Cloud & Networking

Erlang B Calculator

How many calls will be blocked when traffic meets a fixed number of lines?

By TheCalcTools Updated Formula checked and tested

Your numbers

Your results

Blocking probability
Blocking probability
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Carried traffic (erlangs)
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Channel utilisation
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Erlang B Calculator by TheCalcTools

How the Erlang B Calculator works

Enter the offered traffic in erlangs (call-hours per hour) and the number of channels or trunks.

The Erlang B recurrence gives the probability that a new call finds all channels busy.

Blocked calls are lost, not queued.

The formula

B(E, 0) = 1B(E, m) = E·B(E, m−1) ÷ (m + E·B(E, m−1))

Worked example

Using the default values shown in the calculator:

Offered traffic (erlangs)10
Number of channels (m)15
  1. Offered traffic is 10 E on 15 channels.
  2. Blocking probability = 3.65%.
  3. Carried traffic is 9.6350 E, a utilisation of 64.2% per channel.

Result:

Blocking probability3.65%
Carried traffic (erlangs)9.6350
Channel utilisation64.2%

Frequently asked questions

What is an erlang?

One erlang is one channel occupied continuously for an hour. 30 calls an hour of 2 minutes each is 1 erlang.

What blocking rate do operators aim for?

Targets of 1–2% are common for voice trunks, written as a grade of service of 0.01–0.02.

Sources and further reading

VoIP Bandwidth CalculatorWork out how much bandwidth simultaneous voice calls need Poisson Distribution CalculatorFind the probability of k events in an interval when events happen at an average rate λ

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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.