Technical context
Keep diameter in millimeters and density in grams per cubic centimeter when using the grams-per-meter equation. The numerical cancellation between 1,000 mm per meter and 1,000 mm³ per cm³ makes the compact equation possible; it is not a license to mix arbitrary units.
Length from equal filament mass
View data table
| Comparison | m |
|---|---|
| 1.75 mm | 335.2836 |
| 2.85 mm | 126.415 |
Practical workflow
A 2.85 mm strand contains much more volume per meter than a 1.75 mm strand of the same material. Thus equal-mass spools have different lengths. Length helps compare slicer extrusion demands, while mass remains convenient for checking physical stock with a scale.
Calculation and units
Grams/m = ? × (diameter mm/2)² × density g/cm³. Length m = grams/grams per meter.
Worked example
At example density 1.24 and diameter 1.75 mm, one meter weighs 2.983 g; 1,000 g contains about 335.3 m.
Validate the outcome
Diameter enters squared. Measure it and use the exact datasheet instead of treating every polymer grade as identical.
Derive the compact equation step by step
Cross-section in mm² is ?d²/4. Multiplying by a one-meter length of 1,000 mm gives volume in mm³. Dividing by 1,000 converts that volume to cm³. The two thousand factors cancel, leaving ?d²/4 cm³ per meter. Multiplying by density in g/cm³ gives grams per meter. This derivation explains why the diameter must be in millimeters in the compact equation.
To reverse the conversion, multiply meters by grams per meter. For mass-to-length, divide grams by grams per meter. Keep net filament mass separate from spool hardware and never use a price-per-kilogram field as if it were a density input.
Compare 1.75 and 2.85 mm strands
Using an illustrative density of 1.24 g/cm³, the 1.75 mm strand weighs about 2.983 g/m. The 2.85 mm strand weighs about 7.910 g/m. A net 1,000 g spool therefore contains approximately 335.3 m or 126.4 m respectively. Equal mass and polymer do not mean equal length because the thicker strand has a larger area.
This comparison does not mean that one diameter necessarily creates a cheaper printed object. A given deposited volume needs approximately the same polymer mass, while the feed length differs. Printer compatibility and extrusion mechanics determine which diameter is appropriate; a converter does not authorize substituting a strand the machine was not designed to feed.
Uncertainty and practical verification
The formula assumes a solid round strand with constant diameter and density. Real diameter tolerance, ovality, additives and measurement uncertainty make the result an estimate. Measure diameter at multiple locations and directions if the application needs more reliable stock accounting, and use the exact product density when available. Do not present a generic 335 m estimate as a certified length for every spool labeled PLA.
If a slicer reports extrusion length, confirm whether it is millimeters or meters and whether multiple extruders are combined. Use the same product profile in the converter and slicer before comparing. A round-trip conversion should return the starting value apart from rounding; failure of that check is a useful sign of unit or profile mismatch.
Ideal lengths at1.24 g/cm³
| Diameter | Grams per meter | Meters per1000 g |
|---|---|---|
| 1.75 mm | 2.983 | 335.3 |
| 2.85 mm | 7.910 | 126.4 |
Check units with a reversible worked calculation
Using 1.75 mm and example density 1.24, grams per meter is about 2.983. A measured 100 g net remnant corresponds to about 33.53 m; multiplying that rounded length by the same grams-per-meter value returns approximately 100 g. A large round-trip error reveals mismatched units or profiles. Do not compare a millimeter length from G-code with a meter input without conversion, and never include spool tare in the net mass.
Why is length inversely related to diameter squared?
At fixed mass and density, total solid volume is fixed. A larger diameter increases strand area with the square of diameter, so the available volume must occupy proportionally less length. Doubling diameter gives four times area and approximately one quarter length under the same ideal cylinder assumptions. This does not change the material mass available for the printed part.
What if the filament is oval rather than round?
The simple round-diameter formula becomes an approximation. If the two perpendicular diameters can be measured consistently, an ideal elliptical cross-section has area ?ab/4 with a and b as the full measured diameters. Real variation along the spool still limits precision. For ordinary stock planning, measured net mass may be more robust than inferring exact length from one local diameter reading.