# Number of agents in a call center

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

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

The call load varies during the day, and it also varies on different days of the week. The following calculator helps you to address these variations. It estimates the number of agents for other times of day (or another 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
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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

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