Speeds and feeds
Metal removal rate calculator
MRR = width of cut x depth of cut x IPM; a 0.500 in by 0.250 in cut at 12.0 IPM removes 1.500 in³/min.
Technical review pending. Formulas and values are cited. This notice comes down after a machinist review.
Metal removal rate
in³/min
MRR = WOC x DOC x IPM = 0.5 x 0.25 x 12 = 1.500 in³/min
24.58 cm³/min. Enter Kp for power at the cutter. Estimate and starting point.
| Value | Result | Formula with your numbers |
|---|---|---|
| Metal removal rate | 1.500 in³/min (24.58 cm³/min) | MRR = WOC x DOC x IPM = 0.5 x 0.25 x 12 = 1.500 in³/min |
| Power at the cutter | Enter Kp | HPc = MRR x Kp |
| Power at the motor | Enter Kp | HPm = HPc / E |
Source: Machinery's Handbook (metal removal rate formulas); unit power at the cutter: P. Kwon, Michigan State University ME477 course notes, specific energy table (sharp tool, 0.25 mm uncut chip thickness); unit power at the motor: Kalpakjian and Schmid, Manufacturing Processes for Engineering Materials, 5th ed., Table 8.3; machine efficiency range: Sumitomo Electric and Mitsubishi Materials cutting power formulas and the same two texts.
MRR and horsepower are estimates and starting points. Dull tools and heavy feeds raise the power needed.
Unit power by material
| Material | Hardness (HB) | Kp (hp per in³/min) | Kp (kW per cm³/min) |
|---|---|---|---|
| Aluminum | 50 to 100 | 0.25 | 0.0114 |
| Aluminum alloys | 100 to 150 | 0.30 | 0.0137 |
| Magnesium alloys | 50 to 100 | 0.15 | 0.0068 |
| Cast iron | 125 to 175 | 0.40 | 0.0182 |
| Cast iron | 175 to 250 | 0.60 | 0.0273 |
| Carbon steel | 150 to 200 | 0.60 | 0.0273 |
| Carbon steel | 200 to 250 | 0.80 | 0.0364 |
| Carbon steel | 251 to 300 | 1.00 | 0.0455 |
| Alloy steel | 200 to 250 | 0.80 | 0.0364 |
| Alloy steel | 251 to 300 | 1.00 | 0.0455 |
| Alloy steel | 301 to 350 | 1.30 | 0.0592 |
| Alloy steel | 351 to 400 | 1.60 | 0.0728 |
| Stainless steel | 150 to 200 | 1.00 | 0.0455 |
Enter these in the Kp field as is. Basis: sharp tool, 0.25 mm (0.010 in) uncut chip thickness. kW per cm³/min = hp per in³/min x 0.04551.
Source: P. Kwon, Michigan State University ME477 course notes, specific energy table (at the cutter).
| Material | At the motor (hp per in³/min) | At the motor (kW per cm³/min) | At the cutter, x 0.80 (hp per in³/min) |
|---|---|---|---|
| Aluminum alloys | 0.15 to 0.40 | 0.0068 to 0.0182 | 0.12 to 0.32 |
| Magnesium alloys | 0.15 to 0.20 | 0.0068 to 0.0091 | 0.12 to 0.16 |
| Copper alloys | 0.50 to 1.20 | 0.0228 to 0.0546 | 0.40 to 0.96 |
| Cast irons | 0.60 to 2.00 | 0.0273 to 0.0910 | 0.48 to 1.60 |
| Steels | 1.00 to 3.40 | 0.0455 to 0.1547 | 0.80 to 2.72 |
| Stainless steels | 1.10 to 1.90 | 0.0501 to 0.0865 | 0.88 to 1.52 |
| Titanium alloys | 1.10 to 1.50 | 0.0501 to 0.0683 | 0.88 to 1.20 |
| Nickel alloys | 1.80 to 2.50 | 0.0819 to 0.1138 | 1.44 to 2.00 |
These ranges already include 80% machine efficiency. Use the last column in the Kp field so E is not counted twice. The source multiplies by 1.25 for dull tools.
Source: Kalpakjian and Schmid, Manufacturing Processes for Engineering Materials, 5th ed., Table 8.3.
Unit power varies with tool sharpness, rake angle and chip thickness; thinner chips take more power per in³. Treat every value as a starting estimate. Typical machine efficiency is about 0.70 to 0.90; 0.80 is a common planning value and the default in the E field.
