Erlang C Agents Calculator

Work out erlang c agents instantly with clear inputs, formula shown and shareable results.

About Erlang C Agents Calculator

Erlang C models a queue where callers wait, giving the probability of waiting and from that the service level: the share answered within the target. The classic 80 percent in 20 seconds target follows from these formulas. Note how steeply the answer time falls as agents rise past the offered traffic — the last agent or two buys most of the service level.

Formula

Erlang C

C = B / (1 - (a/N)(1 - B)); service level = 1 - C x exp(-(N - a) x target / AHT); ASA = C x AHT / (N - a)

a: Offered traffic
N: Agents
B: Erlang B blocking

Worked example

With the default values below, Erlang C Agents Calculator returns Calls answered within the target of 78.64%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Calls per hourminimum 0.01: 300
Average handling timeminimum 1 s: 240 s
Agents on dutyaccepts 1–500: 24
Service level targetminimum 0.1 s: 20 s

Results

Calls answered within the target: 78.64%
Probability a caller waits: 29.81%
Average speed of answer: 17.9 s
Offered traffic: 20.00 erlangs

Step by step

1Values used
2Erlang C
3Calls answered within the target= 78.64
4Probability a caller waits= 29.81
5Average speed of answer= 17.9 s
6Offered traffic= 20.00 erlangs

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why must agents exceed offered traffic?

Otherwise the queue is unstable and grows without bound. Agents must be strictly greater than the traffic in erlangs for any finite wait time.

What does Erlang C not model?

Caller abandonment, retries, agent breaks and non-Poisson arrival patterns. It tends to overestimate the agents needed because it assumes nobody hangs up.