Erlang C Call Center Calculator

Erlang C is a queueing formula that estimates the probability an inbound call has to wait because every agent is busy. It models a call center as an M/M/c queue, meaning calls arrive at random (Poisson), handle times vary around an average, and c agents share one queue with no caller hanging up. Workforce planners use it to turn a call forecast into the number of agents needed to meet a service level, and to predict the average wait. It was derived by the Danish mathematician A. K. Erlang for telephone traffic in the early 1900s.

You enter the forecast call volume for one reporting interval (15, 30, or 60 minutes), the average handle time (talk time plus after-call work), the target service level, the target answer time, and your shrinkage. From the volume and handle time it first works out the offered load in Erlangs, which is the average number of agents' worth of work arriving. It then searches for the smallest team that answers your target percentage of calls within the target time.

It depends on your offered load, not just the raw call count. For example, 100 calls in a 30 minute interval with a 180 second handle time is 10 Erlangs of load, and Erlang C needs 14 agents to answer 80% of calls within 20 seconds. Thirteen agents would reach only about 79.6%, which misses the target, so the calculator rounds up to the first team that meets or beats it. Heavier call loads need proportionally fewer spare agents because larger teams pool risk more efficiently.

Average speed of answer is the mean time a caller waits in queue, averaged across every call including the ones answered immediately. Erlang C computes it as the probability of waiting times the handle time divided by the spare capacity, written ASA = C * AHT / (N - A), where N is the agent count and A is the offered load. It falls sharply as you add agents past the break-even point. ASA and service level move together, so a team that hits an 80/20 target also keeps the average wait low.

Shrinkage is the share of paid time agents are not available to take calls, covering breaks, meetings, training, and sick leave. The Erlang C requirement tells you how many agents must be on the phones at once, so you divide that by one minus the shrinkage to find how many to roster. With 14 agents required and 30% shrinkage, you schedule ceil(14 / 0.70) = 20 people. Set shrinkage to 0 to see the raw on-phone requirement on its own.

Erlang C assumes calls arrive randomly, handle times follow an exponential spread, the queue is unlimited, and no caller ever abandons. Real callers do hang up, so Erlang C tends to slightly overstate waiting and overstaff compared with models like Erlang A that include abandonment. It also assumes a single skill and steady arrivals within the interval, so treat the result as a solid planning estimate rather than an exact promise. For multi-skill routing, blended work, or callbacks, use it as a starting point and validate against your real data.