How the calculation works
Traffic in Erlangs = calls in the interval × average handle time (seconds) ÷ the interval length in seconds. One Erlang is one agent kept busy for the whole interval.
Erlang C. For N agents and A Erlangs (N must be more than A, or the queue grows without limit), the calculator computes Erlang B with the recursion B(0) = 1, B(k) = A·B(k−1) ÷ (k + A·B(k−1)), then the probability a call waits, C = N·B ÷ (N − A + A·B). The recursion avoids the factorials in the textbook form, which overflow floating-point numbers above about 170 agents.
- Service level = 1 − C × e^(−(N − A) × target seconds ÷ AHT)
- Average speed of answer (ASA) = C × AHT ÷ (N − A)
- Occupancy = A ÷ N
- Agents = the smallest N that meets the service level target and, if set, keeps occupancy at or under the cap
- Scheduled staff = agents ÷ (1 − shrinkage), rounded up
Assumptions. Calls arrive at random during the interval, handle times vary randomly around the average, every caller waits until answered (no abandonment, no retries), and one queue serves all calls with agents who can take any of them. Run each interval separately; the calculator doesn’t carry a queue from one interval to the next. Shrinkage defaults to 30% as a placeholder, not a published figure.
Worked example
100 calls in a 30-minute interval with a 3-minute (180-second) handle time, a target of 80% answered within 20 seconds and 30% shrinkage. This is the example Call Centre Helper uses in its Erlang C walk-through, and the results match:
- Traffic: 100 × 180 ÷ (30 × 60) = 10 Erlangs
- 13 agents: 28.5% of calls wait, 79.6% answered within 20 seconds, short of the target
- 14 agents: 17.4% wait, 88.8% answered within 20 seconds, which meets it
- ASA: 0.1741 × 180 ÷ 4 = 7.8 seconds; 82.6% answered without waiting
- Occupancy: 10 ÷ 14 = 71.4%
- Scheduled: 14 ÷ (1 − 0.30) = 20 agents
With an 85% occupancy cap the answer stays at 14, because 71.4% is already under it. A larger queue shows the cap at work: 600 calls in 30 minutes at a 300-second handle time is 600 × 300 ÷ 1,800 = 100 Erlangs, and with a target of 80% in 30 seconds, 107 agents meet the service level at 93.5% occupancy; an 85% cap raises that to 118.
Beyond one interval
A full schedule repeats this for every interval in the day and week, then fits shifts to the result, which is what workforce management software does. Many contact center platforms include forecasting and scheduling, or connect to a WFM tool. For support teams that work tickets rather than live calls, the help desk staffing calculator is a better fit.
