Material Removal Rate Calculator: Milling, Turning, Drilling

Material Removal Rate Calculator for milling, turning, drilling, grooving and grinding that gives MRR in in³/min and cm³/min, plus spindle speed, motor power, torque and cut times.

Cut Setup

End milling or slotting: radial width × axial depth × table feed, with the feed set by chip load or entered as IPM.

Machining Operation

Feed Entered As

Radial Width of Cut (ae)

Axial Depth of Cut (ap)

Chip Load (fz)

Cutting Speed (Vc)

Cutter Diameter (D)

Number of Flutes (Z)

Table Feed (vf)

Work Diameter Before Cut (Dw)

Feed per Revolution (fn)

Depth of Cut, Radial (ap)

Groove Width (w)

Depth per Pass (ae)

Grinding Width (b)

Table Speed (vw)

Wheel Diameter (ds)

Wheel Speed (vs)

Power, Cut Length and UnitsSAE 1045 Steel, kc 369.6 ksi · 80% · 10 HP

Work Material (kc1, mc)

Tool Rake Angle (γ)

Drive Efficiency (η)

Machine Spindle Power

Length of Cut

Material Density

Result Units

Specific Cutting Force (kc)

Specific Grinding Energy (u)

Hole Depth

Groove Depth (Radial)

Material Removal Rate, Milling

4.584 in³/min Removed

75.11 cm³/min · 1,252 mm³/s

2,292 RPM Spindle Speed

Table Feed (vf)36.7 IPM

Avg Chip Thickness (hm)0.0025 in

Spindle speed from cutting speed and cutter size, with the feed it gives and the true average chip after chip thinning.

5.35 HP at the Motor

Cutting Power at Tool (Pc)4.28 HP

Spindle Torque9.80 lbf·ft

Power the cut needs at the tool from MRR × specific cutting force, and at the motor after drive losses, with the spindle torque.

16.4 s Cut Time

Metal Removed1.250 in³

Chip Weight0.355 lb

Time to finish the cut at this feed, with the metal volume removed and the chip weight it makes for planning and chip bins.

10.23 in³/min at Full Power

Chip Load at Full Power0.0089 IPT

Power Headroom4.65 HP

Highest removal rate the machine motor can hold on this material, the feed that reaches it and the power left over now.

Power ChartLoad 53%

MRR by Feed OverrideFull power at 223%

Override	Chip Load	MRR	Motor Power	Load
50%	0.0020 IPT	2.292 in³/min	3.11 HP	31%
75%	0.0030 IPT	3.438 in³/min	4.27 HP	43%
90%	0.0036 IPT	4.125 in³/min	4.93 HP	49%
100% (Yours)	0.0040 IPT	4.584 in³/min	5.35 HP	53%
110%	0.0044 IPT	5.042 in³/min	5.76 HP	58%
125%	0.0050 IPT	5.730 in³/min	6.36 HP	64%
150%	0.0060 IPT	6.875 in³/min	7.34 HP	73%

Spindle speed stays the same and only the feed changes. MRR rises in a straight line with feed, while power rises a little slower because kc falls as the chip thickens (power ∝ feed^0.78).

Slotting vs Side Cut vs Light PathSame 0.0025 in chip

Path	ae	Chip Load	Table Feed	MRR	Motor Power
Full Slot	0.500 in	0.0040 IPT	36.7 IPM	9.167 in³/min	10.69 HP (Over)
50% Side Cut (Yours)	0.250 in	0.0040 IPT	36.7 IPM	4.584 in³/min	5.35 HP
25% Side Cut	0.125 in	0.0053 IPT	48.9 IPM	3.056 in³/min	3.56 HP
10% Light Path	0.050 in	0.0082 IPT	75.1 IPM	1.878 in³/min	2.19 HP

Every row keeps your 0.0025 in average chip, axial depth and RPM, so kc stays the same and a lighter radial cut needs a higher chip load to hold it. High-efficiency paths pair the light width with a deeper axial cut, so raise ap to model one.

