Erlang Calculator

Erlang B models a loss system where blocked calls are simply rejected or cleared — this is used for dimensioning trunk lines in telephone networks. Erlang C models a queuing system where callers wait in a queue until an agent becomes available — this is the standard model for call center staffing. Choose Erlang B when callers receive a busy signal, and Erlang C when callers are placed on hold.

An Erlang is the unit of telecommunications traffic intensity. One Erlang equals one circuit (or trunk line) occupied continuously for one hour. It is calculated as: Traffic (Erlangs) = (Calls per hour × Average call duration in seconds) / 3600. For example, 600 calls per hour with an average duration of 180 seconds produces 30 Erlangs of traffic.

For trunk line dimensioning with Erlang B, a common target is P.02 (2% blocking probability), meaning only 2% of call attempts are blocked. For call centers using Erlang C, typical targets are 80/20 (80% of calls answered within 20 seconds) or 90/10. The right target depends on your industry, customer expectations, and cost constraints.

If your traffic intensity is 30 Erlangs, you need more than 30 agents because calls arrive randomly — sometimes multiple calls arrive simultaneously. The Erlang formulas account for this statistical variation. Having exactly 30 agents for 30 Erlangs of traffic would result in nearly 100% occupancy and extremely long wait times for callers.

The Erlang C formula assumes calls arrive following a Poisson distribution and call durations follow an exponential distribution. While real-world call patterns may deviate from these assumptions (e.g., daily traffic peaks, non-random arrivals), Erlang C remains the industry standard for initial staffing estimates. Most workforce management platforms use Erlang C as their core engine, supplemented by historical data adjustments.

Agent occupancy is the percentage of time agents spend actively handling calls versus waiting. It is calculated as traffic intensity divided by the number of agents. High occupancy (above 85-90%) leads to agent burnout and degraded service levels. Conversely, very low occupancy means overstaffing. Optimal occupancy typically ranges from 70-85% depending on the service level target.

Yes, Erlang B is widely used for SIP trunk planning. While SIP trunks are virtual rather than physical circuits, the mathematical model still applies. Input your expected concurrent call volume and the calculator determines how many SIP channels you need to maintain your target grade of service. Many VoIP providers use Erlang B calculations for capacity planning.

Erlang C calculates the number of agents needed on the phones. In practice, you must add shrinkage — the percentage of scheduled time agents are unavailable (breaks, training, meetings, absenteeism). Typical shrinkage is 25-35%. If Erlang C recommends 40 agents, with 30% shrinkage you need to schedule approximately 57 agents (40 / 0.70) to ensure 40 are available.

In an Erlang B system, calls that arrive when all trunks are busy receive a busy signal and are lost — the caller must retry. This is called blocking. In an Erlang C system, excess calls are queued and callers wait. If the queue grows unchecked, average wait times increase exponentially. Monitoring real-time traffic against your Erlang calculations helps prevent service degradation during peak periods.

Agner Krarup Erlang (1878-1929) was a Danish mathematician and engineer who pioneered the field of traffic engineering and queuing theory while working at the Copenhagen Telephone Exchange. He published his foundational paper on blocking probabilities in 1917. The unit of telecommunications traffic (the Erlang) and the Erlang programming language are both named in his honor.