Queue Wait Time Calculator
Calculate how long customers will wait in any queue. Covers single-server, multi-server, and Erlang C formula with worked examples.
Expected queue wait time = (Number of people ahead × Average service time) ÷ Number of servers. With 10 people ahead, 5 minutes per customer, and 2 servers, the expected wait is 25 minutes. For complex multi-server queues, the Erlang C formula gives a more accurate estimate.
Queue Wait Time Formulas
Formula 1 — Simple Single-Server Queue:
Wait Time (minutes) = Customers Ahead × Average Service Time
Formula 2 — Multi-Server Queue (Simplified):
Wait Time = (Customers Ahead × Average Service Time) ÷ Number of Servers
Formula 3 — Little's Law (Queueing Theory):
L = λ × W
Where:
- L = average number of customers in the system (queue + being served)
- λ (lambda) = average arrival rate (customers per minute/hour)
- W = average time a customer spends in the system
Little's Law states that any stable queueing system obeys this relationship regardless of the arrival distribution or service time distribution.
How to Use the Queue Wait Time Calculator
- Enter the number of customers currently ahead in the queue.
- Enter the average service time per customer (in minutes).
- Enter the number of servers (tills, agents, or service points).
- Read the estimated wait time.
Worked Examples
Example 1 — Coffee Shop Queue
- Customers ahead: 8
- Average service time: 3 minutes
- Number of servers: 2
- Wait time = (8 × 3) ÷ 2 = 12 minutes
Example 2 — Hospital ER (Applying Little's Law)
- Average 20 patients in the ER at any time (L = 20)
- Average arrival rate: 4 patients per hour (λ = 4)
- Average time per patient: W = L ÷ λ = 20 ÷ 4 = 5 hours per patient
Example 3 — Call Centre
- Calls in queue: 15
- Average handle time: 6 minutes
- Number of agents: 5
- Wait time = (15 × 6) ÷ 5 = 18 minutes
Industry Wait Time Benchmarks
| Setting | Acceptable Wait | Notes |
|---|---|---|
| Retail checkout | 5–7 minutes | Above 8 min = abandoned basket risk |
| Fast food | 2–3 minutes | Drive-through target |
| GP / doctor | 10–20 minutes | NHS England target: <18 weeks for referral |
| Live chat support | < 2 minutes | Customers expect near-instant response |
| Call centre | < 3 minutes | Above 5 min = high abandon rate |
FAQ
How do you calculate wait time in a queue?
Multiply the number of people ahead by the average service time, then divide by the number of servers. For example, 12 people ahead, 4 minutes per person, 3 servers = (12 × 4) ÷ 3 = 16 minutes expected wait.
What is Little's Law in queuing theory?
Little's Law states that the average number of customers in a stable system (L) equals the average arrival rate (λ) multiplied by the average time each customer spends in the system (W). Written as: L = λW. It applies to any queuing system regardless of the distribution of arrivals or service times.
How does adding a second server affect wait times?
Adding a second server roughly halves the expected wait time, but the effect diminishes with each additional server. The first extra server has the greatest impact — going from 1 to 2 servers typically cuts wait time by 40–60%. Going from 5 to 6 servers may only reduce it by 10–15%.
How do you reduce queue wait times?
The four levers are: (1) increase server count, (2) reduce service time per customer, (3) control arrival rate (e.g. appointment scheduling), (4) use virtual queuing so customers wait elsewhere. Virtual queuing doesn't reduce actual wait time but dramatically improves perceived wait.
What is a reasonable queue wait time?
It depends on context. Retail customers typically tolerate 5–7 minutes. Fast food: 3 minutes. GP/doctor: 10–15 minutes. For e-commerce support, 2 minutes for live chat, 24 hours for email.