Queue wait time calculator
How many checkouts or registration desks do you need? Enter your arrival rate, average service time and open counters. Get a steady-state estimate with Erlang C (M/M/c), free, in your browser. No account or AI needed.
Estimated queue
- Counter utilisation
- 66.67%
- Chance a person waits
- 44.44%
- Average wait
- 26.67 s
- 90th-percentile wait
- 1.49 min
- Average queue length
- 0.89 people
Waits exclude service time and include people who do not wait. The 90th percentile is the wait that at least 90% of arrivals do not exceed; it is zero when at least 90% are served immediately. Queue length counts people waiting, not those being served or metres of floor space.
Smallest number of counters for your target
3
Average wait with this many counters: 26.67 s
The target is an average, not a maximum wait or a guarantee for every visitor. This count assumes every counter stays available; breaks, absences and separate lines are not included.
When this estimate applies
- People arrive independently at a steady random rate (Poisson arrivals).
- Service times are independent and exponentially distributed: many short visits and a few long ones, with the average you enter. All counters work at the same average speed.
- One shared, first-come-first-served line feeds every counter. There is unlimited waiting space, and nobody leaves or skips the line.
- The queue has run long enough to reach a steady state. Arrival rates and counter availability do not change. Utilisation must be below 100%.
A show ending, a school bell, or a walk to the counter?
Those create bursts or add walking and layout effects. This steady-state calculator does not predict them. Use a simulation with the actual arrival pattern, service times and routes. Running simulations in Laydyne requires Pro; you can read these worked examples freely.
Queue formula or simulation: when is Erlang C enough? →
- Supermarket checkouts: separate lines and a shared line
- Cinema toilets after two films end
- School toilet queues during a break
- Trade show registration desks and the morning rush
How the Erlang C calculator works
With λ arrivals per hour, s seconds per person and c counters, the offered load is a = λs/3600 and utilisation is ρ = a/c. For ρ < 1, Erlang C gives the chance of waiting, C. Average wait Wq = Cs/(c − a) seconds; average queue length Lq = λWq/3600. The 90th-percentile wait is zero if C ≤ 0.1, otherwise s ln(C/0.1)/(c − a). We test whole counter counts from 1 to 1,000 and return the first with Wq strictly below your target.
Read the Erlang C formulas, units and worked example →
Erlang C definitions and formulas — Abstract Micro Systems