11 Common CNC Calculation Formulas

1. Trigonometric Functions Calculation

• tanθ = b/a, θ = tan^-1 b/a
• Sinθ = b/c, Cos = a/c

2. Cutting Speed Calculation

• Vc = (π * D * S) / 1000
  • Vc: Cutting speed (m/min)
  • π: Pi (3.14159)
  • D: Tool diameter (mm)
  • S: RPM (rotations per minute)

Example: Using a Φ25 cutter, Vc is 25 m/min, find S?

• S = 1000 * 25 / π * 25
• S = 320rpm

3. Feed Rate (F Value) Calculation

• F = S * Z * Fz
  • F: Feed rate (mm/min)
  • S: RPM
  • Z: Number of teeth
  • Fz: Actual feed per tooth (mm)

Example: A standard 2-tooth vertical milling cutter cuts at 2000rpm, what is the feed rate (F value)?

• F = 2000 * 2 * 0.25
• F = 1000 (mm/min)

4. Scallop Height Calculation

• Scallop = (ae * ae) / 8R
  • Scallop: Scallop height (mm)
  • ae: XY pitch (mm)
  • R: Tool radius (mm)

Example: Φ20R10, target scallop height is 0.002mm, what is the Pitch?

• ae = 0.4mm

5. Chip Escape Hole Calculation

• Φ = √2 * R^2, X, Y = D / 4
  • Φ: Chip escape hole diameter (mm)
  • R: Tool radius (mm)
  • D: Tool diameter (mm)

Example: Known milling cutter is ψ10; what is the minimum escape hole diameter? Center coordinates?

• Φ = 7.1(mm)
• X, Y = 2.5 mm
• Center coordinates are (2.5, -2.5)

6. Material Removal Rate Calculation

• Q = (ae * ap * F) / 1000
  • Q: Material removal rate (cm^3/min)
  • ae: XY pitch (mm)
  • ap: Z pitch (mm)

Example: Known mold needs cavity contouring, Φ35R5 cutter XY pitch is 60% of the tool, each layer cuts 1.5mm, feed rate is 2000mm/min, what is the material removal rate?

• Q = 63 cm^3/min

7. Feed per Tooth Calculation

• Fz = hm * √(D / ap)
  • Fz: Actual feed per tooth
  • hm: Theoretical feed per tooth
  • ap: Z pitch (mm)
  • D: Cutter diameter (mm)

Example: depo Φ35R5 cutter, cutting NAK80 material, hm is 0.15mm, Z-axis cutting depth is 1.5mm, what is the feed per tooth?

• Fz = 0.5mm

8. Die Edge Machining Method

• Cutting depth = Sheet thickness – Edge height + Drill tip (0.3D)
  • D represents the diameter of the tool

9. Drilling Time Formula

• T(min) = L(min) / N(rpm) * f(mm/rev)
• = πDL / 1000vf
  • L: Total length of the hole
  • N: Number of rotations
  • f: Feed rate coefficient
  • D: Diameter of the drill bit
  • v: Cutting speed

Example: Hole depth l, total length of the hole L, then L = l + D/3

• T = L / Nf = πDL / 1000vf

10. Feed Rate Coefficient Table (f)

• 1 inch = 25.4 mm = 8 parts
• 25.4 / number of teeth = pitch

Example: 25.4 / 18 = 1.414, the pitch is 5/16 thread

11. Horsepower (Gun Drill)

• W = Md * N / 97.410
  • W: Required power (KW)
  • Md: Torque (kg-cm)
  • N: Number of rotations (rpm)

Torque Calculation Formula:

• Md = 1 / 20 * f * ps *
  • f: Feed rate coefficient (mm/rev)
  • r: Radius of the drill bit (mm)
  • α: Cutting resistance ratio ps. For small feeds, general steel is 500 kg/m²; general cast iron is 300 kg/m²