Industrial Machining & 3D Printing Feed Rates
The millimeter per minute to mm per second converter bridges the two primary unit conventions used in automated manufacturing, CNC milling, laser cutting, and additive manufacturing (3D printing). While CNC G-code programming standards (such as ISO 6983 and NIST RS274NGC) traditionally specify tool axis feed rates ($F$) in millimeters per minute ($text{mm/min}$), desktop 3D printer slicers (such as PrusaSlicer, Cura, and Bambu Studio) and motion controllers frequently configure printhead speeds, retraction rates, and travel accelerations in millimeters per second ($text{mm/s}$).
Translating accurately between these two units is essential for optimizing chip load per tooth, preventing tool deflection or breakage, eliminating stringing in 3D prints, and avoiding thermal degradation of cut stock.
Exact Mathematical Formulas
Because the linear distance unit (the millimeter, $10^{-3}text{ m}$) remains identical in both expressions, the conversion factor is derived entirely from the sexagesimal time ratio ($1text{ minute} = 60text{ seconds}$):
text{mm/s} = frac{text{mm/min}}{60} = text{mm/min} times 0.01666666667…
text{mm/min} = text{mm/s} times 60
Machining Reference Standards & Chip Load
In CNC milling, tool feed rate ($F$) is directly linked to spindle rotational speed ($N$, in RPM), tooth count ($z$), and chip load per tooth ($f_z$):
F_{text{mm/min}} = N times z times f_z
If your CAM software or controller firmware displays feed velocity in $text{mm/s}$, simply divide by $60$ to maintain safe cutting tool chip thickness. For rotational tool velocity calculations, use our RPM to feet per minute calculator and Hertz to RPM converter.
Additive Manufacturing & Slicer Volumetric Flow
In fused filament fabrication (FFF) 3D printing, printhead linear speed ($v$, in $text{mm/s}$) directly dictates the required volumetric extrusion flow rate ($Q$, in $text{mm}^3/text{s}$):
Q = text{Layer Height (mm)} times text{Extrusion Width (mm)} times v_{text{mm/s}}
Most standard hotends feature maximum melt flow capacities of $12text{ to }30text{ mm}^3/text{s}$. If a user inadvertently enters an intended G-code feed rate of $3,600text{ mm/min}$ into an $text{mm/s}$ slicer field, the resulting attempted $3,600text{ mm/s}$ velocity demands impossible melt rates, leading to immediate extruder grinding and stepper motor skipping.
Step-by-Step Worked Examples
Example 1: Converting CNC Milling G-Code Feed Rate
A CNC milling program for cutting 6061-T6 aluminum calls for a table feed rate of $F = 1,800text{ mm/min}$. What is the linear velocity of the cutter relative to the workpiece in millimeters per second?
- Apply the conversion formula: $1,800 div 60 = 30text{ mm/s}$.
- In meters per second: $30 times 10^{-3} = 0.03text{ m/s}$. Compare scientific velocities with our m/s to fps converter.
- In inches per minute (IPM): $1,800 div 25.4 approx 70.866text{ IPM}$.
Example 2: Setting 3D Printer Infill Speed in G-Code
A 3D printer slicer profile configures solid infill speed at $120text{ mm/s}$. What feed rate command ($F$) will the slicer output into the resulting G-code file?
- Multiply by $60$: $120 times 60 = 7,200text{ mm/min}$.
- The resulting G-code line will read:
G1 X50.0 Y80.0 F7200.
Common Workshop Errors & Diagnostic Tips
- Slicer vs. Controller Confusion: Inputting a desired $60text{ mm/s}$ printing speed into a controller prompt expecting $text{mm/min}$ causes the machine to crawl at $1text{ mm/s}$ ($60text{ mm/min}$). Conversely, entering $1,200$ expecting $text{mm/min}$ into an $text{mm/s}$ field causes severe stepper motor stalling.
- Acceleration Limits: Just because a high feed rate like $3,000text{ mm/min}$ ($50text{ mm/s}$) is configured does not guarantee the machine reaches that speed on short toolpaths. Machine acceleration ($mm/s^2$) determines whether top velocity is attained.
- Feed Rate per Tooth vs Table Feed: Catalog values often cite feed per tooth ($f_z$). Multiplying by RPM and flutes yields table feed in mm/min. To compute spindle speed, see our radians per second to RPM converter.
Related Manufacturing & Motion Calculators
Measurement standards and conversion factors conform to authoritative guidelines published in the NIST Special Publication 811 (Guide for the Use of the International System of Units).
