3D Printing Weight Formula
Learn how a small-scale 3D print's filament volume, weight, length, and material cost are estimated.
This calculator estimates the plastic used in a small 3D print by combining the model's fully solid volume with shell coverage and infill. The result helps with rough spool planning and filament-only cost estimates before a final slicer toolpath is available.
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Estimated Print Weight
Where:
Start with the fully solid model volume. Treat the shell and solid layers as fully filled, apply the infill setting to the remaining interior, then multiply the estimated plastic volume by the filament density.
Variables Explained
| Variable | What It Means | Unit |
|---|---|---|
| W - Estimated print weight | Estimated mass of filament deposited in the finished model. | g |
| V - Solid model volume | Volume the model would occupy if it were completely solid. | cm³ |
| S - Shell and solid-layer share | Fraction of the model volume estimated to be occupied by walls, top layers, and bottom layers. | percent |
| I - Infill percentage | Density setting applied to the internal volume outside the shell and solid layers. | percent |
| ρ - Filament density | Mass per unit volume for the selected filament material. | g/cm³ |
| d - Filament diameter | Nominal diameter of the filament used to estimate its length. | mm |
| C - Filament cost per kilogram | Purchase cost of one kilogram of filament in the chosen currency. | currency |
Step-by-Step Calculation
Convert shell coverage to a fraction
The shell and solid-layer share is converted from a percentage into a decimal fraction.
shellFraction = shellPercentage / 100
Convert infill to a fraction
The selected infill percentage is converted into a decimal fraction for the internal portion of the model.
infillFraction = infillPercentage / 100
Find the effective fill fraction
Shells and solid layers are counted as fully filled. The infill percentage applies only to the volume remaining after the shell share.
effectiveFillFraction = shellFraction + ((1 - shellFraction) * infillFraction)
Estimate deposited plastic volume
The effective fill fraction is multiplied by the fully solid model volume.
materialVolume = modelVolume * effectiveFillFraction
Calculate print weight
Estimated deposited plastic volume is multiplied by density to produce weight in grams.
printWeight = materialVolume * filamentDensity
Calculate filament length
The circular cross-sectional area of the filament converts plastic volume into an approximate length in metres. The cm³-to-mm³ and mm-to-m conversions cancel in this expression.
filamentCrossSection = 3.14159265 * pow(filamentDiameter / 2, 2); filamentLength = materialVolume / filamentCrossSection
Calculate filament-only cost
The weight is converted from grams to kilograms and multiplied by the entered spool price.
materialCost = (printWeight / 1000) * filamentCostPerKg
Worked example: 50 cm³ PLA model at 20% infill
Effective fill fraction
0.15 + ((1 - 0.15) × 0.20)
0.32 or 32%
Material volume
50 × 0.32
16.0 cm³
Print weight
16.0 × 1.24
19.84 g
Filament cross-sectional area
3.14159265 × pow(1.75 / 2, 2)
2.405 mm²
Filament length
16.0 / 2.405
6.65 m
Material cost
(19.84 / 1000) × 20.00
$0.40
Final Result
The model is estimated to use 16.0 cm³ of plastic, weigh 19.8 g, consume about 6.7 m of 1.75 mm PLA filament, and cost about $0.40 in filament.
Assumptions
- ✓The entered solid model volume is accurate and is measured in cubic centimetres.
- ✓The shell and solid-layer share reasonably represents walls plus top and bottom solid layers.
- ✓Shell material is treated as fully dense, while the rest of the model uses the selected infill percentage.
- ✓Filament density is uniform and matches the material actually loaded in the printer.
- ✓The nominal filament diameter is suitable for estimating cross-sectional area.
Limitations
- !The calculation does not model the actual sliced toolpath, line width, wall count, or infill pattern.
- !Supports, brims, rafts, purge towers, skirts, and startup extrusion are excluded.
- !Complex geometry can make the shell share substantially different from a simple estimate.
- !Actual filament diameter can vary around its nominal value, affecting real filament length.
- !The cost result excludes electricity, printer time, labor, depreciation, and failed prints.
Common Mistakes to Avoid
Entering a model volume in mm³ when the calculator expects cm³. Divide cubic millimetres by 1000 before entering the value.
Using infill percentage as the total plastic percentage and ignoring walls and solid top or bottom layers.
Entering filament diameter in centimetres instead of millimetres.
Using a material density for a different plastic or an unverified filled or composite filament.
Comparing the estimate with a slicer total that includes supports, a brim, raft, or purge material.
Treating the filament-only cost as the complete cost of producing a part.
Related Formulas
Frequently Asked Questions
What is the formula for 3D print weight?
Estimated print weight equals solid model volume multiplied by effective fill fraction and filament density. The effective fill fraction combines the fully filled shell share with infill in the remaining internal volume.
How is effective fill fraction calculated?
It is shell share plus the remaining volume multiplied by the infill fraction: S + (1 − S) × I, where S and I are percentages converted to decimals.
Why is print weight higher than the infill percentage suggests?
Infill typically applies to the interior only. Perimeters, walls, and solid top and bottom layers use much more plastic than the infill setting alone indicates.
How do you convert filament volume into length?
Divide the estimated material volume by the filament's circular cross-sectional area. With volume in cm³ and diameter in mm, the resulting expression gives approximate length in metres.
What density should I use for PLA filament?
PLA is commonly around 1.24 g/cm³, but the manufacturer's technical data is more appropriate for a specific filament, especially for blends or filled materials.
Does filament diameter change the estimated print weight?
No. For the same deposited plastic volume and density, weight stays the same. Diameter changes the estimated length needed to supply that volume.
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