Volumetric Flow Rate Calculator for 3D Printer

Why calculate flow rate?

Mostly to tune for speed. You can raise acceleration and print speed as far as the motion system allows, but there’s a wall waiting: at some point the hot end can’t melt plastic fast enough to keep up, and you get under-extrusion no matter what the slicer says.

In its simplest form, the volume being laid down is length × width × height of the extruded line, which looks like this:

Filament doesn’t come out in a neat block though. The nozzle squashes it against the layer below and the sides stay round, so the real cross-section looks more like this:

That shape is a stadium: a rectangle with a semicircle stuck on each end. Its area is the straight middle section plus the two half-circles, which together make one full circle of diameter h.

The two forms are the same equation, just rearranged. The second one is easier to compute and makes the correction obvious: you’re subtracting h²(1 − π/4), which is about 0.2146·h², from the naive rectangle.

One thing worth knowing: this only holds while the line is wider than it is tall. If you set a line width below the layer height there’s no straight section left, the shape isn’t a stadium any more, and the calculator will tell you so instead of quietly returning nonsense.

Does it matter?

The gap between the two formulas isn’t huge, but it’s enough to matter when you’re near the limit. Take a line width of 0.6 mm, a layer height of 0.3 mm and 100 mm/s:

Nearly 2 mm³/s of difference. On a stock hot end sitting somewhere around 10 mm³/s that’s the difference between a setting you think is impossible and one that actually prints. It works the other way too: trust the rectangular number and you’ll leave speed on the table.

Measuring your own limit

The calculator asks for your hot end’s maximum flow, and there’s no way around measuring it yourself. Published figures are a starting point at best. E3D say so in their own volumetric flow documentation: the maximum can’t be captured in a single number, because it moves with extruder force, layer height, line width, print temperature and nozzle diameter. A hot end that manages 15 mm³/s in PLA can drop to half that in PETG.

Temperature is the lever most people underestimate. Stefan at CNC Kitchen benchmarked this properly on an i3 MK3s with a V6, and the same hardware that skipped steps trying to hit 15 mm³/s at 185–215 °C managed it with essentially no slipping at 275 °C. Hotter plastic is thinner plastic, which means less back pressure and less work for the extruder. If you’re short of flow, try more heat before you buy a new hot end.

His method is also more precise than the one below: he extrudes a fixed length and weighs what comes out, which catches the gradual losses a ruler misses. Worth doing if you have a scale that reads to a hundredth of a gram. His numbers show why it matters, since under-extrusion was already about 3% at 9 mm³/s, well before anything looked obviously wrong, and only fell off a cliff once the extruder started skipping.

The test itself is the same idea as extruder calibration, and takes about ten minutes:

1. Heat the hot end to the temperature you actually print that filament at. Temperature moves this result more than anything else.
2. Mark the filament 100 mm above the extruder inlet.
3. Extrude 100 mm at a chosen feed rate, then measure how much really went in.
4. Step the feed rate up and repeat.
5. When you’re consistently more than 2–3% short, you’ve passed the limit. Take the last speed that kept up.
6. Multiply: on 1.75 mm filament, feed rate × 2.405 = mm³/s. On 2.85 mm, multiply by 6.379 instead.

Then knock a little off. A bare extrusion test into open air is the easiest job the hot end will ever have. A real print adds back pressure, cooling and constant direction changes, so whatever number you land on, print below it.

Credit where it’s due: the incremental-extrusion method is documented in Ellis’ Print Tuning Guide, which is worth reading in full if you’re tuning a printer properly.

A note on the two models

Slicers don’t agree on this, which is worth knowing before you accuse one of them of being wrong.

Slic3r, and PrusaSlicer which grew out of it, use the rounded shape. Their own flow maths documentation states it directly: the cross-sectional shape of an extrusion is a rectangle with semicircular ends. It also notes the same limit this calculator enforces, that the model only holds while the extrusion is wider than it is tall, and that thinner extrusions fall back to rectangular.

Cura works the other way. CuraEngine treats the path as a plain rectangle of line width by layer height and ignores the rounded ends. That’s discussed at length on UltiMaker’s own community forum. It’s a deliberate simplification rather than an oversight, and for most printing the couple of percent doesn’t matter.

So if this calculator and your slicer disagree by a small margin, that’s usually the reason. Switch the model dropdown to match whichever one you’re checking against and the numbers should line up.