Why filament has three units and how they connect
You buy filament by mass, because that is what the supplier can weigh reliably. Your slicer thinks in volume, because volume is what the extruder meters and what the toolpath deposits. And the spool measures itself in length, because length is what actually runs out. All three describe the same plastic, and two constants connect them: the cross-sectional area of the strand and the density of the polymer.
The strand is a cylinder, so its area is π(d/2)². For 1.75 mm filament that is 2.4053 mm², and for 2.85 mm it is 6.3799 mm² — a strand 2.65 times fatter in cross-section, which is why the same kilogram is far shorter on a 2.85 mm spool. Multiply area by length and you have volume. Multiply volume by density and you have mass.
That last step is where materials differ. A cubic centimetre of PLA weighs 1.24 g and the same cubic centimetre of nylon weighs 1.01 g, so a kilogram of nylon contains 23% more plastic by volume than a kilogram of PLA — and prints 23% more part. When you compare filament prices by the kilogram, you are comparing mass, not the parts you get; for a fair comparison, compare price per cubic centimetre.
The arithmetic, in both directions
From weight to length, divide the mass by the density to get volume in cubic centimetres, multiply by 1,000 to reach cubic millimetres, then divide by the area. A 100 g PLA print is 100 ÷ 1.24 = 80.65 cm³ = 80,645 mm³, and 80,645 ÷ 2.4053 = 33,528 mm = 33.53 m of 1.75 mm filament.
From length to weight, run it backwards: multiply length in millimetres by the area to get cubic millimetres, divide by 1,000 for cubic centimetres, and multiply by density. One metre of 1.75 mm PLA is 1,000 × 2.4053 = 2,405 mm³ = 2.405 cm³ = 2.98 g. That single figure — about 3 g per metre for 1.75 mm PLA — is worth memorising, because it lets you convert any slicer estimate in your head.
From volume to either is the shortest path, because volume is the quantity the slicer computes first. If your slicer reports extruded volume in cubic centimetres, multiply by density for grams and divide by the area for length.
One subtlety about which volume to use. The model volume from your CAD package is the solid volume of the shape. The extruded volume is what the slicer actually deposits, and it is different: infill below 100% reduces it, while perimeters, top and bottom layers, supports, brim, skirt and purge towers add to it. On a typical part at 15% infill the extruded volume is a fraction of the model volume; on a small part with three perimeters it can approach it. Always take the slicer's number rather than the CAD number.
Worked example: 250 g of PETG on 1.75 mm
Your slicer says a plate of parts uses 250 g of PETG. You want to know the length, the cost at $28/kg, and whether the part-used spool in the drawer will cover it.
- Area of the strand. π × (1.75 ÷ 2)² = π × 0.765625 = 2.40528 mm².
- Volume. 250 ÷ 1.27 = 196.85 cm³ = 196,850 mm³.
- Length. 196,850 ÷ 2.40528 = 81,840 mm = 81.84 m.
- Cost. 250 ÷ 1,000 × $28 = $7.00, which is 7.00 ÷ 81.84 = $0.0855 per metre.
- Prints per spool. 1,000 ÷ 250 = 4 prints from a full kilogram.
Now the drawer spool. Put it on a kitchen scale: it reads 620 g, and the empty spool is marked 210 g, so there is 410 g of PETG left — enough for this plate with 160 g to spare, or about 134 m of filament. Weighing the spool and subtracting the tare is far more reliable than judging the remaining diameter by eye.
Using the numbers: spool planning and cost control
Prints per spool is the number to plan around. If a job needs eight copies and a spool yields four, you need three spools of the same batch — and colour batches genuinely differ, so a mid-job spool change on a visible surface will often show. Order all of one colour together.
Cost per metre makes small prints comparable. At $25/kg, 1.75 mm PLA costs about 7.5 cents per metre; a print using 12 m of filament costs 90 cents of plastic, which is almost always less than the electricity plus the machine time it consumes. That ratio is the reason material is rarely the lever worth pulling when a print job is unprofitable — see the 3D print cost calculator for the full picture.
