Erlang C Calculator (Call Centre Staffing and Service Level)
How well a given number of agents will answer incoming calls: the service level, the chance a caller waits, the average wait and the occupancy, from call volume and handling time.
Results
The dashed line marks the value you entered.
What this tool does
Erlang C is the classic formula for staffing queues with random arrivals, such as a call centre. Its main lesson is that workload in Erlangs (calls × handling time ÷ interval) is the minimum number of agents you need, but you must staff above it, and the chart shows how steeply the service level climbs for the first few agents added and how slowly after that. It assumes callers wait as long as it takes; in practice some hang up, which makes the model a little pessimistic, and breaks, shrinkage and calls that vary through the day are not included.
Formula
A = calls × handling time ÷ interval · C = P(wait) = [Aᴺ/N! · N/(N−A)] ÷ [Σₖ₍₀…N−1₎ Aᵏ/k! + Aᴺ/N! · N/(N−A)] · service level = 1 − C·e^(−(N−A)·T/AHT)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
ca | Calls arriving in the interval | — |
iv | Length of the interval in minutes | min |
ah | Average handling time per call (seconds) | s |
ag | Agents on duty | — |
sl | Target service level (% answered in time) | % |
tw | Answer-within threshold (seconds) | s |
SV | Service level reached | % |
TR | Workload (Erlangs) | — |
OC | Agent occupancy | % |
PW | Chance a caller has to wait | % |
AS | Average speed of answer (seconds) | s |
ST | Against your target | — |
Worked example
- Calls arriving in the interval120
- Length of the interval in minutes30 min
- Average handling time per call (seconds)240 s
- Agents on duty20
- Target service level (% answered in time)80 %
- Answer-within threshold (seconds)20 s
- Service level reached81.7 %
- Workload (Erlangs)16.00
- Agent occupancy80.0 %
- Chance a caller has to wait25.6 %
- Average speed of answer (seconds)15.4 s
- Against your targetTarget met
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.