Converting metres of filament into grams requires filament diameter and density. Mass alone does not define a universal length per kilogram. The mass-length calculator uses a cylindrical model and your inputs.
Gather the three required inputs
Choose the conversion direction, then enter quantity, diameter in mm and density in g/cm³. Density here means mass per unit volume, as indicated by the unit. Do not enter nozzle diameter instead of filament diameter.
The cited Prusament PLA sheet gives a typical density of 1.24 g/cm³ and a nominal diameter of 1.75 mm for that product. These are contextual data, not the definition of all PLA. Find the appropriate sheet for a filled filament or another formulation. The diameter and density article explains this choice.
Understand the formula and units
With d in mm, L in m and ρ in g/cm³:
- Area A = π × (d / 2)², in mm².
- Volume V = A × L, numerically in cm³.
- Mass m = A × L × ρ, in g.
- Length L = m / (A × ρ), in m.
Why no further division by one thousand? One metre contains 1000 mm; one cm³ contains 1000 mm³. A × (1000 × L) gives mm³, then dividing by 1000 gives A × L in cm³. The conversions cancel.
Reproduce both conversion directions
Theoretical example, assuming cylindrical filament with diameter 1.75 mm and density 1.24 g/cm³. LayerBench3D did not measure a spool.
| Step | Calculated value |
|---|---|
| Area | π × 0.875² ≈ 2.405281875 mm² |
| Volume for 100 m | ≈ 240.5281875 cm³ |
| Mass for 100 m | ≈ 298.25495255 g, displayed as 298.25 g |
| Length for 1000 g | ≈ 335.28361942 m, displayed as 335.28 m |
Keep intermediate precision. Converting a rounded value back may produce a small difference; it is not a material property. The tool retains separate inputs for the two directions.
Prepare a cost estimate
When a slicer reports length, conversion can provide a theoretical mass under your diameter and density assumptions. Enter it in the cost calculator. Do not confuse job consumption with filament remaining on the spool.
For remaining-filament estimates, net mass excludes spool, packaging and accessories. If tare mass is unknown, state the uncertainty rather than precise remaining autonomy.
Check an unexpected input
Check g versus kg, m versus mm, diameter versus radius, then the material sheet. Enter 1000 for one thousand: the calculator accepts a point or comma as a decimal separator, not a thousands separator. Unknown diameter or density remains missing information; do not replace it with an invented certainty.
Sources consulted
- Prusament PLA — Technical datasheet, version 1.1, 16-02-2022 — Prusa Polymers
Accessed