MRR Formulas by Operation5 operations

Operation	MRR	in³/min	cm³/min
Milling (Yours)	ap × ae × vf	ap × ae × vf (in, IPM)	ap × ae × vf ÷ 1,000 (mm, mm/min)
Turning	π × ap × (Dw - ap) × fn × n	π × ap × (Dw - ap) × fn × n (in, IPR, RPM)	π × ap × (Dw - ap) × fn × n ÷ 1,000 (mm, mm/rev, RPM)
Drilling	D × fn × vc ÷ 4	3 × D × fn × vc (in, IPR, SFM)	D × fn × vc ÷ 4 (mm, mm/rev, m/min)
Grooving	w × fn × vc	12 × w × fn × vc (in, IPR, SFM)	w × fn × vc (mm, mm/rev, m/min)
Grinding	ae × b × vw	ae × b × vw (in, IPM)	ae × b × vw ÷ 1,000 (mm, mm/min)

Power from any of them: Pc = Q × kc ÷ 396,000 HP with Q in in³/min and kc in psi, or Pc = Q × kc ÷ 60,000 kW with Q in cm³/min and kc in N/mm². The handbook turning shortcut vc × ap × fn (12 × vc × ap × fn in US units) is exact only with vc at the mean diameter Dw - ap; with vc at the starting diameter it overstates MRR by Dw ÷ (Dw - ap). Unit power in HP·min/in³ is kc ÷ 396,000, and specific grinding energy in J/mm³ equals kc in N/mm² ÷ 1,000.

Step-by-Step MathMilling

Spindle speed n = Vc × 12 ÷ (π × D) = 300 SFM × 12 ÷ (π × 0.500 in) = 2,292 RPM.
Table feed vf = fz × Z × n = 0.0040 IPT × 4 × 2,292 = 36.7 IPM.
MRR Q = ap × ae × vf = 0.500 in × 0.250 in × 36.7 IPM = 4.584 in³/min.
Engagement angle φ = arccos(1 - 2 × ae ÷ D) = 90.0°, so the average chip hm = fz × (2 × ae ÷ D) ÷ φ (radians) = 0.0025 in, 64% of the chip load.
Specific cutting force kc = kc1 × hm^-mc × (1 - γ ÷ 100) with SAE 1045 Steel kc1 1,500 N/mm² and mc 0.22, the average chip hm = 0.065 mm and rake 7°: kc = 2,548 N/mm² (369.6 ksi).
Cutting power Pc = Q × kc ÷ 396,000 = 4.584 × 369,560 psi ÷ 396,000 = 4.28 HP; at the motor Pc ÷ η = 4.28 ÷ 0.80 = 5.35 HP.
Torque = Pc × 5,252 ÷ n (HP, RPM) = 9.80 lbf·ft, and the machine load = 5.35 HP ÷ 10.00 HP = 53%.
Time = length ÷ feed = 16.4 s; metal removed = 1.250 in³ and chip weight = volume × density = 0.355 lb.
Full-power feed = (machine power ÷ motor power)^(1 ÷ (1 - mc)) = (10.00 ÷ 5.35)^1.282 = 223% of the feed now, since kc falls as the chip thickens; full-power MRR = 10.23 in³/min.

The Machine Uses 53% of Its Rated Power

Power uses kc 369.6 ksi for SAE 1045 Steel at this 0.065 mm chip. If your tool maker lists kc1 and mc for your exact grade, pick Custom and enter its kc.

How a Material Removal Rate Calculator Works

A material removal rate calculator finds the volume of metal a cut removes each minute. It multiplies the area of the cut, seen end-on, by the speed at which the tool sweeps through it, and gives the result in in³/min or cm³/min.

