Erlang C Call-Center Calculator

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%.