Erlang C
Calculate call center agent staffing and wait probability using the Erlang C formula.
About Erlang C
The Erlang C formula calculates the probability that an arriving call finds all agents busy and must wait in queue, assuming blocked callers wait rather than hang up (unlike Erlang B). It's the standard model for call center staffing: C(N,A) = [A^N/N! × N/(N−A)] / [Σ(A^k/k!, k=0..N−1) + A^N/N! × N/(N−A)]. This calculator derives C(N,A) from the numerically stable Erlang B recursion, then computes average wait time and an approximate service level (probability of being answered within 20 seconds) — both standard call-center KPIs.
Formulas
Erlang C wait probability
C(N,A) = [A^N/N! × N/(N−A)] / [Σ(A^k/k!, k=0..N-1) + A^N/N! × N/(N−A)]
- A
- Offered traffic in Erlangs
- N
- Number of agents/circuits
Average wait time
avg_wait = C(N,A) × avg_handle_time / (N − A)
Worked example
With the default values below, Erlang C returns Probability of Waiting of 17.413%. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Offered Traffic Load (A)minimum 0.01 Erlangs
- 10 Erlangs
- Number of Agents/Circuits (N)accepts 1–2,000
- 14
- Average Handle Timeminimum 1 seconds
- 240 seconds
Results
- Probability of Waiting
- 17.413%
- Average Wait Time (all callers)
- 10.45 seconds
- Service Level (answered ≤20s)
- 87.52%
Step by step
- 1Values used
- 2Erlang C wait probability
- 3Average wait time
- 4Probability of Waiting= 17.413
- 5Average Wait Time (all callers)= 10.45 seconds
- 6Service Level (answered ≤20s)= 87.52
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 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
What happens if agents equal or fall below the traffic load?
The queue becomes unstable — calls arrive faster than agents can resolve them, so wait times grow without bound over time. The number of agents must strictly exceed the offered traffic in Erlangs for the system to reach a steady state.
What is 'service level' in call center terms?
Service level is typically defined as the percentage of calls answered within a target time threshold (commonly 20 or 30 seconds), e.g. "80% of calls answered within 20 seconds" is a common target (often written 80/20).
How is Erlang C different from Erlang B?
Erlang B assumes a blocked caller simply disappears (lost calls cleared) — appropriate for circuit-switched trunk sizing. Erlang C assumes the caller waits in a queue for an available agent, which better models real call centers with hold queues.
Does adding one more agent significantly reduce wait time?
Often yes, especially when the agent count is close to the offered traffic — small staffing changes near the boundary have an outsized effect on both wait probability and average wait time, which is why call centers often over-provision by a few agents beyond the bare minimum.