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Amazon Connect · Workforce planning

Erlang C Calculator

Work out how many agents you need for your service level, with ASA, occupancy, shrinkage and chat concurrency — for one interval or a whole day.

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Your contact centre
Examples:
Agents needed
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AgentsService levelASAOccupancyScheduled

Staff a whole day

Paste your forecast, one interval per line: time contacts or time contacts AHT (comma, tab or space separated — copy straight from Excel or an Amazon Connect historical metrics report). Uses the service level, shrinkage and interval length above.

Erlang C assumes callers never hang up while waiting, so it slightly overstates the agents you need when abandonment is high. Treat results as a planning baseline and validate against real queue data. To price the result, use the Amazon Connect pricing calculator.

Frequently asked questions

What is the Erlang C formula?

Erlang C calculates the probability that a contact has to wait, given the traffic intensity in Erlangs (contacts per interval × average handle time ÷ interval length) and the number of agents. From it you get the service level, average speed of answer and occupancy, and you can find the smallest number of agents that meets a target such as 80% answered in 20 seconds.

How many agents do I need for 100 calls in 30 minutes?

With an average handle time of 3 minutes, 100 calls in 30 minutes is 10 Erlangs of traffic. Erlang C gives 13 agents for 79.6% of calls answered in 20 seconds and 14 agents for 88.8%, so 14 agents meets an 80/20 target. Add shrinkage on top to get scheduled headcount.

What is shrinkage in a contact centre?

Shrinkage is the share of paid time agents are not available for contacts: breaks, lunch, training, meetings, coaching, leave and absence. With 30% shrinkage, 14 agents on the phones means scheduling 20. Typical values range from 25% to 35%.

What occupancy should agents run at?

Occupancy is the share of logged-in time agents spend handling contacts. Small teams can hit a service level only with low occupancy, while large teams run more efficiently. Sustained occupancy above about 85–90% leads to burnout, so many centres cap it.

Does Erlang C work for chat?

Erlang C models one contact per agent, so for chat this tool divides the traffic by the number of chats each agent handles at once. That is an approximation: handle time usually rises with concurrency, so measure your real chat AHT at the concurrency you plan to use.

Practical guide

How the Erlang C calculation works

Erlang C turns your forecast into the number of agents needed. It works in four steps:

  1. Traffic. Traffic intensity in Erlangs = contacts in the interval × average handle time ÷ interval length. 100 calls of 3 minutes in 30 minutes = 10 Erlangs: on average, 10 agents are busy all the time.
  2. Chance of waiting. For a given number of agents above the traffic, the Erlang C formula gives the probability a contact waits in queue.
  3. Service level. The share answered within your target time = 1 − P(wait) × e−(agents − traffic) × target ÷ AHT. Average speed of answer = P(wait) × AHT ÷ (agents − traffic).
  4. Agents needed. The calculator adds agents until the service level (and your occupancy and ASA limits) are met, then grosses up for shrinkage to give scheduled headcount.

Using it with Amazon Connect

  • Take contacts per interval and average handle time from Historical metrics (Contacts handled, Average handle time) or from the CTR export, and paste them into "Staff a whole day".
  • Set the same service-level threshold you report on in Connect (for example 20 or 60 seconds).
  • For chat, enter how many chats an agent handles at once; the result is an approximation.
  • To turn the staffing into a bill, use the Amazon Connect pricing calculator.

Limits

Erlang C assumes callers never abandon, calls arrive randomly and agents are interchangeable. With high abandonment it overstates the agents needed; with skills-based routing across several queues, treat each skill group separately. Validate against real interval data before you change a roster.

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