Erlang C calculator
Work out how many agents you need on the phones to hit a service level target in a single interval. Enter the contacts you expect, their average handle time and the target, and the calculator applies the Erlang C formula to find the smallest number of agents that meets it.
On the phones for the whole interval, before shrinkage.
- Service level achieved
- 82.6%
- Occupancy
- 85.5%
- Average speed of answer
- 13.4 s
- Contacts that will wait
- 25.4%
- Workload
- 33.3 erlangs
Show the working
- Workload = 200 contacts ÷ 30 min × 300 s ÷ 60 = 33.3 erlangs.
- The queue is only stable with more agents than erlangs, so the search starts at 34.
- With 39 agents, Erlang C gives a 25.4% chance that a new contact finds every agent busy.
- Service level = 1 − 0.254 × e^(−(39 − 33.3) × 20 ÷ 300) = 82.6%, which clears the 80% target.
- With 38 agents it would be 75.6%, which does not.
- Occupancy = 33.3 ÷ 39 = 85.5%.
Doing this for every interval of the week? Pebble WFM computes the requirement from your forecast and builds the roster. Free month, no card needed.
How the Erlang C calculation works
Erlang C models a queue where every contact waits for the next free agent rather than being turned away. It starts from the workload in erlangs: contacts per minute multiplied by average handle time in minutes. 200 contacts in 30 minutes at a five-minute handle time is 33.3 erlangs, meaning on average 33.3 conversations are in progress at once.
For a given number of agents, the formula gives the probability that a new contact finds every agent busy and has to wait. Combined with how quickly the queue drains, that yields the share answered within your target time, which is your service level.
The calculator increases the agent count one at a time until the predicted service level reaches your target. That is the figure it reports. It is the number of agents who must be logged in and available for the whole interval, so it is a productive requirement: add shrinkage before you put it on a roster, and check that the occupancy it implies is sustainable.
Read the full guide: How to calculate Erlang C staffing for a contact centre
Frequently asked questions
- What is the difference between Erlang C and Erlang B?
- Erlang B assumes a contact that finds every agent busy is lost, which suits trunk or line sizing. Erlang C assumes it queues, which is how a contact centre queue behaves, so it is the right model for staffing.
- Why does the calculator need more agents than the workload in erlangs?
- Erlangs measure average work in progress, but arrivals are random and bunch up. With exactly as many agents as erlangs the queue grows without limit. The extra agents absorb the peaks, and the gap between agents and erlangs is what decides how long people wait.
- Does Erlang C work for email and chat?
- It assumes one contact per agent at a time and immediate handling, which fits voice. Chat needs the concurrency treated properly, which the live chat calculator does. Email and back-office work with a deadline of hours is a workload problem, which the email calculator handles.
- What should I do with the result?
- Treat it as the agents needed on the phones for that interval. Gross it up for shrinkage to get the number to schedule, and if the occupancy shown is above about 85 to 90 per cent, consider adding agents to keep the pace sustainable. The staffing requirement calculator does both steps.
- Why does the answer change when I change the interval length?
- The contacts you enter are per interval, so 100 contacts per 15 minutes is four times the arrival rate of 100 per hour. Keep the volume and interval consistent with how your forecast is reported.
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