What is Erlang C?
Erlang C is the most widely used formula for contact centre staffing. Given how many calls you expect and how long they take to handle, it calculates the probability that a caller will have to wait, and from that how many agents you need to answer a chosen share of calls within a target time.
The formula is named after A.K. Erlang, a Danish engineer who developed queuing theory for telephone networks in the early 1900s. The unit of traffic he used, the erlang, is still used today. One erlang equals one hour of continuous call traffic, so 120 calls in an hour with an average handle time of five minutes is 600 minutes of work, or 10 erlangs.
How Erlang C works
You don’t need to work through the maths by hand. Erlang C calculators and workforce management software do it for you. The process is:
- Calculate traffic intensity.
traffic (erlangs) = calls per interval x AHT / interval length. - Try a number of agents. The formula must have more agents than erlangs, or the queue would grow forever.
- Calculate the probability of waiting. Erlang C works out how likely it is that an arriving call finds every agent busy.
- Calculate the service level. From that probability, it predicts what share of calls will be answered within your target time, along with average speed of answer and occupancy.
- Repeat until the target is met. The smallest number of agents that achieves your service level is the requirement for that interval.
That requirement is then grossed up for shrinkage to give the number of agents to schedule.
What Erlang C reveals about staffing
Erlang C shows a few patterns that are important for anyone planning a contact centre.
- Staffing isn’t linear. Each additional agent improves service level, but by less each time. Moving from 80% to 90% in 20 seconds often needs noticeably more agents than moving from 70% to 80%.
- Big pools are more efficient. Large teams can achieve the same service level at higher occupancy than small teams, because random peaks and gaps in demand average out across more agents. Splitting one team into several small queues usually needs more people overall.
- Handle time drives everything. A small change in AHT changes the traffic intensity across every interval, so it has a large effect on staffing.
Limitations of Erlang C
Erlang C is a model, and it rests on assumptions that don’t always hold:
- No abandonment. It assumes callers wait forever, so it tends to overstate staffing when queues are long. The related Erlang A model accounts for callers who hang up.
- Random, steady arrivals. It assumes calls arrive randomly at a steady average rate within each interval. A sudden call avalanche breaks that assumption completely.
- One queue, identical agents. Real contact centres use skills-based routing, multiple channels and agents with different skills. Simulation models handle that better.
- Live calls only. Email and messaging, where agents handle several conversations or work is deferred, need different methods.
Used with those limits in mind, Erlang C remains a reliable starting point for everyday phone staffing.