3D Printing Volume Formula
Learn how a rectangular model's bounding-box volume, estimated material volume, and filament weight are calculated.
This calculator estimates the space occupied by a rectangular 3D model, then applies a chosen infill percentage and material density to approximate filament use. It is useful for early planning before a slicer calculates the actual toolpaths and material requirements.
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Estimated Filament Weight
Where:
Multiply the outside dimensions to get the bounding-box volume in cubic millimetres. Divide by 1,000 to convert it to millilitres, apply the infill percentage, and multiply by the filament density to estimate weight in grams.
Variables Explained
| Variable | What It Means | Unit |
|---|---|---|
| L - Length | The model's outside length. | mm |
| W - Width | The model's outside width. | mm |
| H - Height | The model's outside height. | mm |
| I - Infill percentage | The planned infill entered as a percentage from 0 to 100. | percent |
| ρ - Filament density | The mass per unit volume of the selected filament material. | g/cm³ |
Step-by-Step Calculation
Calculate bounding-box volume
Multiply the three outside dimensions to find the volume of the rectangular envelope around the model.
boundingVolumeMm3 = length * width * height
Convert cubic millimetres to millilitres
One millilitre equals one cubic centimetre, which equals 1,000 cubic millimetres.
boundingVolumeMl = boundingVolumeMm3 / 1000
Convert infill to a decimal
Divide the entered percentage by 100 so it can be used as a proportion.
infillFactor = infillPercentage / 100
Estimate material volume
Apply the infill proportion to the full rectangular volume for a simple material-volume estimate.
estimatedMaterialVolume = boundingVolumeMl * infillFactor
Estimate filament weight
Multiply estimated material volume in mL by density in g/cm³ to estimate the material weight in grams.
estimatedFilamentWeight = estimatedMaterialVolume * filamentDensity
Example: PLA rectangular storage tray estimate
Find bounding-box volume
100 × 60 × 30
180,000 mm³
Convert to millilitres
180,000 ÷ 1,000
180 mL
Convert infill
20 ÷ 100
0.20
Estimate material volume
180 × 0.20
36 mL
Estimate filament weight
36 × 1.24
44.64 g
Final Result
The rectangular model has a 180 mL bounding-box volume. The simple estimate is 36 mL of material and about 44.6 g of PLA filament.
Assumptions
- ✓The model is treated as a solid rectangular envelope defined by its outside dimensions.
- ✓The selected infill percentage is applied directly to the entire bounding-box volume.
- ✓Filament density is uniform and accurately represents the material being printed.
- ✓One millilitre is treated as one cubic centimetre for the volume-to-density conversion.
Limitations
- !Actual model geometry may occupy much less volume than its rectangular bounding box.
- !Walls, perimeters, solid top and bottom layers, and infill patterns are not calculated separately.
- !Supports, brims, rafts, purge material, and failed prints are excluded.
- !A slicer estimate is normally more precise because it uses the real model geometry and print settings.
Common Mistakes to Avoid
Entering dimensions in centimetres or inches when the calculator expects millimetres.
Treating bounding-box volume as the same as the model's true geometric volume.
Assuming 20% infill means the complete print uses exactly 20% of the material of a solid block.
Using a generic density when the filament manufacturer provides a different specification.
Forgetting to include supports or adhesion material when planning spool usage.
Related Formulas
Frequently Asked Questions
How do you calculate 3D print volume from dimensions?
For a rectangular model, multiply length by width by height. The result is in cubic millimetres; divide by 1,000 to express it in millilitres.
How is filament weight estimated from print volume?
Multiply the estimated material volume in mL by the filament density in g/cm³. Since 1 mL equals 1 cm³, the result is in grams.
Why divide the volume by 1,000?
There are 1,000 cubic millimetres in one cubic centimetre, and one cubic centimetre equals one millilitre.
Does infill percentage accurately predict filament use?
It provides only a simple approximation here. Real prints also use material for shells and solid layers, so slicer results can differ.
What density should I use for PLA?
PLA is commonly around 1.24 g/cm³, but the spool specification is the better value to enter when it is available.
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