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What Is Erlang C? Call Center Staffing Math Explained Simply
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One of the most important questions in any call center is deceptively simple: how many people do we need? Too few, and customers wait too long. Too many, and costs rise unnecessarily while agents sit idle.
For more than a century, call centers and telephone networks have used a mathematical formula called Erlang C to help answer this question. This article explains what Erlang C is, where it came from, how it works in plain language, and where its limits lie.
Where Erlang C Came From
Erlang C is named after Agner Krarup Erlang, a Danish mathematician and engineer who worked for the Copenhagen Telephone Company in the early twentieth century. He studied how telephone calls arrived and how many lines and operators were needed to handle them without excessive delays. His work, published in the 1900s and 1910s, laid the foundations of what's now called queueing theory, the mathematical study of waiting lines.
His name lives on in the erlang, a unit used to measure the volume of telephone traffic, and in the formulas named after him, including Erlang B and Erlang C.
What Erlang C Does
Erlang C estimates how long callers are likely to wait in a queue, based on:
- How many calls arrive in a given period.
- How long each call takes, on average.
- How many agents are available to answer.
From these, it calculates measures such as:
- The probability that a caller will have to wait at all.
- The service level, the percentage of calls answered within a target time.
- The average speed of answer, how long callers wait on average.
- Occupancy, how busy agents will be.
Planners use it in reverse: they choose a target, such as answering 80% of calls within 20 seconds, and use Erlang C to find the smallest number of agents that achieves it.
The Key Idea: Traffic Intensity
Erlang C starts by calculating the workload, measured in erlangs. One erlang represents one hour of call time occurring in one hour, or, put simply, enough work to keep one person continuously busy.
The calculation is:
Traffic intensity (erlangs) = (Number of calls × Average handle time) ÷ Length of the period
Example
Imagine a call center expects 100 calls in a 30-minute period, with an average handle time of 3 minutes.
Total work = 100 calls × 3 minutes = 300 minutes of work.
Period length = 30 minutes.
Traffic intensity = 300 ÷ 30 = 10 erlangs.
This means there's enough work to keep 10 people continuously busy for the whole 30 minutes.
Why 10 Agents Isn't Enough
It might seem that 10 agents would be enough for 10 erlangs of work. But calls don't arrive evenly. They come in random bursts: several at once, then a lull. With exactly 10 agents, they'd be busy almost all the time, and whenever a burst arrived, queues would build and callers would wait a long time.
To answer calls quickly, there need to be agents available when calls arrive, which means having more agents than the raw workload suggests. Erlang C calculates how many more.
Seeing It in Numbers
Using the example above (10 erlangs, average handle time of 3 minutes) and a target of answering 80% of calls within 20 seconds, Erlang C produces results like these:
| Agents | Calls answered within 20 seconds | Average wait | Occupancy |
|---|---|---|---|
| 11 | About 39% | About 2 minutes | About 91% |
| 12 | About 64% | About 40 seconds | About 83% |
| 13 | About 80% (just under target) | About 17 seconds | About 77% |
| 14 | About 89% | About 8 seconds | About 71% |
| 15 | About 94% | About 4 seconds | About 67% |
In this example, 14 agents are needed to meet the 80/20 target comfortably.
The table also shows something important: adding one agent when the team is stretched makes a huge difference, while adding one when the team is already well staffed makes much less. Going from 11 to 12 agents cuts the average wait from about two minutes to about 40 seconds. Going from 14 to 15 saves only a few seconds.
From Agents Needed to Agents Scheduled
Erlang C tells planners how many agents need to be on the phones at a given time. But not everyone who's scheduled is available to take calls at every moment. People take breaks, attend meetings and training, and are sometimes absent.
This lost time is called shrinkage. To account for it, planners schedule more people than Erlang C suggests:
People to schedule = Agents needed ÷ (1 − Shrinkage)
If 14 agents are needed and shrinkage is 30%, the calculation is 14 ÷ 0.7 = 20, so about 20 people should be scheduled.
The Assumptions Behind Erlang C
Erlang C is built on several simplifying assumptions:
- Calls arrive randomly, following a well-understood statistical pattern.
- Callers wait indefinitely and never hang up.
- All agents are equally able to handle any call.
- Handle times follow a typical pattern and stay consistent.
- Callers don't call back after giving up.
The Limitations
Because real call centers don't always match these assumptions, Erlang C isn't perfect.
It ignores abandoned calls. In reality, some callers hang up rather than waiting. Because Erlang C assumes everyone waits, it tends to predict longer waits than actually happen, which can lead to slightly more staff than strictly necessary. A variation called Erlang A accounts for callers abandoning.
It assumes all agents are the same. In practice, agents have different skills and handle different call types. Complex routing setups need more advanced methods, such as simulation.
It relies on accurate forecasts. If call volume or handle time predictions are wrong, the results will be too.
It covers one queue at a time. Operations handling chat, email, and calls together, or many interconnected queues, need more sophisticated planning tools.
Despite these limits, Erlang C remains widely used because it's simple, well understood, and reasonably accurate for many situations. Most workforce management software uses Erlang C or more advanced methods built on similar principles.
Why It Still Matters
Erlang C turns a complicated question, how many people are needed to keep waits reasonable, into a calculation planners can rely on. It also explains something every call center experiences: why a small staffing shortfall can cause queues to grow dramatically, and why a little extra capacity can make a big difference. More than a century after Agner Erlang first studied telephone queues, his work still shapes how calls are answered every day.