Erlang B Blocking Calculator
The Erlang B formula is the classic tool for sizing trunk lines, call-centre lines, and any loss system where a blocked request is simply turned away rather than queued. Given the offered traffic in erlangs and the number of available channels, it returns the probability that an arriving call finds every channel busy and is blocked. This calculator uses the numerically stable recursive form so it works for large channel counts, and also reports the carried traffic and the channels actually busy on average. Offered traffic is your measured input; the model assumes Poisson arrivals and cleared blocked calls.
Erlang B formula
A = offered traffic (erlangs), N = channels
B(0) = 1
B(n) = A * B(n-1) / (n + A * B(n-1))
Blocking = B(N)
Carried = A * (1 - B(N))
Utilisation = carried / N
The recursion is iterated from 1 to N. Carried traffic is the offered traffic that is not blocked; utilisation is the average fraction of channels busy.
Traffic engineering context
- One erlang equals one channel occupied for the full observation period.
- Offered traffic equals arrival rate times mean holding time in consistent units.
- Erlang B assumes blocked calls are cleared, not queued; ITU-T E.520 covers this loss model.
- A common public-network grade of service target is 1 percent blocking (B = 0.01).
- For systems with queueing or retries, Erlang C or extended Erlang B models apply instead.
Erlang B: frequently asked questions
What is the Erlang B formula?
Erlang B gives the probability that an arriving call is blocked because all channels are busy, in a loss system with no queueing. It is computed by the stable recursion B(0) = 1 and B(n) = A times B(n-1) divided by (n plus A times B(n-1)), where A is offered traffic in erlangs and n is the channel count.
What is offered traffic in erlangs?
One erlang is one channel continuously occupied for the observation period. Offered traffic equals call arrival rate times average call holding time in the same units. For example, 30 calls per hour each lasting 3 minutes is 30 times 0.05 hours, which is 1.5 erlangs. It is your measured input.
What assumptions does Erlang B make?
It assumes calls arrive at random (a Poisson process), have exponentially distributed holding times, and that blocked calls are cleared rather than queued or retried. ITU-T Recommendation E.520 covers traffic engineering on this basis. Where retries matter, an extended Erlang B or Erlang C model is used instead.
How does grade of service relate to this?
Grade of service is the target blocking probability, often 1 percent (0.01) for public networks. You size channels so the Erlang B blocking at your offered traffic stays at or below that target. This calculator reports the blocking probability for a given channel count so you can check against the target.
Why is the recursive form used?
The direct Erlang B expression involves a sum of factorial terms that overflow for large channel counts. The recursion B(n) = A times B(n-1) over (n plus A times B(n-1)) is numerically stable to thousands of channels and gives identical results, so it is the standard way to compute the formula.
Official sources
- ITU-T: Recommendation E.520, traffic engineering.
- ITU: International Telecommunication Union reference root.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.