Filament length and weight converter by material density

The formula the tool displays and why the units line up

The tool rests on a single geometric relationship: filament is a cylinder, so its mass is its volume times its density. With d as the diameter in millimeters and ρ as the density in grams per cubic centimeter, mass per meter is: grams per meter = π × (d ÷ 2)² × ρ. You enter d and ρ, the tool computes that factor, then applies it in whichever direction you ask for.

The units look mismatched, square millimeters on one side and cubic centimeters on the other, but they work out exactly. A cross-section of 1 mm² stretched over 1 m is 1,000 mm³, which is precisely 1 cm³. Multiplying an area in mm² by a density in g/cm³ therefore gives grams per meter directly, with no hidden conversion factor. That is what keeps the formula readable and easy to check on a calculator.

Both conversion directions come from the same factor. Length in meters = mass in grams ÷ grams per meter. Mass in grams = length in meters × grams per meter. The tool displays the result in meters and grams, plus the formula, but not the intermediate grams-per-meter factor. You can compute that factor from the formula to check the units you entered.

Where to find density: the data sheet for your exact product

Density is not universal, even within one material family. Polymaker's technical data sheet for its PETG, version 1.0, lists a density of 1.30 g/cm³ at 23 °C, measured per ISO 1183. Spectrum's data sheet for its PCTG, dated 6 April 2022, a copolyester the manufacturer positions as an alternative to PET-G, lists a specific gravity of 1.23 g/cm³ per ASTM D792. Two closely related materials, two different values, two different test standards. Check that the sheet you are reading is the one that applies to your spool.

That is why the tool does not ship with a default PETG value. It asks for the density of the product in your hands, and you record which data sheet it came from. Some product pages do not state density in their overview: the Prusament PETG page, for example, describes printing properties and points to a downloadable tech sheet. A value missing from an excerpt does not prove the manufacturer omits it. Look for the full document.

Do not automatically reuse a base filament's density for a carbon-fiber, wood or metal-filled version. If the manufacturer publishes a density for the exact filled product, enter that value; otherwise ask for it before calculating the conversion. The PCTG vs PETG comparison presents two specific product data sheets, rather than a universal density.

A hypothetical worked example, step by step

Suppose you enter a diameter of 1.75 mm, a purely hypothetical input to be replaced by your own spool's value, and the 1.30 g/cm³ density from the Polymaker sheet. The radius is 0.875 mm, its square is 0.7656 mm², and the cross-section area is π × 0.7656, about 2.405 mm². Multiplied by 1.30, that gives roughly 3.13 g per meter.

With that factor, a hypothetical mass of 1,000 g corresponds to 1,000 ÷ 3.13, roughly 320 m. A mass of 250 g gives about 80 m. In the other direction, 10 m of this filament weighs about 31 g. If you instead enter the 1.23 g/cm³ density from the Spectrum PCTG sheet with the same diameter, the factor drops to about 2.96 g/m and the same 1,000 g stretches to about 338 m.

The gap between 320 m and 338 m for the same mass shows the effect of density alone: a few hundredths of a g/cm³ shift the estimated length by several meters per kilogram. These figures are arithmetic on assumed inputs, not spool measurements. A filament scale gives you the real mass, and the tool does the rest.

Why diameter matters more than density

In the formula, density enters linearly while diameter is squared. An input error on diameter therefore propagates much faster. Back to the hypothetical example: moving from 1.75 mm to 2.85 mm, another diameter entered purely for illustration, raises the cross-section from about 2.405 mm² to about 6.379 mm², and the factor from 3.13 g/m to about 8.29 g/m at the same 1.30 g/cm³ density.

Real filament diameter can differ from the nominal value, vary along the spool, or be slightly oval; any such deviation changes mass per meter without the tool knowing. Neither cited sheet states a diameter tolerance, so look for that figure on your spool's label or its own data sheet. Both the Polymaker and Spectrum sheets present their values as typical, for reference and comparison, not as binding specifications.

In practice, if your calculation is meant to decide whether a spool will last through a part, keep a margin rather than aiming for the exact meter. If you measure the diameter with calipers at several points, enter an average rather than the number printed on the label. The tool accepts any diameter precisely for that reason.

What the estimate does not cover

The model assumes a solid, cylindrical, homogeneous filament. It ignores absorbed moisture, which adds mass without adding length: the Polymaker sheet lists a maximum water absorption rate of 0.51% for its PETG, on a curve recorded at 70% RH and 23 °C, and highly recommends its PolyBox or PolyDryer Box for storing and printing. A damp spool therefore weighs slightly more than the calculation attributes to its length. The filament dryer guide explains how to limit that effect.

The calculation also ignores the spool itself. If you weigh a partly used spool, subtract the empty spool's mass before entering the result; spool-less refills make that step easier. It does not account for purging, multi-material prime towers, or filament lost during changes either: the estimated length is the length of the strand, not the amount a print actually consumes.

Finally, a data sheet density is the material as measured by the manufacturer under a specific standard. Both sheets cited here state that actual values vary with conditions and should not be used for design specifications or quality control. The tool accordingly labels its outputs as estimates, with units, never as certainties.

When to use the converter and when to switch to the cost tool

You can use this calculation in three situations. You have a partly used spool and want to know whether enough is left for a part your slicer reports in meters: weigh it, subtract the empty spool, convert to meters. You are preparing a refill and want the mass of a given length: enter the length. You are comparing two materials of different density for the same length: run the calculation twice.

As soon as money enters the picture, for example the material cost of a part or whether a spool pays for itself, switch tools: the print cost tool adds that layer, and this page deliberately stays price-free. Likewise, choosing between reusable spools and refills is an equipment decision, not a calculation.

Keep both inputs and the density source next to the result whenever you write down an estimate. A length figure without its diameter and density cannot be checked later, whereas with the formula visible, anyone can redo the math and land on the same number.

Sources and limits

• en_tds_spectrum_pctg.pdf
• Polymaker-PETG_TDS_EN_V1.0.pdf
• Prusament PETG | Prusament

We organize manufacturer and community documentation; we have not measured these products ourselves. The manual for your exact model takes precedence over general guidance.