Erlang C Staffing Calculator

Find wait probability, average speed of answer and service level for a staffed queue.

How the Erlang C staffing model works

Erlang C is the standard queueing model used to plan call and contact center staffing. From your call volume, average handle time and agent count, it estimates the probability a caller has to wait, the average speed of answer, and the share of calls answered within your target time (service level).

Enter calls per hour, average handle time in seconds, the number of staffed agents, and your target answer time. The calculator returns the offered load (in Erlangs), the wait probability, the average speed of answer, and the service level.

The model assumes a single queue, agents of equal skill, and no caller abandonment — real contact centers deviate from these assumptions to varying degrees, so treat the result as a planning estimate to validate against your actual data, not an exact prediction.

The formula

A = λ × AHT. Erlang C via the Erlang B recursion. Wq = Pwait ÷ (c·μ − λ). SL = 1 − Pwait·e^(−(c·μ−λ)·T)

Offered load A is the arrival rate times average handle time, in Erlangs. Erlang C's wait probability is derived from the numerically stable Erlang B recursion (avoiding factorial overflow). Average speed of answer and service level follow the model's standard closed-form results.

Worked example

12 calls/hour, 300-second handle time, 2 agents, 20-second target

Offered load = 12 × 300 ÷ 3,600 = 1 Erlang. With 2 agents, the wait probability is 1/3, average speed of answer is 100 seconds, and about 69% of calls are answered within 20 seconds.

Frequently asked questions

Why does the calculator reject some agent counts?

The model requires agent capacity to exceed the offered load (agents > A) — otherwise the queue is unstable and wait times grow without bound. Add agents or reduce call volume/handle time.

What does the model NOT account for?

Caller abandonment, multiple skill/priority queues, agent shrinkage (breaks, training, absence) and time-of-day volume variation are not modeled. Use this as a first-pass planning estimate, then validate against real data.

How is this different from the Capacity Calculator?

Capacity Calculator gives a simple task-throughput estimate. Erlang C is a full queueing model built specifically for the statistics that matter in a staffed queue — wait probability, speed of answer and service level.

Built by PanelRoster

PanelRoster is an enterprise operations management platform for organizations coordinating distributed teams, assignments, workflows, quality assurance and operational execution.

Explore PanelRoster