Vacuum Pump Evacuation Time: Pump-Down Formula and Sizing Guide
HCEM Engineering TeamShare
To size a vacuum pump for a required evacuation time, work the pump-down formula backwards: the pumping speed you need is S = (V / t) × ln[(p₀ − pu) / (p₁ − pu)], where V is the volume, t the time you have, p₀ and p₁ the start and target absolute pressures and pu the pump's ultimate pressure. Then check that hoses and fittings do not eat that speed, add a margin, and pick the pump whose free-air flow clears the figure.
This guide is for engineers choosing a pump for a cycle time in an OEM machine: a packaging chamber, a test fixture, a clamping table. It covers the formula and why the simple version is too optimistic, how pumping speed falls at deeper vacuum, what hoses and a reservoir do to the result, a step-by-step sizing worksheet and two worked examples. To measure the pump-down time of a pump you already have, see how to test a vacuum pump.
What is the vacuum pump down time formula?
For a sealed volume and a pump with constant speed, the time to go from one pressure to another is:
t = (V / S) × ln(p₀ / p₁)
| Symbol | Meaning | Usual unit |
|---|---|---|
| t | Evacuation (pump-down) time | min (× 60 for seconds) |
| V | Total volume evacuated: chamber plus hoses, manifold and valve cavities | L |
| S | Pumping speed at the chamber | L/min |
| p₀ | Start pressure, absolute | mbar (1013 at sea level) |
| p₁ | Target pressure, absolute | mbar |
Some textbooks write the same formula as t = (V / S) × ln(P1 / P2); only the labels differ. Three rules keep the units straight:
- Pressures must be absolute. A gauge reading converts as p = 1013 + 10 × gauge kPa, in mbar: −80 kPa is 213 mbar, −90 kPa is 113 mbar.
- V and S must share a volume unit. Litres with L/min gives minutes. For datasheets in m³/h, 1 m³/h = 16.67 L/min; in cfm, 1 cfm = 28.3 L/min (see what CFM means or the CFM to L/min converter).
- Only the ratio of pressures matters, so mbar, kPa or Torr all work, as long as both are absolute.
Example: a 10 L chamber pumped by 120 L/min from 1013 mbar to −80 kPa (213 mbar) takes (10 ÷ 120) × ln(1013 ÷ 213) = 0.083 min × 1.559 = 0.13 min, about 7.8 seconds.
For sizing, turn it round: S = (V / t) × ln(p₀ / p₁) gives the speed needed to reach p₁ in time t. That is the first pass. The next two sections explain why the real figure is higher.
How does ultimate pressure change evacuation time?
The simple formula assumes the pump keeps its full speed all the way down. A real pump's net speed falls to zero at its ultimate pressure pu, the deepest vacuum it can reach with the inlet closed. A better estimate is:
t = (V / S) × ln[(p₀ − pu) / (p₁ − pu)]
The closer the target is to the ultimate pressure, the larger the difference. Here is the 10 L chamber again, with a standard HC580A (datasheet: 120 L/min free-air flow, ultimate −92 kPa, about 93 mbar absolute):
| Target (gauge) | Target (absolute) | Simple formula | With ultimate pressure | Extra time |
|---|---|---|---|---|
| −50 kPa | 513 mbar | 3.4 s | 3.9 s | +15% |
| −70 kPa | 313 mbar | 5.9 s | 7.2 s | +22% |
| −80 kPa | 213 mbar | 7.8 s | 10.2 s | +31% |
| −85 kPa | 163 mbar | 9.1 s | 12.9 s | +41% |
| −90 kPa | 113 mbar | 11.0 s | 19.1 s | +75% |
A pump that only just reaches your working vacuum will be slow at it. Choose one whose ultimate pressure sits well below the target; our guide to ultimate pressure vs working vacuum explains the gap in more detail.
Why does pumping speed fall at deeper vacuum?
