The Golden Formula
If you only memorize one formula in machining, make it this one. This equation converts the material manufacturer's recommended speed (SFM) into the machine's programming unit (RPM).
Imperial Formula (Inches)
Where:
SFM = Surface Feet per Minute (from tooling catalog)
3.82 = Constant (12 / π)
Dia = Tool Diameter (Milling) or Workpiece Diameter (Turning)
Where does 3.82 come from?
It's not a magic number. It's simply the conversion factor to turn "feet" into "circumferences".
- We start with Surface Feet per Minute.
- But our tool diameter is in Inches.
- To convert feet to inches, we multiply by 12.
- The circumference of a circle is
π × D. - So, the full math is
(SFM × 12) / (π × D). 12 / 3.14159... ≈ 3.82.
Why Diameter Matters
This formula proves a fundamental rule of machining: Smaller tools must run faster.
Imagine a 1/2" end mill and a 4" face mill both cutting aluminum at 1000 SFM.
- 1/2" End Mill: (1000 × 3.82) / 0.5 = 7,640 RPM
- 4" Face Mill: (1000 × 3.82) / 4.0 = 955 RPM
Both tools are moving across the material surface at the exact same speed (the "Surface Speed"), even though their rotational speeds are vastly different.
Metric Formula (Meters)
Where:
Vc = Surface Speed (Meters per Minute)
318.3 = Constant (1000 / π)
Dia = Diameter in Millimeters
Common Conversion Chart (SFM to RPM)
Quick reference for common tool sizes at various surface speeds.
| Tool Dia | 100 SFM (Steel) | 300 SFM (Stainless) | 800 SFM (Alum) | 2000 SFM (HSM) |
|---|---|---|---|---|
| 1/8" (0.125) | 3,056 | 9,168 | 24,448 | 61,120 |
| 1/4" (0.250) | 1,528 | 4,584 | 12,224 | 30,560 |
| 1/2" (0.500) | 764 | 2,292 | 6,112 | 15,280 |
| 3/4" (0.750) | 509 | 1,528 | 4,074 | 10,186 |
| 1.0" (1.000) | 382 | 1,146 | 3,056 | 7,640 |
| 3.0" (Face Mill) | 127 | 382 | 1,018 | N/A |