Print time is a flow-rate problem
An FDM printer lays down a rectangular ribbon of plastic. Its cross-section is the layer height times the extrusion width, and it moves along at the print speed. Multiply the three and you have the volumetric flow rate Q = h·w·v, in cubic millimetres per second. At 0.2 mm layers, 0.42 mm width and 100 mm/s, that is 8.4 mm³/s.
Once you know the flow rate, the extrusion time is just the total extruded volume divided by it. Thirty cubic centimetres — 30,000 mm³, about 37 g of PLA — takes 30,000 ÷ 8.4 = 3,571 seconds of nozzle-down time, an hour flat.
Two corrections turn that into a real estimate. The first is motion efficiency: the nozzle spends part of the print accelerating, travelling between islands, and crawling round small perimeters at a fraction of the profile speed. That is what the efficiency percentage absorbs, and 70 to 80% is typical for a well-tuned machine on a part of moderate complexity. The second is per-layer overhead — the Z move, the seam, the retractions, and any minimum layer time the slicer enforces for cooling. It is a second or two per layer, which is nothing on a big solid part and everything on a tall thin one.
There is also a ceiling. A hotend can only melt so much plastic per second, and above that the extruder skips or the extrusion under-fills. A stock brass V6 manages roughly 11 to 15 mm³/s in PLA; high-flow hotends with longer melt zones reach 30 mm³/s and beyond. If your requested flow exceeds the ceiling, the printer does not achieve the speed in your profile — it achieves flow ÷ (h·w) instead, and this calculator says so.
Why layer height changes the answer twice
Layer height appears in two places in the formula, and they push the same way.
It appears in the flow rate. Doubling the layer height doubles the cross-section of every line, so at the same nozzle speed twice as much plastic leaves the nozzle each second and the extrusion time halves — right up to the point where the hotend cannot keep up.
It also appears in the layer count, ⌈H/h⌉. Doubling the layer height halves the number of layers and therefore halves the total per-layer overhead.
Because both terms scale the same way, the model is exact about a fact people find surprising: below the flow ceiling, doubling the layer height halves the print time precisely. Going from 0.1 mm to 0.2 mm on the worked example takes it from 2.8955 h to 1.4478 h — a ratio of exactly 2.000.
Above the flow ceiling the arithmetic changes. The extrusion term stops improving because the flow is pinned at the maximum, while the layer term keeps falling. So the total time is still non-increasing in layer height — it can never go up — but the returns collapse. In the reference table below, going from 0.32 mm to 0.50 mm layers, a 56% increase, buys only 13% less time.
The volume input deserves a note. It must be the extruded volume, not the volume enclosed by the model's surface. A part with 15% infill and three perimeters might extrude a third of its bounding volume. The reliable source is your slicer's filament-used figure: multiply the length in millimetres by 2.405 mm² for 1.75 mm filament to get mm³, or take the mass in grams and divide by the material density — 1.24 g/cm³ for PLA, 1.04 for ABS, 1.27 for PETG.
Worked example: a 30 cm³ part, 60 mm tall
Your slicer says the part will use 37 g of PLA and stands 60 mm tall. You print at 0.2 mm layers with a 0.4 mm nozzle at 0.42 mm width, 100 mm/s, on a stock hotend rated 15 mm³/s.
- Volume. 37 g ÷ 1.24 g/cm³ = 29.8 cm³. Round to 30 cm³ = 30,000 mm³.
- Requested flow. 0.2 × 0.42 × 100 = 8.4 mm³/s. That is comfortably under the 15 mm³/s ceiling, so the printer achieves the full 100 mm/s.
- Pure extrusion time. 30,000 ÷ 8.4 = 3,571.4 s.
- After efficiency. 3,571.4 ÷ 0.75 = 4,761.9 s, which is 1.32 h.
- Layer count. ⌈60 ÷ 0.2⌉ = 300 layers.
- Overhead. 300 × 1.5 s = 450 s, which is 0.125 h.
- Total. 4,761.9 + 450 = 5,211.9 s = 1.45 h, or 1 h 27 min.
Now push the speed to 200 mm/s without changing anything else. The requested flow becomes 0.2 × 0.42 × 200 = 16.8 mm³/s, which is above the 15 mm³/s ceiling. The hotend delivers 15, so the achievable speed is 15 ÷ 0.084 = 178.6 mm/s, not 200. Extrusion time becomes 30,000 ÷ 15 ÷ 0.75 = 2,666.7 s and the total is 3,116.7 s = 0.87 h. Doubling the requested speed bought a 40% reduction in time, not 50%, and the gap is entirely the hotend.
Print time by layer height for the worked example
| Layer height (mm) | Layers | Flow (mm³/s) | Achievable speed (mm/s) | Print time (h) |
|---|---|---|---|---|
| 0.10 | 600 | 4.20 | 100.0 | 2.896 |
| 0.12 | 500 | 5.04 | 100.0 | 2.413 |
| 0.16 | 375 | 6.72 | 100.0 | 1.810 |
| 0.20 | 300 | 8.40 | 100.0 | 1.448 |
| 0.24 | 250 | 10.08 | 100.0 | 1.206 |
| 0.28 | 215 | 11.76 | 100.0 | 1.034 |
| 0.32 | 188 | 13.44 | 100.0 | 0.905 |
| 0.40 | 150 | 15.00 | 89.3 | 0.803 |
| 0.50 | 120 | 15.00 | 71.4 | 0.791 |
The flow column stops rising at 0.40 mm because 0.40 × 0.42 × 100 = 16.8 mm³/s is above the hotend's 15 mm³/s ceiling. From 0.10 to 0.32 mm — a 3.2× change in layer height — the time falls by a factor of 3.2. From 0.32 to 0.50 mm it falls by only 13%, because the extrusion term is pinned and only the layer count is still improving.
