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# Number of agents in call center

The calculator works out number of call center agents using Erlang C formula for given call load and service level.

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Earlier we described how to calculae number of channels required to handle given call load (PBX channel number calculation). This calculator continues telecommunications series. The calculator helps to estimate the number of persons required to handle the call center phone call load. Number of inbound channels in call center is usually slightly more than number of agents. Lines excess is used for holding calls in peak hours, when all agents are busy. Obviously, the less agents you have, the more a new call is held waiting free agent. If you have too little agents, your service quality is low, ohterwise if you have too much agents your expenses grow unreasonably. Therefore it is very important to calculate right number of agents to handle call load with good quality without extra spendings.
Service level - is a measure of quality in call center. Service level is calculated as percentage of calls handled by the agents within given (small) amount of time. For example, 80% calls, must be handled in 20 seconds or less. The following calculator gives your number of agents required to handle given call number with given service level.

### Call center agents number

Average handling time in seconds

Call ratio to be handled during given maximum waiting time

Maximum allowed waiting time in seconds

Agents number

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The call load varies during the day, it varies also in different days of week. The following calculator helps you to address these variations. It estimates number of agents for different time of day (or other time period).

### Agent work schedule

Items per page:

Average handling time in seconds

Call ratio to be handled during given maximum waiting time

Maximum allowed waiting time in seconds

Agents count per hour
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Both calculators employs Erlang C formula to get the probability that a call is not answered immediately:
$E_c(m,A)=\frac{\frac{A^m}{m!}}{\frac{A^m}{m!}+(1-\frac{A}{m})\sum^{m-1}_{k=0}\frac{A^k}{k!} }$,
where m - agent number,
A - call load in erlangs (see Telecommunications traffic, Erlang).
Here, we get call load by formula $A = T_s\lambda$
where $\lambda$ - call arrival rate (number of calls per time unit), $T_s$ - average handling time. This must be expressed in the same time unit used for the call arrival rate.

Service level (the probability that a call will be answered in less than a target waiting time) formula:
$SL = 1-E_c(m,A)e^{-(m-A)\frac{t}{T_s}}$,
where t- service level limit