Volumetric Flow Rate Formula
Reference for the FDM volumetric flow formula Q = h x w x v.
Includes hotend flow limits by nozzle size, under-extrusion causes, and worked examples.
The Formula
Q is volumetric flow in mm³/s. h is layer height in mm, w is line width in mm, and v is print speed in mm/s. This single formula governs how fast any FDM printer can move without under-extruding.
Variables
| Symbol | Meaning |
|---|---|
| Q | Volumetric flow rate (mm³/s) |
| h | Layer height (mm) |
| w | Line width (mm) |
| v | Print speed (mm/s) |
Example 1 — Standard 0.4mm nozzle
0.2mm layer height, 0.45mm line width, 60 mm/s print speed
Q = 0.2 × 0.45 × 60
Q = 5.4 mm³/s
A standard brass 0.4mm hotend (E3D V6, Dragon, Mosquito) handles about 8-12 mm³/s before temperature-dependent under-extrusion sets in. At 5.4 mm³/s you have headroom; at 15 mm³/s you need a high-flow hotend or will see gaps.
Example 2 — Finding max speed from flow limit
Hotend rated at 15 mm³/s, 0.3mm layer height, 0.5mm line width
v_max = Q_max / (h × w) = 15 / (0.3 × 0.5)
v_max = 100 mm/s
Hotend Flow Limits (approximate)
| Hotend type | Max flow (mm³/s) |
|---|---|
| Standard brass V6, MK3 clone | 8–12 |
| Rapido, Dragon HF, Revo | 15–22 |
| Volcano, CHC Pro (0.6mm+) | 20–35 |
| High-flow (Bambu, K1, E3D ObXidian) | 30–60 |
Key Notes
- The formula uses a rectangular cross-section approximation. Actual filament cross-section is more of a stadium shape (rectangle with rounded ends), but the error is small for typical layer heights and line widths.
- Flow limit is not fixed. A hotend that handles 15 mm³/s at 220C PLA may only manage 10 mm³/s at 200C. Raising print temperature by 10-15C is often the easiest way to recover flow margin without changing hardware.
- Infill usually runs at higher speed than perimeters. Slicer volumetric speed limit settings apply a global cap to prevent the hotend from being asked to exceed Q_max on any move, regardless of what speed each feature is set to.
- Abrasive and composite filaments (carbon fiber, glow-in-dark) reduce flow capacity in brass nozzles over time as the bore wears oval. Hardened steel or ruby-tipped nozzles maintain their flow rating much longer.