Dry cuts call for lower numbers.
- Adjust by sound, chip color and finish.
Worked example: inch
2.000 in bar, 400 SFM, 0.008 IPR, DOC 0.050 in, 1/32 in nose radius.
- RPM = (400 x 12) / (3.1416 x 2.000) = 763.9, so 764 RPM.
- IPM = 764 x 0.008 = 6.11 IPM.
- MRR = 12 x 0.050 x 0.008 x 400 = 1.92 in³/min.
- Ra = 0.000064 / (32 x 0.03125) = 0.000064 in = 64 µin.
Result: 764 RPM, 6.11 IPM, 1.92 in³/min, 64 µin Ra theoretical.
Worked example: metric
50 mm bar, Vc 200 m/min, 0.20 mm/rev, ap 1.5 mm, 0.8 mm nose radius. Vc and feeds are example inputs, not recommendations.
- RPM = (200 x 1000) / (3.1416 x 50) = 1,273 RPM.
- vf = 1,273 x 0.20 = 254.60 mm/min.
- Q = 200 x 1.5 x 0.20 = 60.00 cm³/min.
- Ra = 0.04 / 25.6 = 0.0015625 mm = 1.56 µm.
Result: 1,273 RPM, 254.60 mm/min, 60.00 cm³/min, 1.56 µm Ra theoretical.
FAQ
What diameter goes into the lathe RPM formula?
The work diameter at the cut, not the tool. 2.000 in bar at 400 SFM runs 764 RPM.
How do you convert IPR to IPM on a lathe?
IPM = RPM x IPR: 764 x 0.008 = 6.11 IPM.
What finish will 0.008 IPR give with a 1/32 in nose radius?
About 64 µin Ra, theoretical: 0.008^2 / (32 x 0.03125) = 0.000064 in. The part will measure rougher.
Why does a lathe need a spindle speed limit with constant surface speed?
Under constant surface speed, RPM rises as the diameter falls. 400 SFM at 0.250 in asks for 6,112 RPM, so a G50 spindle cap goes ahead of G96 on a Fanuc-style lathe.
Is SFM different for HSS and carbide?
Yes. Rule of thumb from tool-maker data: carbide runs about 2 to 4 times the HSS surface speed in the same material.
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