Erlang Calculator

How To Use This Erlang Calculator

If you have 200 calls per hour, then enter the number of incoming contacts as 200 and the period is 60 minutes.
The Average Handling Time is the amount of time that a person (an agent) takes to handle a phone contact. This includes the talk time as well any paperwork time (wrap-up time) before they are able to answer the next call. This should be in seconds.
Put in your Service Level target and time. So if you wanted to handle 90% of calls in 15 seconds, put in 90 and 15. If you are uncertain of this the industry “average” is 80% of calls answered in 20 seconds.
This contact centre staffing Erlang calculator is a hybrid model based on both the Erlang C formula the Erlang A formula. The Erlang C formula was invented by the Danish Mathematician A.K. Erlang and is used to calculate the number of advisors and the service level. Call Abandons are calculated using the Erlang A formula which was devised by Swedish statistician Conny Palm in 1946. This assumes an Average Patience – also know as Average Time to Abandon (ATA).
This calculator works on probabilities, so may appear to overstate the number of agents needed at low levels. So for example, if you enter O calls per hour it will say that you need 1 agent. This is quite correct, as there may be a possibility that one call may come in. In practicality, you may decide to not schedule any staff.
The maximum number of agents that the calculator can calculate before shrinkage is applied is 10,000 Agents.
Shrinkage is a factor designed to take into account holidays, sickness etc.
The maximum occupancy is designed to improve accuracy. If you take Occupancy over 85%-90% for long periods you will find that it gets hidden in a longer AHT figure, and agent burn out happens.
Call Abandons are calculated using the Erlang A formula, which assumes an Average Patience -also know as Average Time to Abandon (ATA).
The Calculator can deal with up to 10,000 agents, thanks to some help with the maths from Philip Wright CEng – (Former Technical Director & CTO Europe at Aspect Telecommunications/Communications 1988-2001).

An Erlang calculator is one of the most useful Workforce Management (WFM) tools in the call centre toolkit.
An Erlang Calculator is a mathematical calculation that allows you to calculate the number of staff that you need for a given number of calls, to meet a given service level.
It is based on the Erlang C formula (a derivative of the Poisson distribution) that was designed by the Danish Mathematician A.K. Erlang around 100 years ago. The formula is quite involved, but is relatively easy to follow if you studied maths to a reasonable level at school.
You simply enter in the number of phone calls that you receive in a period of time (say per half hour), along with the average duration of the calls and also the service level that you are looking for.
Typical Inputs
Number of phone calls
Time period (e.g. per half hour)
Average Call Duration (Average Handling Time)
Service Level (Percentage of calls answered within a period of time, e.g. 80% of calls in 20 seconds)
Some Erlang calculators also include a shrinkage input.
Typical Outputs
Number of agents (advisors) needed to meet the service level target


Number of calls 100
In a period of minutes 30
Average Handling Time (seconds) 180
Required Service Level 80%
Target Answer Time (Seconds) 20
Maximum Occupancy 85%
Shrinkage 30%

Calls per hour 200

Traffic Intensity (Erlangs) A 10

Estimate the Raw Number of Agents N 11 Start with the number of Erlangs + 1

Calculate the Erlang Formula for Probability a Call Waits

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