Erlang C Call-Center Calculator
Compute number of agents needed in a call center using the Erlang C formula — given traffic, service level and mean call time.
Erlang C: probability of waiting
Erlang C predicts the probability a caller waits when N agents handle a Poisson arrival stream with traffic load A = λ/μ (in Erlangs, with λ in calls/hour and 1/μ as average handle time): P(wait) = C(N,A) / (C(N,A) + (1 − A/N) · Σk=0..N−1 Ak/k!). The model was published by A. K. Erlang in 1909 while at Copenhagen Telephone Company and remains the industry baseline. Typical contact-centre SLA is 80/20 — 80% of calls answered within 20 seconds. Example: 60 calls/hour, AHT 3 min → A = 3 Erlangs; with 5 agents, P(wait) ≈ 35% and the 80/20 target is met.
Applications
Customer-service staffing (banking — Banco do Brasil, Nubank — telecom, retail), technical support, ITSM helpdesk, reception desk sizing, hospital emergency triage, and on-call rota planning. Operational tools: NICE inContact, Genesys Cloud, Mitan, and Excel-based planners using Erlang C tables.
FAQ
Erlang B vs C? Erlang B assumes blocked calls are lost (no queue) — used for trunk lines; Erlang C assumes infinite queue with waiting — used for contact centres.
What if A ≥ N? The queue is unstable and grows without bound — you need more agents or a shorter AHT, period.
Limitations? Assumes Poisson arrivals, exponential service times, identical agents, and infinite patience. Real centres need shrinkage (breaks, training) and abandonment (Erlang A) corrections — typically add 25–35%.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.