A piston pump sweeps the same volume on every stroke, but at deeper vacuum it has to compress that gas over a larger pressure ratio to push it out to atmosphere. Gas left in the clearance space at the top of the stroke re-expands, and a little leaks back past the ring and valves. Less of each stroke is left for new gas from the chamber, until at the ultimate pressure the pump moves nothing at all.
The datasheet gives the two end points of that speed curve: the free-air flow, measured near atmospheric pressure, and the ultimate vacuum, where the speed is zero. The ultimate-pressure formula above assumes the net speed in between is S × (1 − pu / p). Many of our oil-free piston pumps come in a standard and a high-vacuum version, and the two curves cross. Modelled values for the HC580A:
| Chamber pressure (gauge) | Absolute | HC580A standard (120 L/min, −92 kPa) | HC580A high-vacuum (60 L/min, −98 kPa) |
|---|---|---|---|
| −50 kPa | 513 mbar | 98 L/min | 56 L/min |
| −70 kPa | 313 mbar | 84 L/min | 54 L/min |
| −80 kPa | 213 mbar | 68 L/min | 51 L/min |
| −85 kPa | 163 mbar | 52 L/min | 48 L/min |
| −90 kPa | 113 mbar | 21 L/min | 42 L/min |
| −92 kPa | 93 mbar | 0 (ultimate) | 39 L/min |
| −95 kPa | 63 mbar | no flow | 29 L/min |
| −98 kPa | 33 mbar | no flow | 0 (ultimate) |
Below about −86 kPa (153 mbar) the high-vacuum version moves more gas, despite half the free-air flow. Starting from atmosphere, though, the standard version still reaches any target down to about −91 kPa first, because most of the pump-down happens at higher pressure. Choose the high-vacuum version when the target is deeper than that, or when the pump spends most of its time below −86 kPa, for example topping up a reservoir held near −90 kPa.
The model is a fair first estimate, not a measurement. The real curve comes from the datasheet's flow-versus-vacuum chart for the exact model, voltage and frequency; our guide on how to request and compare performance curves lists what to ask for. With a measured curve, split the pump-down into steps and add them up: t = Σ (V / Si) × ln(pi / pi+1), using the average speed Si read from the curve in each step.
How much do hoses and fittings slow the pump-down?
The pump's speed is measured at its inlet. The chamber sees less, because every hose, valve and fitting in between is a restriction. The two combine like resistances in series:
1 / Seff = 1 / S + 1 / C
where C is the conductance of the line. In the rough vacuum range where oil-free piston pumps work, air in a hose flows as a viscous fluid, and for laminar flow of air at 20 °C a round hose has a conductance of about:
C ≈ 135 × d⁴ × p̄ / L in L/s (multiply by 60 for L/min), with the bore d and length L in cm and the mean pressure p̄ in mbar.
Two things follow. Conductance scales with the fourth power of the bore, so halving the bore cuts it sixteen times. And it falls in proportion to pressure, so a hose that does not matter at −50 kPa can matter at −86 kPa. Here is the effect at 150 mbar (−86 kPa) on a standard HC580A, which has a modelled speed of about 46 L/min at that pressure, and on the 10 L pump-down to −80 kPa from the tables above:
| Hose (bore × length) | Conductance at 150 mbar | Speed at the chamber | Loss | 10 L to −80 kPa |
|---|---|---|---|---|
| No hose | – | 46 L/min | – | 10.2 s |
| 10 mm × 1 m | about 12,150 L/min | 45 L/min | under 1% | 10.2 s |
| 8 mm × 2 m | about 2,490 L/min | 45 L/min | 2% | 10.3 s |
| 6 mm × 2 m | about 790 L/min | 43 L/min | 5% | 10.6 s |
| 4 mm × 3 m | about 104 L/min | 32 L/min | 31% | at least 13.4 s |
The pump-down times come from integrating pump speed and hose conductance together over the whole pressure range. Near atmospheric pressure, the gas in a narrow hose moves fast enough to become turbulent, and then the laminar formula overstates the conductance, so treat the narrow-hose figure as a best case. Valves, filters, quick couplings and the pump's own inlet port are restrictions too: ask for their flow data, or measure the pump-down with and without them. Our inlet piping pressure-loss review covers line layout in more detail. Remember to add the hose's own volume to V: 2 m of 8 mm bore holds about 0.1 L.