$Q = chip cross-section \times feed speed perpendicular to it$

Every operation in a material removal rate calculator uses that same idea with its own geometry. MRR, written Q, is the number shops use to compare toolpaths, estimate spindle power and plan cycle time, because it measures productivity directly rather than through speeds and feeds alone.

Worked Example: 1/2 in End Mill in Steel

Here is a material removal rate calculator for milling worked by hand. A 1/2 in four-flute end mill runs at 300 SFM with 0.004 in per tooth, cutting 0.500 in deep (axial) and 0.250 in wide (radial). The spindle speed, table feed and removal rate follow in three steps.

$n = \frac{12 \times V _{c}}{π \times D} = \frac{12 \times 300}{π \times 0.5} = 2, 292 RPM$

$v_{f} = f_{z} \times Z \times n = 0.004 \times 4 \times 2, 292 = 36.7 in/min$

$Q = a_{p} \times a_{e} \times v_{f} = 0.5 \times 0.25 \times 36.7 = 4.58 in^{3} /min$

That is 75.1 cm³/min, or 1,252 mm³/s. A 10 in long pass takes 16.4 seconds, removes 1.25 in³ and turns 0.355 lb of steel into chips at 0.284 lb/in³.

Chip weight follows the density of the metal, not the removal rate. The same 1.25 in³ weighs 0.121 lb in 5052 aluminum at 0.0968 lb/in³ and 0.204 lb in Grade 2 titanium at 0.163 lb/in³, which matters when you size chip bins or estimate scrap value.

Material Removal Rate Formula for Each Operation

The material removal rate formula changes with the shape of the chip. These are the forms a material removal rate calculator uses for each process, with the unit constants built in.

Operation	Formula	US Units (in³/min)	Metric (cm³/min)
Milling	a_p × a_e × v_f	in, in, IPM	mm, mm, mm/min, ÷ 1,000
Turning (exact)	π × a_p × (D_w - a_p) × f_n × n	in, in, IPR, RPM	mm, mm, mm/rev, RPM, ÷ 1,000
Turning (shortcut)	V_c × a_p × f_n	× 12, with SFM	with m/min
Drilling	D × f_n × V_c ÷ 4	3 × D × f_n × V_c	D × f_n × V_c ÷ 4
Grooving / parting	w × f_n × V_c	12 × w × f_n × V_c	w × f_n × V_c
Surface grinding	a_e × b × v_w	in, in, IPM	mm, mm, mm/min, ÷ 1,000

The milling, turning, drilling and grooving forms match the formula table on Machining Doctor's metal removal rate reference. In the imperial forms, the 12 converts SFM to in/min and the 3 comes from π/4 × 12/π.

Material Removal Rate Formula for Milling

In a milling material removal rate calculator, the chip cross-section is axial depth a_p × radial width a_e, and the speed through it is the table feed v_f. Doubling any one of the three doubles MRR, which is why a light, deep cut at high feed can match a heavy slot.

The feed itself comes from chip load: v_f = f_z × Z × n. The Spindle Speed Calculator finds n and v_f from cutting speed and chip load if you start from a tool maker's recommendation.

Material Removal Rate for Turning

A material removal rate calculator for turning treats the cut as a ring of depth a_p on a bar of diameter D_w, removed at f_n per revolution. The exact formula uses the ring's mean diameter, D_w - a_p.

Example: a 2 in bar at 500 SFM (955 RPM), 0.100 in depth and 0.010 IPR removes π × 0.1 × 1.9 × 0.01 × 955 = 5.70 in³/min. The handbook shortcut 12 × V_c × a_p × f_n gives 6.00 in³/min, high by D_w ÷ (D_w - a_p), or 5%, because it uses surface speed at the outside of the cut.

Material Removal Rate for Drilling

A material removal rate calculator for drilling starts from the hole itself: the drill removes a full circle of area π D²/4 at a penetration rate of f_n × n. Rewritten with cutting speed, that becomes D × f_n × V_c ÷ 4 in metric.

