Metal removal rate (MRR) expresses the volume removed per unit time. Its equation changes with the operation because the cutting geometry and feed are defined differently in milling and turning. The values here follow Sandvik Coromant’s metric formula sheets and keep the inputs beside each equation. Use the table to calculate a geometric rate from a known cut; it does not choose a safe speed, feed, tool, or machine load.

Metal Removal Rate Formula Reference

Milling formula

For milling, the reference uses Q = (ap × ae × vf) / 1000. Axial cutting depth ap and radial engagement ae are in millimetres, while table feed vf is in millimetres per minute. Dividing the resulting cubic millimetres per minute by 1,000 gives cubic centimetres per minute. If the cutter engages only part of its diameter, use the actual radial engagement rather than the cutter diameter.

The table feed can be determined from feed per tooth, spindle speed and the number of effective teeth: vf = fz × n × zc. Keep the cutter’s effective tooth count and the programmed feed consistent with the tool path. A value entered as feed per revolution cannot be substituted for feed per tooth without accounting for the number of teeth.

Turning formula

For turning, the Sandvik relation is Q = vc × ap × fn. Cutting speed vc is in metres per minute, depth of cut ap is in millimetres and feed per revolution fn is in millimetres per revolution. These units produce cubic centimetres per minute directly. The machined diameter and spindle speed relate cutting speed to rotation, but are not extra multipliers once vc is known.

When a lathe displays surface speed in another unit, convert it before calculating. Do not enter feet per minute as metres per minute. Feed stated in millimetres per minute must likewise be converted to feed per revolution using spindle speed before applying the turning equation.

Check units before comparing cuts

MRR is a volume rate, not a measure of finish quality or tool life. Compare operations only when the removed volume is defined in the same way and the input units match. If dimensions are in inches or feed is in inches per minute, convert the complete set consistently or use a formula sheet written for those units. Rounding intermediate values can create differences between a hand calculation and a machine display.

A dimensional check helps catch errors. Milling multiplies millimetres by millimetres by millimetres per minute, producing cubic millimetres per minute; the divisor converts that rate to cubic centimetres per minute. In turning, speed in metres per minute combines with the millimetre-based section and feed exactly as defined in the metric formula sheet. Keep the convention with saved calculations.

MRR does not set machine capability

The formulas describe how quickly material is removed for the stated geometry and feed. They do not guarantee that the cutting edge can sustain the operation. Specific cutting force, tool overhang, insert grade, workholding, coolant, chip evacuation and machine power affect whether a proposed setting is practical. A high calculated rate can exceed spindle power or torque limits even when every unit is correct.

The formula sheets provide separate power and torque equations because those checks need inputs such as specific cutting force and rotational speed. This table does not invent a generic cutting-force coefficient or recommend a material-specific setting. Obtain those inputs from current tool-maker or process data matching the work material and cutting condition.

Scope of this reference

The lookup includes one manufacturer’s metric MRR equations for milling and turning. It does not reproduce a handbook table or claim to cover drilling, boring, grinding or every machining operation. Use the formula that matches the process and verify each variable definition in the linked source. Do not infer a conversion when a process uses another feed convention or unit system.

For production, compare calculated MRR with tool-supplier cutting data and machine power, torque and speed envelopes. Confirm the tool path, engagement and material condition. The equation is a calculation aid, not a validated process plan.

Source and verification

Formula definitions and units were checked against Sandvik Coromant’s metric milling and turning formula sheets. The table retains only the MRR relationships and required variables, paraphrased as a compact lookup. The linked documents provide the full symbol definitions and related equations.