When does a vacuum reservoir shorten the cycle?
When the machine needs vacuum fast but only briefly, a pre-evacuated reservoir can do the quick part and leave the pump the rest of the cycle to recover. When the valve between them opens, the chamber and reservoir share their gas, and once it settles to room temperature the pressure is:
peq = (pc × Vc + pr × Vr) / (Vc + Vr)
where c is the chamber and r the reservoir. Rearranged, the reservoir needed to reach a target pressure pt is Vr = Vc × (pc − pt) / (pt − pr). The pump must then bring the combined volume back from peq to pr before the next cycle, which is the ultimate-pressure formula again. Worked example 2 below puts numbers on it. The valve and line between reservoir and chamber must be large enough for the gas to equalise in the time allowed, and the reservoir must be a vessel rated for vacuum. Our vacuum reservoir sizing review covers the design checks.
How do you size a vacuum pump for a required cycle time?
Work through these steps, writing each number down. Each step corrects the one before.
- Total volume, V. Chamber plus hoses, manifold and valve cavities. A hose holds π × d² / 4 × L.
- Target as absolute pressure, p₁. Convert gauge readings with p = 1013 + 10 × gauge kPa (mbar). At altitude the atmosphere, and so p₀, is lower; see our guide to altitude and ambient conditions.
- Time available, t. The cycle time minus valve switching, settling, hold and vent time.
- First-pass speed. S = (V / t) × ln(p₀ / p₁).
- Correct for ultimate pressure. For each candidate pump, S = (V / t) × ln[(p₀ − pu) / (p₁ − pu)] with its pu. If the target is close to pu, the number climbs steeply: take the high-vacuum version or a different type of pump.
- Check the line. Work out the hose conductance at the target pressure and keep the loss to a few per cent by shortening the line or opening up the bore.
- Allow for leaks and gas release. A steady leak Q raises the lowest pressure the system reaches by about Q / S. A leak of 2 mbar·L/s on a pump moving 50 L/min (0.83 L/s) adds about 2.4 mbar, small in rough vacuum. Wet, porous or plastic parts release vapour and gas, which can matter more; measure it on a prototype. Our leak rate acceptance test guide covers the limits.
- Add margin. A 20% margin on the speed is a reasonable starting point for the effects the formula leaves out, and tighten or relax it once the prototype is measured. Use the flow figure for your supply: UK and European mains are 50 Hz, and 60 Hz figures are higher.
- Check duty and supply. How many seconds per cycle the pump runs and how often it starts decide whether a model's duty rating fits; see our guide to duty cycle and start-stop frequency. Confirm AC voltage and frequency, or the DC voltage at the pump terminals.
- Measure on the prototype. Time the real pump-down, as in how to test a vacuum pump, and compare it with your estimate.
Worked example 1: a 12-litre chamber to −80 kPa in 9 seconds
An AC machine on a 220 V/50 Hz supply has an 11 L chamber with about 1 L of manifold and hose, so V = 12 L. The target is −80 kPa, 213 mbar absolute. The cycle is 12 seconds, of which 9 seconds (0.15 min) are available for evacuation.
- First pass: V / t = 12 ÷ 0.15 = 80 L/min. S = 80 × ln(1013 ÷ 213) = 80 × 1.559 = 125 L/min.
- With ultimate pressure (standard versions, −92 kPa, 93 mbar): S = 80 × ln(920 ÷ 120) = 80 × 2.037 = 163 L/min.
- With 20% margin: 163 × 1.2 = 196 L/min, about 6.9 cfm.