A 1/2 in drill at 100 SFM and 0.008 IPR removes 3 × 0.5 × 0.008 × 100 = 1.20 in³/min. A 10 mm drill at 80 m/min and 0.20 mm/rev removes 10 × 0.2 × 80 ÷ 4 = 40 cm³/min.

When the feed is given as a penetration rate instead, MRR is simply hole area × feed rate. A 1 mm drill advancing 12 mm/min removes 0.785 mm² × 12 = 9.42 mm³/min; at 5 mm/min it removes 3.93 mm³/min.

Grooving and Surface Grinding

Grooving and parting cut a chip as wide as the insert, so MRR is width × feed × surface speed. Surface speed falls as the insert moves toward center, so MRR drops through the cut at constant RPM.

Surface grinding removes a layer a_e deep and b wide at table speed v_w. A 0.001 in downfeed across a 1 in wide pass at 50 ft/min (600 IPM) removes 0.6 in³/min, a fraction of milling rates, which is why grinding is kept for finishing.

Spindle Power From Material Removal Rate

MRR times the material's specific cutting force gives the power the cut needs at the tool, which is the main reason a material removal rate calculator for machining asks for k_c. A metal removal rate calculator then divides by drive efficiency to find the power the motor must supply.

$P_{c} = \frac{Q \times k _{c}}{396 , 000} HP (Q in in^{3} /min, k_{c} in psi)$

$P_{c} = \frac{Q \times k _{c}}{60 , 000} kW (Q in cm^{3} /min, k_{c} in N/mm^{2})$

The 396,000 is 33,000 ft·lbf/min per HP × 12 in/ft. Unit power in HP·min/in³ is simply k_c ÷ 396,000, so a k_c of 370 ksi means 0.93 HP for every in³/min removed.

For the end mill example in SAE 1045 steel (k_c 370 ksi at this chip), the cut takes 4.28 HP at the tool and 5.35 HP at the motor with 80% drive efficiency. Spindle torque is 4.28 × 5,252 ÷ 2,292 = 9.80 lbf·ft, and a 10 HP spindle could push the same cut to about 10.2 in³/min.

Specific Cutting Force Depends on Chip Thickness

Specific cutting force is not a fixed property. It rises as the chip gets thinner and falls as the tool's rake angle opens up, so a material removal rate calculator with a material list applies the relation tool makers use.

$k_{c} = k_{c 1} \times h_{m}^{- m_{c}} \times (1 - \frac{γ}{100})$

k_c1 is the force for a 1 mm chip, m_c the slope of the curve, h_m the average chip thickness in mm and γ the rake angle in degrees, with +7° as a common default. The k_c1 and m_c values below are from Machining Doctor's specific cutting force table; the other columns apply them to the end mill example's 0.065 mm average chip.

Material	k_c1 (N/mm²)	m_c	k_c at 0.065 mm, +7° Rake	Motor HP at 4.58 in³/min	Max MRR on 10 HP
Aluminum, non-heat-treatable	700	0.25	1,291 N/mm² (187 ksi)	2.71 HP	26.2 in³/min
Aluminum 2024	800	0.25	1,475 N/mm² (214 ksi)	3.10 HP	21.9 in³/min
Gray cast iron	1,150	0.20	1,849 N/mm² (268 ksi)	3.88 HP	15.0 in³/min
Low-carbon steel, 0.15% C	1,350	0.21	2,231 N/mm² (324 ksi)	4.68 HP	12.0 in³/min
SAE 1045 steel	1,500	0.22	2,548 N/mm² (370 ksi)	5.35 HP	10.2 in³/min
SAE 4140 alloy steel	1,775	0.24	3,185 N/mm² (462 ksi)	6.68 HP	7.8 in³/min
Pure titanium	1,700	0.23	2,968 N/mm² (431 ksi)	6.23 HP	8.5 in³/min
Stainless 304, austenitic	2,150	0.20	3,458 N/mm² (502 ksi)	7.26 HP	6.8 in³/min
Tool steel, annealed	2,450	0.23	4,277 N/mm² (620 ksi)	8.98 HP	5.3 in³/min
Nickel or cobalt superalloy	3,300	0.24	5,921 N/mm² (859 ksi)	12.43 HP	3.4 in³/min

