Erlang C Calculator
Calculate how many call center agents you need to hit your service level target. Enter your call volume, handle time, and shrinkage — results appear instantly.
Inputs
Total inbound calls expected in a typical hour.
Talk time + hold time + after-call work, in seconds.
Percentage of calls to answer within the target time (e.g. 80).
Maximum acceptable wait time for the service level (e.g. 20).
Time agents are unavailable: breaks, training, absence (typically 25–35%).
Results
What Is Erlang C?
Erlang C is a queuing formula developed by Danish mathematician Agner Krarup Erlang in the early twentieth century. It models a system where callers who cannot immediately reach a free agent wait in a queue rather than abandoning or receiving a busy signal. The formula calculates the probability that an arriving caller will have to wait — which then lets you work out the minimum number of agents required to meet a defined service level.
In call center operations, Erlang C is the standard method for workforce management (WFM) and scheduling. It underpins the staffing modules in most WFM platforms and is used directly in spreadsheet-based planning when a dedicated tool is unavailable.
For more context on the metrics that feed into this calculation, see our guide to call center metrics and the reporting available through call analytics.
How the Calculator Works
The calculator performs these steps:
- Traffic intensity (Erlangs): calls per hour × AHT ÷ 3600. This is the average number of agents that would be fully occupied if calls arrived evenly.
- Minimum raw agents: starting from the ceiling of traffic intensity plus one, the calculator increments the agent count until the Erlang C service level formula returns a value at or above your target percentage.
- Shrinkage adjustment: the raw agent count is divided by (1 − shrinkage ÷ 100) and rounded up, giving a rostered headcount that accounts for unavailability.
- Estimated wait time: derived from the Erlang C probability and the difference between agent capacity and traffic intensity.
Formula Reference
Erlang C (C) = (A^N / N!) × N/(N−A) ÷ [ Σ(A^i / i!, i=0..N−1) + (A^N / N!) × N/(N−A) ]
Service level = 1 − C × exp(−(N − A) × (1/AHT) × T)
Avg wait = C / ((N − A) × (1/AHT))
Agents with shrinkage = ceil(N / (1 − shrinkage/100))
Where N is the number of agents, A is traffic intensity in Erlangs, and T is the target answer time in seconds.
About Shrinkage
Shrinkage covers all the time scheduled agents spend away from call-handling: scheduled breaks, meal periods, team meetings, training sessions, coaching, unplanned absence, and administrative work. Because it is not possible for every scheduled agent to be available at every moment, the raw Erlang C agent count understates the number of people you need to roster.
A shrinkage of 30% means that for every 10 agents you schedule, only 7 are available at any given moment. The calculator uses ceil(rawAgents / (1 − shrinkage/100)) to convert the theoretical minimum into a realistic headcount.
Limitations of Erlang C
Erlang C assumes callers wait indefinitely rather than abandoning. Real call centers see abandonment, so actual service levels can be slightly better than predicted when queues grow long. The formula also assumes calls arrive randomly (Poisson distribution) and all agents are equally skilled. For highly segmented or blended environments, more sophisticated simulation tools may give better results. Use this calculator for initial planning and validate against your historical data.
To see how a modern contact center platform can help you manage real-time staffing against these targets, explore MCC's contact center features.
Frequently Asked Questions
- What is Erlang C?
- Erlang C is a mathematical formula used to calculate the number of agents needed in a call center to achieve a target service level. It takes call volume, average handle time, and desired answer speed as inputs and returns the probability that a caller will have to wait — allowing managers to determine minimum staffing.
- How do I use this Erlang C calculator?
- Enter your calls per hour, average handle time in seconds, target service level percentage, target answer time in seconds, and shrinkage percentage. The calculator instantly shows the minimum agents needed, traffic intensity in Erlangs, and estimated service level and wait time.
- What is shrinkage in call center staffing?
- Shrinkage is the percentage of scheduled time when agents are unavailable to handle calls — covering breaks, lunch, training, coaching, absence, and administrative tasks. A typical shrinkage figure is 25–35%. The calculator adds shrinkage on top of the raw Erlang C agent count to give a realistic rostered headcount.
- What is traffic intensity in Erlangs?
- Traffic intensity (measured in Erlangs) represents the volume of work arriving at the call center per unit of time. It is calculated as: Erlangs = (calls per hour × average handle time in seconds) ÷ 3600. If Erlangs equals or exceeds the number of agents, the queue becomes unstable and wait times grow without limit.
- What service level should I target for my call center?
- The most common service level target is 80% of calls answered within 20 seconds (written as 80/20). Some operations target 90/15 for higher service or 70/30 for cost-optimised environments. The right target depends on your customer expectations, contract SLAs, and operational budget.
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