This page is a collection of basic milling calculators and formulas. Each topic includes an online calculator, formulas, and explanations. For easier use, you can toggle between the units (Metric/Imperial) and choose if to view everything or only the calculators (Hide the explanations and formulas)

This page includes only elementary calculators. For more complex topics, there is a separate page for each calculator. Go to the Machining Calculators Page for the complete list.

Cutting Speed

Milling cutting speed calculator and formula. (How to calculate the cutting speed based on the milling cutter’s diameter and spindle speed)

Spindle speed and cutting speed sketch

Theory

Cutting speed is the relative linear velocity between the tip of the cutting edge and the workpiece. It is a result of the product between the rotation speed of the milling cutter (Spindle speed) and its circumference.

\( \large C = 2 \times \pi \times r = \pi \times d \)
\( \large V_c = n \times C \)

Important Note: The Diameter (d) should be the effective diameter and not the cutter diameter. In 90° mills, both have the same value, However, on round and chamfer cutters, the effective diameter depends on the depth of cut and the cutter geometry.

Formula in metric units

  • d – [mm]
  • n – [rpm] (Revolutions per minutes)
  • Vc – [m/min]
\( \large V_c = \huge \frac{n \times \pi \times d}{1000} \)

Formula in Imperial units

  • d – [Inch]
  • n – [rpm] (Revolutions per minutes)
  • Vc – [SFM] (Surface feet per minute)
\( \large V_c = \huge \frac{n \times \pi \times d}{12} \)


Spindle Speed

Milling spindle speed calculator and formula. (How to calculate the spindle speed based on the milling cutter’s diameter and cutting speed)

Spindle speed and cutting speed sketch

Theory

The milling cutter’s catalog or our experience tells us the cutting speed we need to use for a given application. On the other hand, the CNC machine is programmed with spindle speed. Therefore it is common that we need to compute the RPM from a given cutting speed either for programming or to ensure that the speed we want to run at is within the machine’s limit. It is calculated by dividing the cutting speed by the cutter’s circumference.

Power Tip – Use our Speed and Feed Calculator to get the recommended cutting speed based on dozens of parameters!

\( \large C = 2 \times \pi \times r = \pi \times d \)
\( \large n= \huge \frac{V_c}{d} \)

Important Note: for accurate results, you should use the Effective Diameter. In 90° mills, it is simply the cutter’s diameter, However, on round and chamfer cutters, the effective diameter depends on the depth of cut and the cutter geometry.

Formula in metric units

  • d – [mm]
  • n – [rpm] (Revolutions per minutes)
  • Vc – [m/min]
\( \large n = \huge \frac{1000 \times V_c}{\pi \times d} \)

Formula in Imperial units

  • d – [Inch]
  • n – [rpm] (Revolutions per minutes)
  • Vc – [SFM] (Surface feet per minute)
\( \large n = \huge \frac{12 \times V_c}{\pi \times d} \)


Feed Per Tooth

The Feed per Tooth calculator will help you calculate the Feed based on the table feed, spindle speed and the number of flutes.

Feed Per Tooth Sketch

Theory

Feed per Tooth represents the load that is acting on a single cutting edge of a milling cutter (chip load). It is a good indicator to check if certain cutting conditions (Spindle speed and table feed) are reasonable for a given cutter geometry. It is calculated by dividing the table feed by the spindle speed and the number of flutes.

Power Tip – fz is equal to the chip load only when on a 90° milling cutter working at a radial depth of cut that is larger than the cutter’s radius (ae>r). In other cases, you can use a higher feed depending on the Chip Thinning Factor.

Formula (metric/inch)

  • z – Number of teeth
  • n – Spindle speed [RPM]
  • fz – Feed per tooth [mm or Inch]
  • fn – Feed per revolution [mm or Inch]
  • Vf – Table feed [mm/min] or [inch/min]
\( \large f_z= \huge \frac{V_f}{n \times z} \)


Table Feed

Milling feedrate calculator. How to calculate the feedrate based on the feed per tooth, spindle speed and number of flutes.

Feed Per Tooth Sketch

Theory

Milling Feedrate (Also called Table Feed and Feed Speed), is the linear velocity of a milling cutter relative to the workpiece, measured in [mm/min] or [inch/min]. It is the actual parameter that is programmed into the machine. However, it is not a property of the cutter’s geometry, and it needs to be calculated based on the spindle speed and the number of teeth. The basic parameters that we can obtain from the tool catalog are the cutting speed and the feed per tooth (Chip load). From the cutting speed, we can calculate the spindle speed with the above calculator. after that, we can proceed with the following formula

Power Tip – The primary parameter that yields the table feed (Vf) is the Feed per Tooth (fz). A common mistake is to use the chip load recommendation provided by the catalogs as the feed per tooth. However, this assumption is correct only when using a 90° milling cutter with a radial depth of cut that is larger than the cutter’s radius (ae>r). In other cases, you can use a much higher fz depending on the Chip Thinning Factor.

Formula (metric/inch)

  • z – Number of teeth
  • n – Spindle speed [RPM]
  • fz – Feed per tooth [mm or Inch]
  • fn – Feed per revolution [mm or Inch]
  • Vf – Table feed [mm/min] or [inch/min]
\( \large f_n = z \times f_z \)
\( \large V_f= n \times f_n \)
\( \normalsize \text {Or directly} \)
\( \large V_f= n \times z \times f_z \ \)


Metal Removal Rate

The MRR Calculator determines the volume of material removed per minute in certain cutting conditions.

Theory

The Metal roval rate (MRR) is measured in cubic inches (Or cubic mm) per minute and indicates how much material is machined in one minute at a set of cutting conditions. In milling, it is the product of the Table Feed, Radial depth of cut, and axial depth of cut. Learn more in our in-depth Metal Removal Page. MRR is used for two purposes:

  • Comapring the productivity between two sets of cutting conditions.
  • Estimating the required power consumption.

Formula (metric/inch)

  • ae – Radial depth of cut [mm] or [inch]
  • ap -Axial depth of cut [mm] or [inch]
  • Vf – Table feed [mm/min] or [inch/min]
  • Q – Metal Removal Rate [mm3/min] or [inch3/min]
\( \large Q = V_f \times a_e \times a_p \)

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