Erlang C formula

How it works

How it works

The formula models a queue as N agents handling a traffic load of A erlangs. One erlang is one hour of continuous work per hour. Traffic equals the number of calls in an interval times the average handle time, divided by the interval length.

The formula assumes calls arrive at random and customers wait in the queue as long as it takes, without hanging up.

• Calls per interval, for example 100 in 30 minutes
• Average handle time, for example 180 seconds
• Target service level – say, 80/20
• Shrinkage – to turn agents on the line into people on the schedule

Example

Sample calculation

100 calls arrive in 30 minutes (1,800 seconds), each lasting 180 seconds on average. Traffic is 100 × 180 ÷ 1,800 = 10 erlangs.

With 13 agents, 28.5% of callers end up waiting and 79.6% are answered within 20 seconds – just short of 80/20. With 14 agents, only 17.4% wait, 88.8% are answered within 20 seconds, and the average speed of answer is about 8 seconds. So you need a 14th agent on the line.

If breaks and absences take up 30% of working time, you staff 14 ÷ (1 − 0.3) = 20 people.

Limits

Limitations

The formula ignores callers who hang up before they're answered. In real life they exist, so Erlang C usually gives slightly more agents than you actually need. If you have a lot of abandoned calls, the Erlang A formula is more accurate – it's the second mode of our calculator. One more assumption: all agents are identical and work a single queue. If your agents have different skills, you need workforce management software.

In CONTACT.WORK

How it works in CONTACT.WORK

Use our free Erlang calculator – it runs both the C and A models. Workforce management uses the same model but on real call volume and handle time data from the platform: you get a forecast for every interval and an auto-generated schedule.