Erlang C calculator: agents required for your service level target.
Enter contacts per interval, average handle time, and a service level goal such as 80 percent in 20 seconds. The calculator returns required agents, predicted service level, average speed of answer, and occupancy, with the Erlang C formula written out below.
Erlang C is the classic queueing model used to staff call centers. Given the offered traffic and a number of agents, it computes the probability that a contact has to wait in queue instead of being answered immediately. From that waiting probability you can derive the two numbers every operations leader cares about: the service level, meaning the share of contacts answered within a threshold such as 20 seconds, and the average speed of answer. The model is more than a century old, it was developed by the Danish engineer A. K. Erlang for telephone exchanges, and it remains the backbone of nearly every commercial workforce management tool.
The reason Erlang C beats simple workload math for service level questions is that queues are nonlinear. Going from 20 to 21 agents on a 16.7 erlang workload does not improve service level by 5 percent, it improves it by almost 10 points, from about 73 percent to about 83 percent answered in 20 seconds. Near the edge of stability, single agents swing service levels dramatically, which is exactly why understaffing by two or three people can melt a queue.
The Erlang C formula, written out in text
First compute the traffic intensity A in erlangs: contacts per interval multiplied by average handle time in seconds, divided by the interval length in seconds. With N agents, the Erlang C formula says the probability that a contact has to wait equals A to the power of N divided by N factorial, divided by the quantity: A to the power of N divided by N factorial, plus one minus A over N, multiplied by the sum over k from 0 to N minus 1 of A to the power of k divided by k factorial.
From that waiting probability, service level equals one minus the waiting probability multiplied by the exponential of negative (N minus A) times the answer threshold divided by AHT. Average speed of answer equals the waiting probability times AHT divided by (N minus A). This calculator finds the smallest N that meets your service level target, then grosses the schedule up for shrinkage by dividing by one minus shrinkage, and keeps adding agents if planned occupancy, A divided by N, would exceed your maximum occupancy cap.
How to choose your inputs
Volume and AHT should come from the same interval, queue, and channel, and AHT must include after-call work. The service level target is a business decision, not a math fact: 80 percent in 20 seconds is the traditional voice benchmark, but plenty of healthy operations run 70/30 or 90/15 depending on what their customers actually tolerate. The threshold matters as much as the percentage, hitting 80 percent in 60 seconds requires far fewer agents than 80 percent in 10 seconds.
Set a maximum occupancy cap around 85 to 90 percent so the model never hands you a technically-feasible roster that grinds agents into the ground. And treat shrinkage honestly: the Erlang answer is productive bodies on the queue, while your schedule has to supply humans who also take breaks, attend meetings, and call in sick.
Where Erlang C breaks down
Erlang C assumes random arrivals, exponential handle times, no abandonment, and a single skill group. Real contact centers have callers who hang up, multi-skilled agents, chat concurrency, and volume that arrives in bursts. The model therefore tends to overstaff slightly at high abandonment rates and understaff when arrivals are spiky. It is an excellent planning baseline and a poor autopilot, which is why QueuePilot pairs interval-level Erlang-style requirements with forecast confidence ranges, real adherence data, and intraday recommendations when reality diverges from the model.
Frequently asked questions
What does 80/20 service level mean?
An 80/20 service level target means 80 percent of contacts should be answered within 20 seconds. Both numbers are choices: 80/20 is the traditional voice benchmark, but the right target depends on your customers, channel, and economics.
How many agents do I need for 100 calls per half hour at 300 seconds AHT?
That workload is 16.7 erlangs. Erlang C says 21 productive agents meet an 80/20 target, delivering roughly an 83 percent service level with an average speed of answer near 16 seconds at 79 percent occupancy. With 30 percent shrinkage you would schedule 30 agents.
What is an erlang?
One erlang is one hour of workload per hour, or equivalently one continuously busy agent. Traffic intensity in erlangs equals contacts per interval times average handle time, divided by the interval length.
Why does Erlang C sometimes overstaff?
Erlang C assumes nobody abandons the queue, so every waiting caller keeps consuming future agent time. In centers with meaningful abandonment, real service levels are slightly better than the model predicts. Erlang A models abandonment, but Erlang C remains the standard conservative planning baseline.