Speeds and feeds
What are the speeds and feeds formulas for milling and turning?
Technical review pending. Formulas and values are cited. This notice comes down after a machinist review.
Spindle speed is RPM = (SFM x 12) / (pi x D), and milling feed rate is IPM = RPM x IPT x Z. A 1/2 in HSS end mill at 100 SFM runs 764 RPM, and at 0.002 in per tooth on 4 flutes it feeds at 6.1 IPM.
SFM (surface feet per minute) is cutting speed, IPM (inches per minute) is feed rate, IPR (inches per revolution) is feed per turn, and IPT (feed per tooth) is chip load.
Source: Machinery's Handbook (speeds and feeds; power required for machining)
| Quantity | Inch | Metric |
|---|---|---|
| Spindle speed | RPM = (SFM x 12) / (pi x D) | RPM = (Vc x 1000) / (pi x D) |
| Spindle speed, shorthand | RPM = SFM x 3.82 / D | RPM = Vc x 318.3 / D |
| Cutting speed from RPM | SFM = (pi x D x RPM) / 12 | Vc = (pi x D x RPM) / 1000 |
| Milling feed rate | IPM = RPM x IPT x Z | vf = RPM x fz x Z |
| Feed per tooth (chip load) | IPT = IPM / (RPM x Z) | fz = vf / (RPM x Z) |
| Turning and drilling feed rate | IPM = RPM x IPR | vf = RPM x fn |
| Feed per revolution | IPR = IPM / RPM | fn = vf / RPM |
| Metal removal rate, milling | MRR = WOC x DOC x IPM (in³/min) | Q = (ae x ap x vf) / 1000 (cm³/min) |
| Metal removal rate, turning | MRR = 12 x DOC x IPR x SFM (in³/min) | Q = Vc x ap x fn (cm³/min) |
| Power at the cutter | HP = MRR x unit power | Same form, with metric unit power from the Handbook |
| Symbol | Meaning | Inch unit | Metric unit |
|---|---|---|---|
| RPM | Spindle speed | rev/min | rev/min |
| SFM, Vc | Cutting speed | ft/min (SFM) | m/min |
| D | Tool diameter (milling, drilling) or work diameter (turning) | in | mm |
| Z | Number of flutes or teeth | count | count |
| IPT, fz | Feed per tooth (chip load) | in/tooth | mm/tooth |
| IPR, fn | Feed per revolution | in/rev | mm/rev |
| IPM, vf | Feed rate | in/min | mm/min |
| WOC, ae | Width of cut (radial engagement) | in | mm |
| DOC, ap | Depth of cut (axial in milling, radial in turning) | in | mm |
| MRR, Q | Metal removal rate | in³/min | cm³/min |
| Unit power | Power per unit of metal removed, by material, from the Handbook table | hp per in³/min | Handbook metric table |
| pi | 3.1416 | none | none |
Calculators
Spindle speed (RPM)
Spindle speed
RPM
RPM = (SFM x 12) / (pi x D) = (100 x 12) / (3.1416 x 0.5) = 764 RPM
Milling feed rate
Feed rate
IPM
IPM = RPM x IPT x Z = 764 x 0.002 x 4 = 6.1 IPM
155 mm/min
IPR and IPM
Feed rate
IPM
IPM = RPM x IPR = 1,200 x 0.005 = 6.0 IPM
Metal removal rate (milling)
Metal removal rate
in³/min
MRR = WOC x DOC x IPM = 0.25 x 0.5 x 6.1 = 0.76 in³/min
12.5 cm³/min
Worked example: one milling cut, start to finish
A 1/2 in (0.500 in) 4-flute HSS end mill in mild steel, 100 SFM, 0.002 in per tooth, 0.250 in width and 0.500 in depth of cut.
- Pick the cutting speed for the tool and material from the tool maker or the Handbook. This example uses a 1/2 in HSS end mill in mild steel at 100 SFM.
- Compute spindle speed: (100 x 12) / (3.1416 x 0.500) = 1,200 / 1.5708 = 763.9, so 764 RPM.
- Pick a feed per tooth from the tool maker's chart. This example uses 0.002 in per tooth on a 4-flute end mill.
- Compute feed rate: 764 x 0.002 x 4 = 6.11, so 6.1 IPM.
- Compute metal removal rate at 0.250 in width and 0.500 in depth of cut: 0.250 x 0.500 x 6.1 = 0.76 in³/min.
- Multiply the MRR by the Handbook unit power for the material to estimate horsepower at the cutter, and compare it with the machine's spindle horsepower.
Result: 764 RPM, 6.1 IPM and 0.76 in³/min. These are starting points; adjust by sound and chip.
Spindle horsepower
Power at the cutter is metal removal rate times unit power: HP = MRR x unit power. Unit power (horsepower per in³/min) depends on the material and its hardness, so take it from the Machinery's Handbook table for your material. The Handbook also applies a feed factor, a tool wear factor and machine efficiency. Required horsepower depends on the material and the metal removal rate.
Common mistakes
- Using the radius, or the shank diameter of a necked tool, for D. D is the cutting diameter.
- Using the tool diameter when turning. On a lathe, D is the work diameter at the cut.
- Leaving the number of flutes out of the feed formula, which cuts the feed rate by a factor of Z.
- Mixing systems: SFM with a diameter in mm, or m/min with a diameter in inches.
- Treating the top of the tool maker's SFM range as a target on a light machine.
Shop notes
- Tool-maker speeds and feeds assume a rigid machine, a short, stiff setup and coolant. On a benchtop mill or a light knee mill, start at the low end of the SFM range and at a lighter chip load, then adjust by sound and chip.
- On a rigid CNC machine, the tool maker's numbers are the intended starting point; horsepower and torque at the RPM you run set the limit on MRR.
- Tool makers give a minimum chip load. Below it the edge rubs instead of cutting, which dulls the tool and work-hardens stainless. If the machine is short on rigidity, lower the RPM before you drop the chip load under that minimum.
- If the RPM is above what the spindle can run, run top speed and keep the feed per tooth. The IPM drops in proportion.
FAQ
What is the formula for spindle speed?
RPM = (SFM x 12) / (pi x D). A 1/2 in end mill at 100 SFM runs 764 RPM. In metric, RPM = (Vc x 1000) / (pi x D) with Vc in m/min and D in mm.
How do you calculate milling feed rate?
IPM = RPM x IPT x Z, where IPT is feed per tooth and Z is the number of flutes. At 764 RPM, 0.002 in per tooth and 4 flutes, the feed is 6.1 IPM.
How do you convert IPR to IPM?
Multiply feed per revolution by spindle speed: IPM = RPM x IPR. At 1,200 RPM and 0.005 IPR the feed is 6.0 IPM. To go back, IPR = IPM / RPM.
What does 3.82 mean in the RPM formula?
It is 12 / pi rounded, so RPM = SFM x 3.82 / D is shorthand for RPM = (SFM x 12) / (pi x D). At 100 SFM and 0.5 in it gives 764 RPM.
How do you estimate the horsepower a cut needs?
Multiply metal removal rate by the unit power for the material from the Machinery's Handbook table. The Handbook adds factors for feed, tool wear and machine efficiency.
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