Enter the calls you expect in your busiest hour, how long each call lasts and the answer-time target you want to meet. The calculator returns the smallest number of agents, or concurrent lines, that meets it.
The answer is peak concurrency: how many calls you must be able to handle at the same moment, whether people take them or an AI voice agent for order calls runs them as parallel lines.
The calculator uses the Erlang C formula, the queueing model published by the Danish engineer A. K. Erlang and still widely used to size inbound call handling. It assumes calls arrive at random, callers wait rather than hang up, and every agent can take any call.
To avoid overflow with large numbers, the script computes P(wait) through the equivalent Erlang B recursion instead of raw factorials; the result is the same.
Say a helpline expects 200 calls in its busiest hour, each lasting 180 seconds on average, and the target is 80% of calls answered within 20 seconds. Traffic is 200 × 180 ÷ 3,600 = 10 Erlangs. Adding agents one at a time:
| Agents (N) | Calls that wait | Service level in 20 s | Average speed of answer | Occupancy |
|---|---|---|---|---|
| 11 | 68.2% | 39.0% | 122.8 s | 90.9% |
| 12 | 44.9% | 64.0% | 40.4 s | 83.3% |
| 13 | 28.5% | 79.6% | 17.1 s | 76.9% |
| 14 | 17.4% | 88.8% | 7.8 s | 71.4% |
Thirteen agents fall just short of 80%, so the answer is 14. Notice how much each extra agent changes the result near the target: going from 12 to 14 agents cuts the average wait from about 40 seconds to under 8. These figures come only from the formula and the example inputs above.
The same arithmetic applies whether the calls are handled by people or by software: the number that matters is peak concurrency. AI Calling answers the helpline and calls outlets with many calls running in parallel, so the figure this calculator gives is the number of simultaneous lines to plan for, while people take the complaints and credit questions it hands over. For deciding which calls to automate, read AI calling vs human telecalling, and for the out-of-hours peak, see after-hours lead response.
Work out traffic as peak-hour calls × average handle time in seconds ÷ 3,600, then use the Erlang C formula to find the smallest number of agents whose service level meets your target, and add shrinkage for breaks and leave.
A queueing formula by A. K. Erlang that gives the probability a caller has to wait when calls arrive at random and callers queue rather than hang up. Call centres use it to size staffing for a service-level target.
That 80% of calls are answered within 20 seconds. It is a common convention, not a rule; choose the target that suits your callers and enter it in the calculator.
Yes, as a way to size concurrent lines: the traffic in Erlangs is the average number of calls in progress at once, and the result is the number of simultaneous channels needed to meet your answer-time target.
See it on your own data. AI Calling — Voice agents that take orders. Book a 30-minute working session with an engineer.
