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Vacuum Pump-Down Time Calculator

Estimate how long it takes to evacuate a chamber, tank or system — or size the vacuum pump you need to hit a target pressure within a set time.

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Pump-down curve (ideal, log pressure scale).

The pump-down equation

In the rough vacuum range the gas in a chamber behaves like a well-mixed volume being drawn off at a constant volumetric rate. The pressure then falls exponentially:

p(t) = pᵤ + (p₀ − pᵤ) · e−S·t / V

Solving for time and pumping speed:

t = (V / S) · ln[(p₀ − pᵤ) / (p₁ − pᵤ)]
S = (V / t) · ln[(p₀ − pᵤ) / (p₁ − pᵤ)]

The quantity V/S is the system's time constant τ. Each time constant reduces the pressure by a factor of e (≈2.72); going from atmosphere to 1 mbar takes about 6.9 τ.

Getting realistic results

References & further reading

  1. J. F. O’Hanlon & T. A. Gessert. A User’s Guide to Vacuum Technology, 4th ed.. Wiley (2023). Practical design of vacuum systems, pump-down and outgassing.
  2. K. Jousten (ed.). Handbook of Vacuum Technology, 2nd ed.. Wiley-VCH (2016). Standard reference on gas flow, conductance, pumps and gauges.
  3. CERN Accelerator School. CAS Vacuum in Accelerators, Platja d’Aro, Spain, 2006 — proceedings (CERN-2007-003). CERN (2007), free to read. Lectures on gas dynamics, conductance, pumps and outgassing.

Frequently asked questions

How do you calculate vacuum pump-down time?

For the rough vacuum range with a constant pumping speed, t = (V / S) × ln((p₀ − pᵤ) / (p₁ − pᵤ)), where V is the chamber volume, S the effective pumping speed, p₀ the start pressure, p₁ the target pressure and pᵤ the pump’s ultimate pressure. Use consistent units, e.g. V in m³ and S in m³/s gives t in seconds.

How long does it take to pump a 100 litre chamber down to 1 mbar?

With a 10 m³/h pump and no leaks or outgassing: t = (0.1 m³ / 10 m³/h) × ln(1013 / 1) ≈ 0.069 h ≈ 4.1 minutes. In practice allow 25–50 % more for pipe losses and falling pump speed near ultimate pressure.

What size vacuum pump do I need?

Rearrange the pump-down equation: S = (V / t) × ln(p₀ / p₁). To evacuate 1 m³ from atmosphere to 1 mbar in 10 minutes you need S = (1 / 600 s) × ln(1013) ≈ 0.0115 m³/s ≈ 41.5 m³/h effective speed, before applying a safety factor. Choose a pump whose speed curve still delivers that at your working pressure.

Why is real pump-down slower than calculated?

Three main reasons: (1) pumping speed falls as you approach the pump’s ultimate pressure, (2) pipes and valves have finite conductance, reducing the effective speed at the chamber, and (3) below about 1 mbar, gas desorbing from surfaces (outgassing, especially water vapour) and small leaks add load. That is why the calculator offers a correction factor.

Does this work for high vacuum?

The formula is reliable in the rough vacuum range (atmosphere down to ~1 mbar). In high vacuum, pump-down is dominated by outgassing rather than volume, and time depends on surface area, materials, cleanliness and bake-out. Use this tool for the roughing stage and allow for outgassing separately.

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