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Waiting Time In Queue Calculator

Work out waiting time in queue instantly with clear inputs, formula shown and shareable results.

About Waiting Time In Queue Calculator

Waiting time follows from Little's law applied to the M/M/1 queue: the wait is utilisation divided by capacity times one minus utilisation. Because the wait depends on one minus utilisation, adding a small amount of capacity at a busy till cuts waiting time far more than it cuts utilisation.

Formulas

Average wait

Wq = rho / (capacity x (1 - rho))

Time in system

W = Wq + 1 / capacity

Worked example

With the default values below, Waiting Time In Queue Calculator returns Average wait before service of 4.800. Change any input above and every figure here is recalculated in your browser.

Inputs used

Arrivals per hourminimum 0.1
40
Customers one server handles per hourminimum 0.1
50
Number of serversminimum 1
1

Results

Average wait before service
4.800 min
Average total time in the system
6.000 min
Server utilisation
80.00%
Average people ahead of you
3.200

Step by step

  1. 1Values used
  2. 2Average wait
  3. 3Time in system
  4. 4Average wait before service= 4.800 min
  5. 5Average total time in the system= 6.000 min
  6. 6Server utilisation= 80.00
  7. 7Average people ahead of you= 3.200

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is the Waiting Time In Queue figure worked out?

Wq = rho / (capacity x (1 - rho)). Waiting time follows from Little's law applied to the M/M/1 queue: the wait is utilisation divided by capacity times one minus utilisation.

Why does this matter?

Because the wait depends on one minus utilisation, adding a small amount of capacity at a busy till cuts waiting time far more than it cuts utilisation.

What do I need to enter?

Enter arrivals per hour, customers one server handles per hour, number of servers. The defaults shown are a realistic worked example — swap in your own figures to get a result you can use.

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