CNC / machinist calculator
Material Removal Rate (MRR) Calculator
Material removal rate (also called metal removal rate, or MRR) is the volume of stock a cut clears per minute, and the number shops use to compare toolpaths, size spindles and estimate cycle time. Pick the operation - milling, turning or drilling - enter the cut, and this calculator returns the MRR in cubic inches per minute and cubic centimetres per minute, and estimates the spindle power the cut demands from the chosen material's unit power.
- Required power (sharp tool, 80% drive efficiency)
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How it works
For milling, material removal rate is the table feed times the axial depth of cut times the radial width of cut: the rectangular channel the cutter sweeps, extruded along the table travel each minute. Sandvik Coromant writes it Q = ap x ae x vf, in cubic inches per minute directly, or divided by 1000 for cubic centimetres per minute when ap and ae are in millimetres and vf in mm/min.
For turning, each revolution peels off a chip whose cross-section is the depth of cut times the feed per revolution, and that ribbon comes off at the cutting speed. In inch units the standard form is MRR = 12 x cutting speed (SFM) x depth of cut x feed (in/rev); the 12 only converts the surface feet of ribbon per minute into inches, so the product comes out in cubic inches per minute. In metric the same physics is MRR = vc x ap x fn, which lands directly in cubic centimetres per minute with vc in m/min, ap in mm and fn in mm/rev.
A drill in solid stock removes the full hole cross-section, pi/4 times the diameter squared, at whatever rate it advances, so drilling MRR is pi/4 x D^2 x penetration rate. The penetration rate is just the feed per revolution times the RPM. Tool makers often print the algebraically identical form Q = D x fn x vc / 4 (metric) or Q = 3 x D x fn x vc (inch), which this calculator matches exactly.
MRR is what actually loads the spindle, and it is the honest denominator for cycle time: a roughing pass that clears twice the volume per minute halves the cutting time for that stock, whatever its feed rate reads. Required power scales directly with it - multiply MRR by the material's unit power for cutting horsepower - which is why a deep roughing cut can stall a spindle that a fast finishing pass barely warms.
Worked examples
Milling. Harvey Performance's published example: 0.500 in radial width x 0.100 in axial depth x 41.5 in/min of feed removes 0.500 x 0.100 x 41.5 = 2.08 in³/min. ISCAR's face-milling example: 5 mm deep and 180 mm wide at a 459 mm/min table feed removes 5 x 180 x 459 = 413,100 mm³/min, i.e. 413.1 cm³/min.
Turning. ISCAR's example: a 2.5 in bar at 1,000 RPM runs at pi x 2.5 x 1000 = 7,854 in/min of surface speed (654.5 SFM). At 0.080 in depth of cut and 0.006 in/rev, MRR = 7854 x 0.08 x 0.006 = 3.77 in³/min. At 200 m/min cutting speed, 2 mm depth of cut and 0.25 mm/rev feed, MRR = 200 x 2 x 0.25 = 100 cm³/min.
Drilling. A 1/2 in drill at 1,500 RPM and 0.004 in/rev penetrates at 6 in/min, so MRR = (pi/4) x 0.5² x 6 = 1.18 in³/min. A 10 mm drill at 1,000 RPM and 0.2 mm/rev penetrates at 200 mm/min, so MRR = (pi/4) x 10² x 200 = 15,708 mm³/min, about 15.7 cm³/min.
Frequently asked questions
What is material removal rate?
Material removal rate, or MRR, is the volume of material a machining operation removes per minute, usually stated in cubic inches per minute or cubic centimetres per minute. It condenses speed, feed and depth of cut into one productivity number, so it is the standard way to compare cuts and toolpaths.
What is the material removal rate formula for turning?
In inch units, turning MRR = 12 x cutting speed (SFM) x depth of cut (in) x feed (in/rev); the 12 converts surface feet per minute to inches. In metric, MRR = cutting speed (m/min) x depth of cut (mm) x feed (mm/rev), which comes out directly in cubic centimetres per minute.
How do I calculate MRR for milling?
Multiply the table feed rate by the axial depth of cut and the radial width of cut. In inch units the result is cubic inches per minute; in metric, millimetre inputs give cubic millimetres per minute, and dividing by 1000 gives cubic centimetres per minute.
What is the MRR formula for drilling?
A drill in solid material removes the full hole cross-section, so MRR = pi/4 x diameter squared x penetration rate, where the penetration rate is the feed per revolution times the RPM. The equivalent form Q = D x feed/rev x cutting speed / 4 that tool makers publish gives the same removal rate in a different unit convention: with millimetre inputs the pi/4 form returns cubic millimetres per minute, while the Sandvik metric form returns cubic centimetres per minute.
Why does MRR matter for cycle time?
The volume of stock to remove is fixed by the part, so the time a roughing operation takes is that volume divided by the MRR. Doubling the removal rate halves the roughing time, which is why MRR, not feed rate alone, is the number to optimize when quoting or speeding up a job.
Is metal removal rate the same as material removal rate?
Yes. Metal removal rate and material removal rate both abbreviate to MRR and mean the volume removed per unit time; tooling catalogs aimed at metal cutting tend to say metal, while textbooks say material because the same formulas apply to plastics and composites.
How is MRR related to spindle power?
Cutting power is approximately the MRR times the material's unit power (HP per cubic inch per minute), divided by drive efficiency for the power at the motor. Higher MRR demands proportionally more horsepower, so MRR is the direct input to checking whether a machine can hold a cut.
Related calculators
Sources
- Sandvik Coromant - milling formulas and definitions (Q = ap x ae x vf)
- Sandvik Coromant - general turning formulas and definitions (Q from vc, ap, fn)
- Sandvik Coromant - drilling formulas and definitions (Q = D x fn x vc / 4)
- ISCAR - Machining calculations (worked MRR examples for turning and milling)
- Harvey Performance - Optimizing material removal rates (milling example)
- Isakov, Aerospace Manufacturing and Design - Metal removal rates for turning (Q = 12 Vc ap f)
- HRC CNC - Milling rate or material removal rate (MRR): a complete guide (metric drilling example)
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.