Essential CNC Calculation Formulas You Should Know

Looking to take your metalworking skills to the next level? Look no further than MachineMfg’s comprehensive guide to CNC calculation formulas.

Whether you’re a seasoned pro or just starting out, our expertly curated collection of formulas and insights will help you get the most out of your metalworking machines.

From calculating cutting speeds and feed rates to determining torque and horsepower requirements, our guide has everything you need to take your metalworking game to the next level.

So why wait? Dive into our guide today and start honing your skills with the best in the business.

CNC Commonly Used Calculation Formula

I. The calculation of trigonometric

1.tgθ=b/a      ctgθ=a/b

2.Sinθ=b/c      Cos=a/c

II. Calculation of cutting speed


  • Vc: linear velocity (m/min)
  • π: Circumference (3.14159)
  • D: Tool diameter (mm)
  • S: Rotational speed (rpm)

III. Calculation of the feed (F-value)


  • F: Feed rate (mm/min)
  • S: Rotational speed (rpm)
  • Z: Number of blades
  • Fz: (actual feed per blade)

IV. Calculation of residue height


  • Scallop: Residue height(mm)
  • ae: XY  pitch(mm)
  • R: Tool radius(mm)

V. Calculation of slug holes


X. Y=D/4

  • Φ: Diameter of slug holes(mm)
  • R: Tool radius (mm)
  • D: Tool diameter (mm)
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VI. Calculation of material intake


  • Q: The quantity of material taken(cm3/min)
  • ae: XY  pitch(mm)
  • ap: Z  pitch(mm)

VII. Calculation of the feed rate per blade

Fz=hm * √(D/ap )

  • Fz: Actual feed per blade
  • hm: theoretical feed per blade
  • ap:Z  pitch(mm)
  • D: Blade diameter (mm)

VIII. Die cutting edge processing method

Tooling depth = plate thickness – tool height + drill tip (0.3D)

  • D : Knife diameter

IX. Drill drilling time formula


  • L: Full length of the drilling
  • N: Number of turns
  • f: feed volume factor
  • D: Bit diameter
  • v: Cutting speed

Drill factor table fz 

Dia. mmFeed knife mm/rev

X. Formulas for calculating pipe teeth

1 inch = 25.4 mm.

XI. Horsepower (gun drill)

  • W = Md*N/97.410.
  • W: Power required (KW)
  • Md: torque (kg-cm)
  • N: Number of rotations (r.p.m.)

XII. The formula for calculating torque is as follows.

  • Md=1/20*f*ps*r2
  • f is the coefficient of feed mm/rev.
  • r is the drill radius (mm)
  • α: cutting resistance ratio ps. at small feed, general steel 500kg/m²; general cast iron 300kg/m²

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1 thought on “Essential CNC Calculation Formulas You Should Know”

  1. Question: I have a screen shot of a tooling estimate spreadsheet that was included in a tooling estimating seminar I attended. I have tried to fill in the formulas to utilize it for myself to quote tools but the one thing I cant figure out is the CNC portion of the sheet.
    The formula calls for ‘cut volume’, ‘# of details’, Machine run rate (3″/hr.) [with a given number of 10] & a formula for machine time (cut volume x # of details / machine run rate)
    Once you get the machine time you can calculate the cost by multiplying it by the amount per hour charged. for example it the volume was 25 & there were 2 details then it would be ((25 x 2)/10) x $95.00/hr. = $474.00 The only thing I cant figure out is how to get the cut volume. Any ideas?

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