CNC Calculation Formula: Commonly Used You Should Know

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)

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. mm Feed knife mm/rev
1.6~3.2 0.025~0.075
3.2~6.4 0.05~0.15
6.4~12.8 0.10~0.25
12.8~25 0.175~0.375
>25 0.376~0.625

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 “CNC Calculation Formula: Commonly Used 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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