Last updated: 2026-07-01

Erlang C Staffing

Erlang C is the formula behind almost every call-center staffing tool. It takes the call volume, the average handle time, and the number of agents on shift, and it predicts how the queue behaves: the chance a caller waits, how long the average wait runs, and the share of calls answered inside a target time. This calculator frames those outputs for workforce management — service level, average speed of answer, offered load, and occupancy.

Offered load and occupancy

Everything starts with the offered load, measured in Erlangs. It is the arrival rate multiplied by how long each call ties up an agent:

$A = \lambda \, H = \dfrac{N}{T_i}\,H$

where $N$ is the number of calls in an interval of length $T_i$, so $\lambda = N / T_i$ is the arrival rate, and $H$ is the average handle time. One Erlang is one continuous call-hour of work per hour. Spreading that load across $c$ agents gives the occupancy:

$\rho = \dfrac{A}{c}$

the fraction of paid time agents actually spend on calls. The team is stable only when $A < c$. Staffing exactly at the load ($c = A$) never works: calls arrive in random bunches, so you always need a cushion of agents above the raw load.

The wait probability

The central quantity is the Erlang C probability that an arriving caller finds every agent busy and joins the queue:

$P_{\text{wait}} = \dfrac{\dfrac{A^{c}}{c!\,(1-\rho)}}{\displaystyle\sum_{n=0}^{c-1}\dfrac{A^{n}}{n!} + \dfrac{A^{c}}{c!\,(1-\rho)}}$

Once the wait probability is known, the two staffing headline numbers follow. The average speed of answer (ASA) — the mean wait across all calls — is

$\text{ASA} = \dfrac{P_{\text{wait}}\,H}{c - A}$

and the service level, the fraction of calls answered within a target time $T_t$, is

$\text{SL} = 1 - P_{\text{wait}}\,e^{-(c - A)\,T_t / H}$

The exponential term is how fast the queue drains once all agents are busy; a larger agent surplus $c - A$ clears waiting callers more quickly and lifts the service level.

Worked example

A support line takes 100 calls in a half-hour interval ($N = 100$, $T_i = 1800$ s), each call runs about three minutes ($H = 180$ s), and 14 agents are on shift. The target is to answer within 20 seconds ($T_t = 20$ s).

First the offered load and occupancy:

Feeding $A = 10$ and $c = 14$ into Erlang C gives $P_{\text{wait}} \approx 0.174$, so about 17% of callers wait at all. The staffing metrics follow:

So with 14 agents the line answers about 89% of calls within 20 seconds, the typical wait is under eight seconds, and agents are busy roughly 71% of the time. Dropping to 13 agents would push occupancy higher and the service level lower; the calculator makes that trade-off easy to scan.

Choosing a staffing level

The usual workflow is to fix a service-level target — a common one is 80/20, meaning 80% of calls answered within 20 seconds — and raise the agent count until the model meets it. Near the threshold a single agent can move the service level by several points, because the surplus $c - A$ in the exponent grows. Occupancy works the other way: fewer agents means higher occupancy but a worse caller experience and more burnout, so most centers cap occupancy well below 100%.

Erlang C assumes callers never abandon the queue, which overstates the load when hold times are long; the related Erlang A model adds abandonment. It also assumes a single skill, a steady arrival rate within the interval, and exponential handle times. Treat the numbers as a planning guide: choose a short interval so the arrival rate is roughly constant, and check the result against historical data before committing a roster. The underlying queue is the same multi-server model covered by M/M/c Queue Calculator, and the throughput-and-concurrency relationship it rests on is Little's Law Calculator.