The Erlang Formula: A Comprehensive Guide for Call Center Optimization

Greetings, readers! In this digital age, where customer satisfaction is of utmost importance, call centers have become a crucial component of businesses. Increasingly, call center managers and operators are adopting the Erlang formula to optimize their operations for optimum efficiency and productivity. In this article, we will provide a detailed breakdown of the Erlang formula, its application in call centers, its advantages, and much more. So, sit back, relax, and get ready to delve into the fascinating world of call center optimization!

What is the Erlang Formula?

The Erlang formula is a mathematical formula used to calculate the number of call center agents required to handle incoming calls at a given time. It is based on the work of Agner Krarup Erlang, a Danish mathematician and engineer, who first proposed the formula in 1909. The Erlang formula calculates the number of agents required to handle calls within a certain period and takes into consideration factors such as call arrival rate, average call duration, and service level targets.

How does the Erlang Formula Work?

The Erlang formula works by taking into consideration the following factors:

Factors Definitions
Call Arrival Rate The number of calls arriving in a given time period, usually measured in calls per hour (CPH).
Average Call Duration The length of time each call lasts, usually measured in minutes.
Service Level Target The desired percentage of calls answered within a certain time, usually measured in seconds.

Using these factors, the Erlang formula calculates the number of agents required to handle incoming calls at a given time, taking into consideration the expected call volume and service level targets.

Benefits of Using the Erlang Formula in Call Centers

The Erlang formula has several benefits, including:

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Increased Efficiency

By accurately calculating the number of agents required to handle incoming calls, call centers can ensure that they have just the right number of agents at the right time, which results in better efficiency and cost savings.

Improved Customer Experience

With the Erlang formula, call centers can meet service level targets by ensuring that enough agents are available during peak calling hours, thus reducing wait times and improving the overall customer experience.

Better Forecasting and Planning

The Erlang formula allows call centers to forecast and plan for future call volumes by analyzing historical data and projecting future trends. This enables call center managers to make informed decisions about staffing requirements and other resources.

Greater Flexibility

The Erlang formula is flexible and can be adapted to meet the specific needs of individual call centers. It can be customized to consider factors such as agent skill sets, call types, and other variables that can affect call handling time and service level targets.

How to Implement the Erlang Formula in Your Call Center

Implementing the Erlang formula in your call center requires careful planning and analysis. Here are some steps to guide you:

1. Gather Historical Data

To use the Erlang formula, you need historical data on call volumes, average call duration, and other factors. Collect this data over a significant period of time to get a reliable data set.

2. Define Service Level Targets

Define your service level targets to ensure that you are meeting your customer’s needs. Your service level targets will determine how many agents you need to have available at any given time.

3. Calculate the Required Number of Agents

Using the Erlang formula, calculate the number of agents required to handle incoming calls at any given time. This will enable you to determine the optimal staffing levels for your call center.

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4. Monitor and Adjust

Monitor your call center’s performance regularly and make adjustments as needed. The Erlang formula is not static and will change as your call volumes fluctuate, so it is essential to keep an eye on your numbers to ensure that your staffing levels remain optimal.


1. Can the Erlang formula be used for other industries besides call centers?

Yes, the Erlang formula can be used for any industry that deals with queuing systems, such as healthcare, transportation, and logistics.

2. How accurate is the Erlang formula?

The Erlang formula is generally considered an accurate tool for predicting staffing requirements, but it does have its limitations.

3. How can I get started with implementing the Erlang formula in my call center?

The best way to get started is to gather historical data on your call center’s performance, define your service level targets, and use an Erlang calculator to calculate the number of agents required to handle incoming calls at any given time.

4. Are there any drawbacks to using the Erlang formula?

One potential drawback is that the Erlang formula assumes a constant arrival rate, which may not be the case in real-world situations.

5. Can the Erlang formula be used for outbound call centers?

Yes, the Erlang formula can be used for outbound call centers, but the calculation will be different since the call volumes and average call duration may vary.

6. What is the difference between the Erlang formula and the Erlang C formula?

The Erlang C formula takes into consideration the probability that a caller may have to wait for service, while the Erlang formula assumes that all calls are answered immediately.

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7. How often should I recalculate my agent staffing levels?

It is recommended that you recalculate your agent staffing levels regularly, depending on your call volumes and service level targets. Most call centers recalculate every 15 minutes to ensure optimal staffing levels.


The Erlang formula is a powerful tool that can be used to optimize call center operations for maximum efficiency and productivity. By using this formula, call centers can accurately calculate the number of agents required to handle incoming calls at any given time, resulting in reduced wait times, improved customer experience, and cost savings. We encourage you to implement the Erlang formula in your call center and take your operations to the next level!

Thank you for reading this article. We hope you found it informative and helpful. If you have any questions or comments, please feel free to leave them below!


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