The max-MRR column lets k_c fall as the feed rises and the chip thickens, so it is higher than a straight power ratio would suggest. A tool maker's k_c for your exact grade and insert beats any table, especially for the low-carbon row, which sits below Sandvik Coromant's 1,500 N/mm² figure for unalloyed steel quoted in Wikipedia's cutting force article.

Average Chip Thickness and Chip Thinning

When the radial width is less than half the cutter diameter, each tooth takes a chip thinner than the programmed chip load. The average chip thickness over the engagement arc is the value that drives tool life and specific cutting force.

$φ = arccos (1 - \frac{2 a _{e}}{D}), h_{m} = f_{z} \times \frac{2 a _{e} / D}{φ}$

φ is the engagement angle in radians. At 50% radial width, φ is 90° and h_m is 64% of f_z; at 10% radial width, φ is 36.9° and h_m falls to 31% of f_z. To keep the same chip, the programmed chip load must rise to make up the difference.

Roughing vs Finishing MRR Strategies

A material removal rate calculator makes roughing strategies easy to compare. Roughing aims for the highest MRR the machine and tool can hold; finishing gives up MRR for accuracy and surface. The table compares three roughing approaches with the same 1/2 in four-flute tool at 300 SFM, each fed to hold a 0.0025 in average chip.

Strategy	Axial × Radial	Engagement	Chip Load Needed	Table Feed	MRR
Full slot	0.25 × 0.50 in	180°	0.0040 in	36.7 IPM	4.58 in³/min
50% side cut	0.50 × 0.25 in	90°	0.0040 in	36.7 IPM	4.58 in³/min
High-efficiency (10% radial)	1.00 × 0.05 in	36.9°	0.0082 in	75.1 IPM	3.76 in³/min

The high-efficiency path removes slightly less at the same surface speed, but its short engagement keeps heat out of the tool, so tool makers allow much higher SFM. At 1.5 × the speed it would reach about 5.6 in³/min with far less tool wear.

Finishing passes often run 0.005-0.020 in radial stock, where MRR is a small fraction of roughing. Planning cycle time with a single MRR number therefore splits into roughing volume at roughing MRR and finishing area at finishing feed.

Material Removal Rate Chart for Common Cuts

A material removal rate chart puts the operations side by side. At typical settings, turning and milling remove several times more metal per minute than drilling, and grinding trails all of them.

Operation	Settings	MRR (in³/min)	MRR (cm³/min)
Milling, 1/2 in end mill	300 SFM, 0.004 IPT, 0.5 × 0.25 in	4.58	75.1
Turning, 2 in bar	500 SFM, 0.010 IPR, 0.100 in depth	5.70	93.4
Drilling, 1/2 in drill	100 SFM, 0.008 IPR	1.20	19.7
Drilling, 10 mm drill	80 m/min, 0.20 mm/rev	2.44	40.0
Surface grinding	0.001 in × 1 in at 50 ft/min	0.60	9.8

What counts as a high MRR depends on the material, because power is the usual limit a material removal rate calculator checks against. On a 10 HP spindle, the same cutting conditions support about 26 in³/min in non-heat-treatable aluminum but only about 7 in³/min in 304 stainless.