How it works
Metal removal rate, inch
Milling MRR = WOC x DOC x IPM; turning MRR = 12 x DOC x IPR x SFM; drilling MRR = (pi x D^2 / 4) x IPR x RPM
| Symbol | Meaning | Unit |
|---|---|---|
| MRR | Metal removal rate | in³/min |
| WOC | Width of cut (radial engagement in milling) | in |
| DOC | Depth of cut (axial in milling, on the radius in turning) | in |
| IPM | Feed rate, inches per minute | in/min |
| IPR | Feed per revolution, inches per revolution | in/rev |
| SFM | Cutting speed, surface feet per minute | ft/min |
| D | Drill diameter | in |
| 12 | Inches per foot, to put SFM in inches | in/ft |
Metal removal rate, metric
Milling Q = (ae x ap x vf) / 1000; turning Q = Vc x ap x fn; drilling Q = (pi x D^2 / 4) x fn x RPM / 1000
| Symbol | Meaning | Unit |
|---|---|---|
| Q | Metal removal rate | cm³/min |
| ae, ap | Width and depth of cut | mm |
| vf | Feed rate | mm/min |
| fn | Feed per revolution | mm/rev |
| Vc | Cutting speed | m/min |
| D | Drill diameter | mm |
Power
HPc = MRR x Kp; HPm = HPc / E; metric Pc = Q x Kp
| Symbol | Meaning | Unit |
|---|---|---|
| Kp | Unit power for the material at the cutter, from the unit power table | hp per in³/min (kW per cm³/min) |
| E | Machine efficiency, as a decimal, typically 0.70 to 0.90 | none |
| HPc, Pc | Power at the cutter | hp (kW) |
| HPm, Pm | Power at the motor | hp (kW) |
Metric unit power is Kp x 0.04551: 0.7457 kW per hp divided by 16.387 cm³ per in³. The motor has to supply the cutter horsepower divided by efficiency; spindle horsepower at the RPM you run is what limits MRR and what sets motor size.
Worked example: milling, inch
WOC 0.500 in, DOC 0.250 in, 12.0 IPM in stainless steel at 150 to 200 HB: Kp 1.0 hp per in³/min at the cutter from the table, E 0.80.
- MRR = 0.500 x 0.250 x 12.0 = 1.500 in³/min (1.500 x 16.387 = 24.58 cm³/min).
- HPc = 1.500 x 1.0 = 1.50 hp.
- HPm = 1.50 / 0.80 = 1.875, so 1.88 hp at the motor.
Result: 1.500 in³/min, 1.50 hp at the cutter, 1.88 hp at the motor.
Worked example: turning, inch
DOC 0.100 in, 0.010 IPR, 400 SFM in carbon steel at 251 to 300 HB: Kp 1.0 hp per in³/min at the cutter from the table, E 0.80.
- MRR = 12 x 0.100 x 0.010 x 400 = 4.800 in³/min.
- HPc = 4.800 x 1.0 = 4.80 hp.
- HPm = 4.80 / 0.80 = 6.00 hp.
Result: 4.800 in³/min, 4.80 hp at the cutter, 6.00 hp at the motor.
Worked example: turning, metric
Vc 150 m/min, ap 2 mm, fn 0.25 mm/rev, E 0.80. Kp 0.04 kW per cm³/min is an example input between the carbon steel rows at 200 to 250 HB (0.0364) and 251 to 300 HB (0.0455).
- Q = 150 x 2 x 0.25 = 75.00 cm³/min (4.577 in³/min).
- Pc = 75.00 x 0.04 = 3.00 kW.
- At the motor: 3.00 / 0.80 = 3.75 kW (3.75 / 0.7457 = 5.03 hp).
Result: 75.00 cm³/min, 3.00 kW at the cutter, 3.75 kW (5.03 hp) at the motor.
Shop notes
- Tool-maker charts assume rigid machines. On a light machine, spindle horsepower, not the tool, usually sets the limit.
- Start low and adjust by sound and chip.
- Kp from a tool maker or another table may be at the motor rather than at the cutter. Check the basis before you divide by E.
- Same cut as the machining formulas page: 0.250 in x 0.500 in x 6.1 IPM = 0.7625 in³/min (0.76 in³/min there, at 2 places).
FAQ
How do you calculate metal removal rate for milling?
MRR = WOC x DOC x IPM. A 0.500 in wide, 0.250 in deep cut at 12.0 IPM removes 0.500 x 0.250 x 12.0 = 1.500 in³/min.
How do you calculate MRR for turning?
MRR = 12 x DOC x IPR x SFM. A 0.100 in depth of cut at 0.010 IPR and 400 SFM removes 4.800 in³/min.
How much horsepower does a cut need?
Horsepower at the cutter = MRR x Kp, with Kp from the unit power table on this page: 1.00 hp per in³/min for stainless steel at 150 to 200 HB, for example. Divide by machine efficiency E, typically 0.70 to 0.90 with 0.80 a common planning value, for horsepower at the motor.
Why is spindle horsepower lower than the motor rating?
Belts, gears and the drive lose power on the way to the cutter. Efficiency E accounts for it: HPm = HPc / E, with E typically 0.70 to 0.90.
What unit power does aluminum need?
At the cutter with a sharp tool, about 0.25 hp per in³/min (0.0114 kW per cm³/min) for aluminum at 50 to 100 HB and 0.30 hp per in³/min (0.0137 kW per cm³/min) for aluminum alloys at 100 to 150 HB.
What is 1.500 in³/min in cm³/min?
24.58 cm³/min: 1.500 x 16.387 = 24.58.
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