Filament length to weight (and back) from diameter and density

How the conversion works

A strand of filament is a long cylinder. Its volume is the cross-section times the length, and its mass is that volume times the material’s density:

• cross-section (mm²) = π × (d ÷ 2)²
• grams per metre = density (g/cm³) × cross-section (mm²)

The second line looks too simple, but the units cancel neatly: one metre is 1,000 mm, and 1,000 mm³ is 1 cm³, so a strand with a cross-section of 1 mm² holds exactly 1 cm³ per metre.

For the two common diameters:

The 1.24 g/cm³ figure is the density Bambu Lab and Prusament publish for their standard PLA, both measured to ISO 1183 ^{[1, 2]}.

Why density matters more than people expect

Spools are sold by weight, but prints consume length. Two 1 kg spools of different materials hold different lengths. Bambu Lab lists 1.05 g/cm³ for its ABS ^[3], so a kilogram of it is about 396 m of 1.75 mm filament, roughly 18% more than the same weight of PLA at 1.24 g/cm³. Polymaker lists 1.12 g/cm³ for PolyMide CoPA nylon ^[4].

Filled and specialty filaments vary even within one material family, because additives change the density. Matte, silk, carbon-fiber and “plus” variants all appear in the data with their own values. The density comparison lists every value the makers in the database publish, and the preset menu in the calculator above fills the density field from that list.

Using it with your slicer

Slicers report filament used per print as length, weight, or both. The weight figure comes from the density in the slicer’s filament profile; OrcaSlicer, for example, has a Density field that it uses for statistics such as weight and cost estimates ^[5]. If you switch brands within a material and keep the same profile, the length estimate stays right but the weight can be off by the density ratio. Copy the data-sheet density into the profile to fix it.

Common uses:

1. Will this spool finish the print? Weigh the spool, subtract the empty spool weight, convert grams to metres, and compare with the slicer’s length estimate.
2. Cost per print. Convert the slicer’s length to grams, then use the print cost calculator.
3. Buying by length. Some filaments, especially samples, are sold in metres. Convert to grams to compare price per kilogram.

Diameter tolerance

The calculation assumes the nominal diameter. Real filament varies slightly along the spool, and since the cross-section scales with diameter squared, a 1% diameter error is about a 2% weight error. For estimating a spool’s remaining length that is usually acceptable; for flow calibration it is not, which is why extrusion is calibrated by printing and measuring rather than by arithmetic alone (see flow rate calibration).