3D Printing Feed Calculator Formula
Learn how layer height, line width, print speed, filament diameter, and flow multiplier determine volumetric flow and filament feed rate.
The 3D Printing Feed Calculator estimates the steady material demand of an extrusion move. It converts the planned extrusion line size and print speed into volumetric flow, then converts that volume into the linear filament speed the extruder must supply.
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Volumetric Flow Rate
Where:
Multiply layer height by line width to estimate the deposited line area. Multiply that by print speed and the flow multiplier to estimate the material volume needed each second.
Variables Explained
| Variable | What It Means | Unit |
|---|---|---|
| Q - Volumetric flow rate | Estimated material volume required per second. | mm³/s |
| H - Layer height | Height of each deposited print layer. | mm |
| W - Line width | Extrusion width set in the slicer. | mm |
| V - Print speed | Linear speed of the extrusion move being evaluated. | mm/s |
| F - Flow multiplier | Slicer extrusion or flow adjustment as a percentage. | percent |
| D - Filament diameter | Measured or nominal diameter of the round input filament. | mm |
| A_f - Filament cross-sectional area | Area of the filament used to convert material volume into filament length. | mm² |
Step-by-Step Calculation
Estimate deposited line area
The calculation treats the deposited line as a rectangle with the selected layer height and line width.
extrusionArea = layerHeight * lineWidth
Apply print speed
This gives the material volume required per second before any flow adjustment.
baseFlow = extrusionArea * printSpeed
Apply the flow multiplier
A 100% multiplier leaves the base flow unchanged; higher or lower values scale it proportionally.
volumetricFlow = baseFlow * (flowMultiplier / 100)
Calculate filament area
Filament is modeled as a round strand.
filamentArea = 3.141592653589793 * pow(filamentDiameter / 2, 2)
Convert volume to filament feed
Dividing required volume by the volume contained in each millimetre of filament gives the required filament movement in mm/s.
filamentFeedRate = volumetricFlow / filamentArea
Convert to feed per minute
This expresses the same feed demand in mm/min.
filamentFeedPerMinute = filamentFeedRate * 60
Example: Standard 0.20 mm layer profile at 60 mm/s
Extrusion area
0.20 × 0.42
0.084 mm²
Volumetric flow
0.084 × 60 × (100 / 100)
5.04 mm³/s
Filament area
3.141592653589793 × pow(1.75 / 2, 2)
2.405 mm²
Filament feed rate
5.04 / 2.405
2.10 mm/s
Filament feed per minute
2.10 × 60
125.7 mm/min
Final Result
At these settings, the estimated volumetric flow is 5.04 mm³/s and the required 1.75 mm filament feed rate is about 2.10 mm/s, or 125.7 mm/min.
Assumptions
- ✓The deposited extrusion path is approximated as a rectangle using layer height and line width.
- ✓The stated print speed is maintained during the extrusion move.
- ✓The flow multiplier applies evenly to the calculated move.
- ✓Filament is round and has a consistent diameter along its length.
- ✓The calculation represents steady extrusion rather than changing-speed motion.
Limitations
- !Actual line shapes can be rounded, squashed, overlapped, or adjusted by slicer-specific extrusion models.
- !Acceleration, deceleration, pressure advance, retraction, and extrusion dynamics are not included.
- !A calculated flow rate does not establish whether a particular hotend, nozzle, material, or temperature can sustain it.
- !Filament diameter variation, drive-gear slip, and calibration errors can change actual feed requirements.
Common Mistakes to Avoid
Using travel speed instead of the speed of the extrusion move.
Entering a flow multiplier such as 1 instead of 100 for normal flow.
Using nozzle diameter as line width when the slicer uses a different extrusion width.
Assuming a higher calculated filament mm/s always means a higher material flow without accounting for filament diameter.
Comparing volumetric flow with a hotend limit measured for a different material or temperature.
Related Formulas
Frequently Asked Questions
What is the formula for 3D printing volumetric flow?
Using this calculator's line-area approximation, volumetric flow is layer height multiplied by line width, print speed, and flow multiplier divided by 100.
How is filament feed rate calculated from volumetric flow?
Filament feed rate equals volumetric flow divided by the circular cross-sectional area of the filament.
Why does 2.85 mm filament have a lower feed rate than 1.75 mm filament?
Thicker filament has more cross-sectional area, so each millimetre contains more material. Less linear filament movement is needed for the same volumetric flow.
Does flow multiplier change volumetric flow?
Yes. For example, a 105% flow multiplier increases the calculated volumetric flow by 5% compared with 100%.
Is line width the same as nozzle diameter?
Not necessarily. Line width is the extrusion width selected or generated by the slicer and may be narrower or wider than the nozzle diameter.
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