How to make the estimate accurate for your machine
The one number worth calibrating is the efficiency. Everything else is measurable, but efficiency wraps up acceleration limits, travel distances, the ratio of perimeter to infill, and how much of the part is small features. Time one real print, put the slicer's extruded volume and your actual settings into this page, and solve backwards: efficiency = extrusion-only time ÷ (measured time − layer overhead).
Do that once for a chunky part and once for a fiddly one and you will have a range. Large simple solids land near 85%; models full of small islands, text, or 5 mm towers land near 50% because the nozzle never reaches cruising speed before it has to turn. Machines with input shaping and high acceleration sit higher than bedslingers with 500 mm/s² limits.
Per-layer overhead is easier. Print a 20 mm calibration cube and a 40 mm one at the same settings, then difference the times: the extra 100 layers at 0.2 mm plus the extra volume gives you both terms directly. On most machines the figure lands between 0.5 s and 3 s, rising sharply if your slicer enforces a minimum layer time for cooling on small parts — in that regime the overhead per layer can be 10 s or more and it dominates everything.
Once the estimate is close, it becomes a planning tool. It tells you whether a change of layer height is worth the loss of surface quality, whether a faster hotend would help or whether you are motion-limited, and whether a print farm's queue fits into a shift. To turn the hours into money, feed them into the 3D print cost calculator, which handles machine rate, filament and failure allowance; the filament usage calculator converts between length, mass and volume if you only have one of them.
What this model does not know
- Your part's geometry. Time depends heavily on how the volume is distributed. A tall thin spire and a flat plate of the same volume print very differently, and only the layer count captures any of that here.
- Minimum layer time. Slicers slow down or add a pause on small layers so they can cool. On a part with a 10 mm² top section, that alone can double the print time and the effect appears nowhere in this formula.
- Different speeds for different features. Real profiles run outer perimeters at half the infill speed and solid layers slower still. Enter a volume-weighted average, not the fastest number in the profile.
- Supports and prime towers. Include their volume in the volume input and their height in the height input, or the estimate will be short.
- Multi-material tool changes. Every purge and swap is fixed time per layer, which you can approximate by raising the per-layer overhead.
- Whether the print succeeds. A failure allowance belongs in the cost calculation, not the time one.
Check whether you are flow-limited before buying speed
Raising a profile from 150 to 250 mm/s does nothing if the hotend was already at its ceiling — the extra speed simply cannot be fed. Work out your requested flow as h×w×v and compare it with the hotend's rating. If you are at the ceiling, the useful upgrades are a higher-flow hotend or a larger nozzle, because a 0.6 mm nozzle at 0.68 mm width moves 62% more plastic per millimetre of travel than a 0.4 mm one at 0.42 mm. If you are well below the ceiling, the useful upgrade is acceleration and input shaping, which raise the efficiency figure rather than the flow.
Key terms
- Volumetric flow rate
- Plastic leaving the nozzle per second, in mm³/s. Equal to layer height × extrusion width × nozzle speed. It is the quantity a hotend is actually rated in.
- Extrusion width
- The width of one deposited line, set in the slicer rather than by the nozzle alone. Usually 100 to 120% of nozzle diameter.
- Motion efficiency
- The share of extruding time actually spent at the profile speed, after acceleration ramps, travel moves and slowed perimeters.
- Per-layer overhead
- Fixed time spent on each layer regardless of how much plastic it contains: the Z lift, the seam, retractions, and any enforced minimum layer time.
- Minimum layer time
- A slicer setting that slows a layer down so the plastic has time to cool before the next one lands. It dominates print time on small, tall parts.
Where this fits among the other estimates
The authoritative print-time number always comes from the slicer, because only the slicer knows the toolpath. What a flow model gives you is the ability to answer questions the slicer cannot answer quickly: what would this cost me at half the layer height, would a high-flow hotend help, is this queue going to finish overnight. Those are decisions you make before slicing, and re-slicing at four settings to find out is slow.
Resin printing works on completely different arithmetic. An MSLA machine exposes an entire layer at once, so its print time depends only on layer count and exposure time and is completely independent of how much resin the layer contains — a plate of forty miniatures takes the same time as one. If that is your machine, the resin print cost calculator is the right page, and note that its whole economics are about volume rather than time for exactly this reason.
Subtractive machining inverts the model again. On a CNC router, time is governed by feed rate and the number of passes needed to clear a depth of cut, which is what the feeds and speeds calculator works out; on a laser, by engraving area, line interval and head speed, which the laser engraving time calculator handles. All four processes share one structural feature worth remembering: each has a physical delivery limit — melt rate, cure time, chip load, laser power — that no amount of commanded speed can exceed.