Material Removal Rate Calculator in Excel

A material removal rate calculator in Excel needs one row per input. For milling in US units, put SFM in B1, cutter diameter in B2, flutes in B3, chip load in B4, axial depth in B5, radial width in B6 and k_c in psi in B7:

RPM:        =B1*12/(PI()*B2)
Feed (IPM): =B4*B3*B1*12/(PI()*B2)
MRR:        =B5*B6*B4*B3*B1*12/(PI()*B2)
HP at tool: =B5*B6*B4*B3*B1*12/(PI()*B2)*B7/396000

With 300, 0.5, 4, 0.004, 0.5, 0.25 and 369,560 these return 2,292 RPM, 36.7 IPM, 4.58 in³/min and 4.28 HP. Divide the last line by drive efficiency for motor power.

To convert, 1 in³/min equals 16.387 cm³/min, and 1 cm³/min equals 0.0610 in³/min. Values in mm³/s multiply by 0.06 to give cm³/min, so 1,252 mm³/s is 75.1 cm³/min.

Material Removal Rate Questions

MRR connects to the everyday speed and feed questions on a CNC machine, and to a few percentage questions that share the word "removal."

What is the material removal rate?

Material removal rate is the volume of workpiece material cut away per unit of time, usually in in³/min or cm³/min. Metal removal rate is the same measure applied to metals, and both are written as Q or MRR.

What is the material removal rate (MRR) calculator?

A material removal rate calculator is a tool that turns cutting parameters (depths, feed and speed) into cubic inches or cubic centimeters of metal removed per minute. Better versions add spindle speed, chip thickness, power, torque and cut time from the same inputs.

How does the material removal rate calculator help with production planning?

Divide the volume to be removed by MRR to get cutting time. Roughing a 6 × 4 × 1 in pocket (24 in³) at 4.58 in³/min takes about 5.2 minutes of cutting, before tool changes, rapids and finishing passes.

How does a material removal rate calculator work?

It multiplies the chip's cross-section by the feed speed through it, using the formula for the chosen operation. Fuller tools then use MRR with specific cutting force to estimate spindle power, torque and cut time.

How does spindle speed relate to material removal rate?

MRR rises in a straight line with spindle speed when chip load and depths stay the same, because table feed is f_z × Z × n. Raising RPM by 20% raises MRR and power by 20%, but also raises heat at the cutting edge.

What is the SFM formula?

Surface feet per minute is SFM = π × D × RPM ÷ 12, with D in inches. A 1/2 in cutter at 2,292 RPM runs at 300 SFM.

How do you calculate Vc on a VMC?

Cutting speed in metric is V_c = π × D × n ÷ 1,000 in m/min, with D in mm. A 12 mm end mill at 2,500 RPM runs at 94.2 m/min.

How do you calculate CNC feed rate?

For milling, feed rate is chip load × number of flutes × RPM. A four-flute cutter at 0.004 in per tooth and 2,292 RPM feeds at 36.7 IPM; for turning, feed rate is IPR × RPM.

What factors affect material removal rate in machining?

Depth of cut, width of cut, chip load, number of teeth and cutting speed set MRR directly. Machine power, rigidity, tool strength, chip evacuation and workpiece material set how high those can safely go.

How do I convert between metric and imperial MRR units?

Multiply in³/min by 16.387 to get cm³/min, or cm³/min by 0.0610 to get in³/min. A material removal rate calculator online usually shows both, plus mm³/s, where 1 cm³/min equals 16.67 mm³/s.

How do you calculate percent removal?

Percent removal is (initial - final) ÷ initial × 100. In wastewater, the values are influent and effluent concentrations; in machining, they are volumes, so turning a 4 in bar down to 3 in removes 1 - (3/4)² = 43.75% of the material.

How do you remove a percentage with a calculator?

Multiply by one minus the percentage. Removing 40% from a price of $250 is 250 × 0.60 = $150. To allow 5% wastage on a material order, multiply the net quantity by 1.05, so 200 lb becomes 210 lb.

Does material removal rate apply to welding?

Welding adds metal, so it is measured by deposition rate in lb/hr instead of removal rate. The Welding Calculator estimates weld metal and filler; MRR applies to gouging and to machining the weld afterward.