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Erlang C calculator for support staffing

Enter how many chats or calls arrive in your busiest hour, how long each takes and the service level you promise. You get the agents you need on duty, the agents to schedule after shrinkage, and the wait times to expect.

Your workload

Shrinkage is the share of paid time agents are not available: breaks, meetings, training, absence. For phone, leave chats per agent at 1. The example numbers are a sample.

Agents to schedule

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On duty
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Service level
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Avg. wait
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Occupancy
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Agents on dutyService levelAvg. waitOccupancy

How the calculation works

  1. Workload in Erlangs. Contacts per hour times handle time in hours. 120 chats an hour at 6 minutes each is 120 × 0.1 = 12 Erlangs: on average, 12 agents are busy at any moment.
  2. Chance of waiting. For each number of agents above the workload, Erlang C gives the probability that a new contact has to wait.
  3. Service level. The share answered within your target time: 1 - P(wait) × e^(-(agents - workload) × target time / handle time).
  4. Agents on duty. The smallest number of agents that meets your service level target.
  5. Agents to schedule. Agents on duty divided by (1 - shrinkage), rounded up.

Reading the table

The table shows the service level, average wait and occupancy for one or two agents fewer and more than the answer. Each added agent improves the service level by less than the one before, which helps when you weigh cost against speed.

What Erlang C assumes

  • Contacts arrive at random, and the hour you enter is representative. Use your busiest hour, not a daily average.
  • Nobody hangs up while waiting. In practice some customers abandon, so real waits are a little shorter than the formula predicts.
  • Every agent handles every type of contact. If you route by skill or language, run the calculator for each group.

Frequently asked questions

What is Erlang C?

Erlang C is a queueing formula, published by the Danish engineer A. K. Erlang in 1917, that gives the chance a new contact has to wait when a set number of agents handles random arrivals. Contact centers use it to find how many agents meet a service level target.

What is a service level of 80/20?

It means 80% of contacts are answered within 20 seconds. Enter 80 as the service level target and 20 in the answered-within field.

What is shrinkage?

The share of paid time agents cannot take contacts: breaks, meetings, training, holidays and sick leave. If 30% of time is lost, you schedule more agents than need to be on duty, which the calculator does for you.

Does Erlang C work for live chat and email?

For live chat, yes, with care: set how many chats an agent handles at once and the calculator treats each agent as that many slots. Email does not queue in real time, so plan it from total workload (volume times handle time) instead.

Why does the calculator say occupancy is high?

Occupancy is the share of on-duty time agents spend handling contacts. Small teams reach a service level only with more slack, and large teams can run hotter. Sustained occupancy above about 85 to 90% tends to burn agents out, so treat high numbers as a warning.

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