Call Capacity (Erlang B) Calculator

Work out call capacity (erlang b) instantly with clear inputs, formula shown and shareable results.

About Call Capacity (Erlang B) Calculator

Erlang B gives the probability that a call is blocked when all channels are busy, assuming blocked calls are cleared rather than queued. It is computed by the recursion B(n) = aB(n-1) / (n + aB(n-1)) starting from B(0) = 1. The relationship is strongly non-linear, so adding a couple of channels near the target can cut blocking by an order of magnitude.

Formula

Erlang B recursion

B(0) = 1; B(n) = a x B(n-1) / (n + a x B(n-1)); carried traffic = offered x (1 - B)

a: Offered traffic in erlangs
n: Number of channels

Worked example

With the default values below, Call Capacity (Erlang B) Calculator returns Blocking probability of 2.654%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Offered trafficminimum 0.001 erlangs: 12 erlangs
Available channelsaccepts 1–500: 18
Target blocking probabilityaccepts 0.001–50 %: 1 %

Results

Blocking probability: 2.654%
Channels needed for the target: 20
Traffic actually carried: 11.682 erlangs
Channel utilisation: 64.90%

Step by step

1Values used
2Erlang B recursion
3Blocking probability= 2.654
4Channels needed for the target= 20
5Traffic actually carried= 11.682 erlangs
6Channel utilisation= 64.90

Assumptions and limits

The result is derived only from the 3 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 3 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

What is an erlang?

One erlang is one circuit continuously occupied. Traffic in erlangs is calls per hour multiplied by average call duration in hours.

When is Erlang C the right model instead?

When blocked calls wait in a queue rather than being rejected — a contact centre with hold music. Erlang B suits trunk groups where a busy signal is returned.