Check the candidates with the ultimate-pressure formula, t = (12 ÷ S) × 2.037:
| Option | Free-air flow at 50 Hz | Estimated evacuation time | Inside the 9 s |
|---|---|---|---|
| HC680A | 165 L/min | 8.9 s | 1% |
| HC1100A | 185 L/min | 7.9 s | 12% |
| HC1500A | 210 L/min | 7.0 s | 22% |
| Two HC680A in parallel | 330 L/min | 4.4 s | 51% |
The simple formula alone would have pointed to the HC680A, which would only just make it on paper and miss in practice. The HC1500A meets the 20% margin. Two HC680A pumps give more headroom and keep the machine running at reduced speed if one is out of service, at the cost of more space. Either way, use a short line of 10 mm bore or more: at these flows a narrow hose runs turbulent near atmospheric pressure and costs more than the table above suggests.
Worked example 2: a 2-litre fixture in under 1 second, on 24 V DC
A battery-powered test device has a 2 L fixture that must reach −50 kPa (513 mbar absolute) within 1 second, once every 20 seconds.
Option A, pump directly. V / t = 2 ÷ (1/60 min) = 120 L/min. First pass: 120 × ln(1013 ÷ 513) = 120 × 0.680 = 82 L/min. With a −92 kPa pump: 120 × ln(920 ÷ 420) = 120 × 0.784 = 94 L/min; with 20% margin, 113 L/min. A HC580D (120 L/min, 12/24/48 V DC, ≤260 W) does it in (2 ÷ 120) × 0.784 = 0.0131 min, about 0.78 s.
Option B, pump into a reservoir. A HC100D (50 L/min, ultimate −90 kPa, about 113 mbar, ≤150 W) keeps a reservoir at 200 mbar (−81 kPa).
- Reservoir needed: Vr = 2 × (1013 − 513) ÷ (513 − 200) = 2 × 500 ÷ 313 = 3.2 L. Choose 4 L.
- Check: peq = (2 × 1013 + 4 × 200) ÷ 6 = 471 mbar, about −54 kPa, so the target is met with room to spare.
- Recovery of all 6 L from 471 to 200 mbar: (6 ÷ 50) × ln[(471 − 113) ÷ (200 − 113)] = 0.12 × 1.415 = 0.170 min, about 10.2 s, inside the 19 s left in the cycle.
- First pump-down of the reservoir at switch-on: (4 ÷ 50) × ln(900 ÷ 87) = 0.08 × 2.336 = 0.187 min, about 11.2 s, once.
Option B uses a smaller pump with a lower rated power, which matters on a battery. In exchange it needs a vacuum-rated vessel, a valve and line large enough to equalise within the second, and a pump that runs about half of every cycle, so check its duty rating. Option A is simpler, with fewer parts to fail.
Which HCEM vacuum pump fits your evacuation time?
The tables below give estimated times to pump 10 L from 1013 mbar, using the ultimate-pressure formula and datasheet figures for 220 V/50 Hz AC and for DC supplies, with no allowance for hoses. Times scale with volume: for 25 L, multiply by 2.5. Use them to shortlist, then size with the worksheet above.