Diameter tolerance matters more than it looks. Area varies with the square of diameter, so filament running 1.80 mm instead of 1.75 mm carries 5.8% more plastic per metre. Good filament is specified to ±0.02 mm, which is a ±2.3% swing in mass per metre; loose filament at ±0.05 mm is ±5.7%. That variation shows up as over- or under-extrusion, which is why calibrating the flow rate for a new brand is worth the twenty minutes.
Density figures are nominal. The values here are for unfilled base polymers. Wood-filled, carbon-filled, glass-filled and metal-filled filaments can differ by 20% or more, and foaming filaments such as LW-PLA change density during printing by design. When precision matters, take the density from the manufacturer's technical data sheet and enter it as a custom value.
Filament length and weight per kilogram, by material and diameter
| Material | Density (g/cm³) | g/m at 1.75 mm | m per kg at 1.75 mm | g/m at 2.85 mm | m per kg at 2.85 mm |
|---|---|---|---|---|---|
| PLA | 1.24 | 2.98 | 335 | 7.91 | 126 |
| PETG | 1.27 | 3.05 | 327 | 8.10 | 123 |
| ABS | 1.04 | 2.50 | 400 | 6.64 | 151 |
| ASA | 1.07 | 2.57 | 389 | 6.83 | 147 |
| TPU 95A | 1.21 | 2.91 | 344 | 7.72 | 130 |
| Nylon PA12 | 1.01 | 2.43 | 412 | 6.44 | 155 |
| Polycarbonate | 1.20 | 2.89 | 347 | 7.66 | 131 |
| HIPS | 1.04 | 2.50 | 400 | 6.64 | 151 |
| PVA | 1.23 | 2.96 | 338 | 7.85 | 127 |
Densities are nominal values for unfilled polymers. Composite and foaming filaments differ, sometimes substantially — check the data sheet.
How much filament is left on that spool?
Weigh it. Put the spool on a kitchen scale, subtract the empty spool weight — most manufacturers print it on the side or the cardboard core, and a typical plastic spool is 180-250 g — and you have the plastic remaining in grams. Enter that as the weight and the calculator gives you the length left. Judging by the diameter of the remaining coil is unreliable, because the wound cross-section is not proportional to length, and the last 200 g always looks like more than it is.
Common mistakes
- Using model volume instead of extruded volume. Infill, perimeters, supports and purge make the two different in both directions. Take the slicer's figure.
- Assuming 2.85 mm and 3.00 mm are the same. They differ by 11% in area, and using the wrong one skews every length figure by that much.
- Applying PLA's density to everything. Nylon is 19% less dense than PLA, so a kilogram of it is nearly a fifth more plastic by volume.
- Forgetting the spool tare when weighing a part-used spool. A 210 g spool counted as filament overstates what is left by that much.
- Comparing filament prices by the kilogram across materials. Compare price per cubic centimetre if you want to know what a part actually costs.
- Ignoring the purge tower on multi-material prints. On a four-colour print the purge can exceed the part, and the slicer counts it in the filament total — so use that total, not the part volume.
Resin, pellets and where volume accounting differs
This model rests on one assumption: the volume of plastic that enters the hot end equals the volume deposited. That holds well for FDM, which is why slicer estimates based on extruded length are accurate to within a few percent when the flow rate is calibrated. The residual error comes from diameter tolerance, from over-extrusion set in the slicer, and from any material lost to stringing, oozing or an ooze shield.
Resin printing does not work this way. MSLA machines cure resin in a vat and the meaningful unit is millilitres of resin, sold by the litre or kilogram with densities usually between 1.05 and 1.20 g/cm³. Slicers report the resin volume for the plate, and there is no length dimension at all. The failed-print penalty is also different in kind: a failed resin print contaminates the vat with cured fragments that must be filtered out before the next attempt.
Pellet extrusion systems on large-format machines skip filament entirely and feed granules, priced per kilogram at a fraction of filament cost. The volume-to-mass step is identical — density does not care what shape the feedstock was — but the length dimension disappears.
If you are converting these numbers into a customer price rather than a shopping list, the print job cost calculator adds machine time, electricity, labour and a failure allowance to the material figure. For CNC work in the same shop, the feeds and speeds calculator handles the equivalent removal-rate arithmetic, and the board feet calculator does the volume-to-cost conversion for lumber.