3D Printing Yield Formula
Learn how to estimate filament required per part, batch material use, and spool yield from model volume and print settings.
This calculation converts an estimated printed volume into filament mass, then adds an allowance for waste. It helps plan a print run before relying on the more detailed estimate produced by a slicer.
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Filament Required per Part
Where:
Estimate the printed share of the solid model volume, convert that volume to grams using filament density, and increase the result for expected waste.
Variables Explained
| Variable | What It Means | Unit |
|---|---|---|
| V - modelVolume | Solid volume of one model before infill and shell reductions. | cm³ |
| I - infillPercent | Percentage of the model volume estimated to be occupied by infill. | percent |
| S - shellMaterialPercent | Estimated percentage of solid model volume used by walls, surfaces, and included supports. | percent |
| D - filamentDensity | Mass per unit volume of the selected filament. | g/cm³ |
| W - wastePercent | Allowance for purge material, brims, failures, and other losses. | percent |
| N - partsToPrint | Number of identical parts in the planned run. | number |
| SW - spoolWeight | Usable net filament weight available on the spool. | g |
Step-by-Step Calculation
Calculate material fraction
Add the infill and shell allowances to estimate the portion of the solid model volume made from plastic.
materialFraction = (infillPercent + shellMaterialPercent) / 100
Estimate printed volume
Apply the material fraction to the solid model volume.
printedVolumePerPart = modelVolume * materialFraction
Convert volume to base mass
Multiply estimated plastic volume by density to obtain grams before waste.
baseMaterialPerPart = printedVolumePerPart * filamentDensity
Add the waste allowance
Increase the base mass for expected extra filament use.
materialPerPart = baseMaterialPerPart * (1 + wastePercent / 100)
Calculate batch material
Multiply the per-part estimate by the number of parts planned.
totalMaterialRequired = materialPerPart * partsToPrint
Calculate spool yield
Divide usable spool weight by grams per part and round down because only complete parts count.
numberOfPartsFromSpool = floor(spoolWeight / materialPerPart)
PLA parts from a 1 kg spool
Material fraction
(20 + 15) / 100
0.35
Printed volume
50 × 0.35
17.5 cm³
Base material per part
17.5 × 1.24
21.7 g
Material per part including waste
21.7 × 1.10
23.9 g
Material for 10 parts
23.9 × 10
238.7 g
Spool yield
floor(1000 / 23.9)
41 parts
Final Result
Each part requires about 23.9 g of filament. Ten parts require about 238.7 g, and a 1 kg spool yields about 41 complete parts.
Assumptions
- ✓The entered model volume is the volume of a fully solid version of one part.
- ✓Infill percentage and shell material percentage are reasonable simplified estimates of plastic occupancy.
- ✓The selected filament has uniform density matching the entered value.
- ✓The waste allowance represents likely extra material across the job.
Limitations
- !The calculation does not model exact wall thickness, layer height, infill pattern, or internal geometry.
- !Supports, rafts, purge towers, and multicolor transitions can materially change actual usage.
- !A filament spool may have less usable material than its stated net weight if the remaining amount is uncertain.
- !Slicer estimates are usually more detailed and should be checked before a large batch.
Common Mistakes to Avoid
Entering model volume in mm³ without converting it to cm³; divide mm³ by 1,000 first.
Using only infill percentage and setting shell material to zero.
Treating the spool's gross weight, including the reel, as usable filament weight.
Using PLA density for a different material or filled filament.
Rounding spool yield up instead of down to complete parts.
Related Formulas
Frequently Asked Questions
What is the formula for filament required per 3D printed part?
Multiply solid model volume by the combined infill and shell fraction, then by filament density and the waste multiplier.
How is parts per spool calculated?
Usable spool weight is divided by estimated grams per part, and the result is rounded down to whole parts.
Why is filament density included?
The same printed volume has a different mass when made from materials with different densities.
Can infill plus shell material exceed 100%?
No. For this simplified model, their combined percentage should not exceed 100% of solid model volume.
Should I use this instead of my slicer estimate?
Use it for early planning and use the slicer estimate as a final check when it is available.
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