Estimate filament mass from length, or length from a separate mass input. Both calculations share your measured diameter and density. Enter diameter in millimetres (mm), density in grams per cubic centimetre (g/cm³), length in metres (m), and net filament mass in grams (g). Here, “weight” means mass, not gravitational force.
Use density supplied for your specific filament or measured independently. The default density is an illustrative input, not a material recommendation. Exclude the spool, packaging and other hardware from the mass input.
Enter numerical values in the units printed beside each input; do not substitute centimetres for millimetres or kilograms for grams. The formulas operate on numerical ratios to those fixed units: diameter/(1 mm), density/(1 g/cm³), length/(1 m), and mass/(1 g).
Accepted ranges are diameter 0.01–10 mm, density 0.001–30 g/cm³, length 0–1,000,000 m, and mass 0–1,000,000 g. These are calculator input limits, not specifications for printable filament. Diameter and density must be positive. The geometric factor is fixed at π/4 and should remain unchanged.
The length input controls only the mass result; the separate mass input controls only the length result. Zero length produces zero mass, and zero mass produces zero length. An unavailable result is not zero: check for invalid inputs, a zero divisor or a numerical range error.
Model the filament as a solid circular cylinder. Its volume is V = πd²L/4, using consistent length units, as described by Wolfram’s cylinder volume formula. Density is mass divided by volume, so m = ρV; see OpenStax’s explanation of density.
For diameter in mm and length in m, 1 mm² × 1 m = 1 cm³. Consequently, the numerical volume in cm³ is (π/4) × diameter² × length. Multiplying by density in g/cm³ gives grams. Dividing a separate mass by the calculated grams per metre gives metres.
| Calculation | Diameter (mm) | Density (g/cm³) | Known input | Working | Result |
|---|---|---|---|---|---|
| Length to mass | 1.75 | 1.24 | 100 m | (π/4) × 1.75² × 1.24 × 100 | 298.255 g |
| Mass to length | 1.75 | 1.24 | 1,000 g | 1,000 ÷ [(π/4) × 1.75² × 1.24] | 335.284 m |
| Double the density | 1.75 | 2.48 | 100 m | (π/4) × 1.75² × 2.48 × 100 | 596.510 g |
At fixed diameter and length, mass is directly proportional to density: doubling density doubles mass. At fixed mass and diameter, doubling density halves the calculated length. There is no universal length-to-mass conversion without diameter and density.
Diameter enters the formula squared. At fixed density and length, a diameter 1% larger produces a calculated mass 2.01% larger. Measure the filament at several positions and orientations to assess variation; a single diameter assumes a uniform circular cross-section throughout.
The estimate assumes solid filament with uniform density. Hollow, foamed, irregular or substantially variable filament needs a more appropriate volume or density model. Results describe the filament itself and do not predict printed-part mass after purge, supports, waste or other processing losses. Displayed decimal places are calculation precision, not a guarantee of measurement accuracy.
Formula sources
- Wolfram Formula Repository — Cylinder Volume: volume from diameter and length.
- OpenStax, College Physics — 11.2 Density: the relationship between density, mass and volume.
Create and register a 400 × 400 pixel WebP thumbnail before activation, then insert it as the first image block using its registered asset ID. Match neighboring thumbnails: a cute yellow five-point star with a cheerful face and hands, floating without separate legs or feet, on a white background with playful navy, blue and teal graphics depicting a filament spool, diameter measurement and a mass scale. No asset ID is supplied because a suitable registered asset was not provided.