Standard versions
| Model | Supply | Rated power | Free-air flow | Ultimate | 10 L to −80 kPa | 10 L to −90 kPa |
|---|---|---|---|---|---|---|
| HC100A | AC | ≤110 W | 45 L/min | −90 kPa | 29.3 s | not reached |
| HC100D | 12/24/48 V DC | ≤150 W | 50 L/min | −90 kPa | 26.4 s | not reached |
| HC280D | 12/24/48 V DC | ≤180 W | 90 L/min | −92 kPa | 13.6 s | 25.5 s |
| HC480D | 12/24/48 V DC | ≤200 W | 100 L/min | −92 kPa | 12.2 s | 23.0 s |
| HC580A | AC | ≤340 W | 120 L/min | −92 kPa | 10.2 s | 19.1 s |
| HC580D | 12/24/48 V DC | ≤260 W | 120 L/min | −92 kPa | 10.2 s | 19.1 s |
| HC680A | AC | ≤340 W | 165 L/min | −92 kPa | 7.4 s | 13.9 s |
| HC1100A | AC | ≤600 W | 185 L/min | −92 kPa | 6.6 s | 12.4 s |
| HC1100D | 12/24/48 V DC | ≤600 W | 200 L/min | −92 kPa | 6.1 s | 11.5 s |
| HC1500A | AC | ≤700 W | 210 L/min | −92 kPa | 5.8 s | 10.9 s |
| HC1500D | 12/24/48 V DC | ≤700 W | 240 L/min | −92 kPa | 5.1 s | 9.6 s |
High-vacuum versions (ultimate −98 kPa, about 33 mbar absolute)
| Model | Free-air flow | 10 L to −80 kPa | 10 L to −90 kPa | 10 L to −95 kPa |
|---|---|---|---|---|
| HC100A | 22.5 L/min | 45.2 s | 66.8 s | 93.0 s |
| HC100D | 25 L/min | 40.7 s | 60.1 s | 83.7 s |
| HC280D | 45 L/min | 22.6 s | 33.4 s | 46.5 s |
| HC480D | 50 L/min | 20.3 s | 30.1 s | 41.8 s |
| HC580A and HC580D | 60 L/min | 16.9 s | 25.1 s | 34.9 s |
| HC680A | 82.5 L/min | 12.3 s | 18.2 s | 25.4 s |
| HC1100A | 90 L/min | 11.3 s | 16.7 s | 23.2 s |
| HC1100D | 100 L/min | 10.2 s | 15.0 s | 20.9 s |
| HC1500A | 110 L/min | 9.2 s | 13.7 s | 19.0 s |
| HC1500D | 130 L/min | 7.8 s | 11.6 s | 16.1 s |
AC models are built for 220 V/50 Hz or 110 V/60 Hz. The 60 Hz versions move more air: 50 L/min for the HC100A, 170 L/min for the HC680A, 200 L/min for the HC1100A and 250 L/min for the HC1500A, standard version. If one pump cannot meet the time, two in parallel roughly halve it, as in example 1. For the other figures to put in an enquiry, see our vacuum pump specification checklist for OEM buyers. Application guides show the same sizing in context for food tray sealing, CNC workholding and SMT pick-and-place.
Common questions
How long does it take a vacuum pump to pull down a chamber?
It depends on the volume, the pump's speed and how deep you go. Time grows in proportion to volume and falls in proportion to speed: a standard HC580A takes about 10 seconds to bring 10 L to −80 kPa, so 20 L takes about 20 seconds. The last few kPa before the ultimate pressure take the longest.
How do I calculate what size vacuum pump I need?
Use S = (V / t) × ln[(p₀ − pu) / (p₁ − pu)] with absolute pressures, then add hose losses and a margin. The worksheet above goes through each step.
Is ln(p0/p1) the same as ln(P1/P2)?
Yes. Both are the natural logarithm of start pressure over target pressure. Some sources number the pressures from 0, others from 1.
Does a bigger hose make the pump-down faster?
Only until the hose stops being the restriction. In the example above, 2 m of 8 mm bore costs about 2% of the speed at −86 kPa, while 3 m of 4 mm bore costs about 30%. Short and generous is the rule; beyond that, only a faster pump helps.
Should I size on free-air flow or on the flow at my vacuum level?
On the flow at your vacuum level, which is lower. The ultimate-pressure formula allows for that roughly; the datasheet's flow curve allows for it exactly.
Browse our oil-free vacuum pumps, or send us your chamber volume, target vacuum, available time, supply voltage and duty cycle and our engineers will suggest a model, including OEM versions for your machine. For background on how these pumps work, see how vacuum pumps work.