Erlang B
Calculate call blocking probability and required trunk lines using the Erlang B formula.
About Erlang B
The Erlang B formula calculates the probability that an incoming call finds all circuits busy and is blocked, given a fixed number of circuits and offered traffic load with no queuing or retries (lost calls cleared). It's the classic model used since the early 20th century for sizing telephone trunk groups: B(N,A) = (A^N/N!) / Σ(A^k/k!, k=0 to N). This calculator uses the numerically stable recursive form B(0,A)=1, B(n,A) = A·B(n-1,A) / (n + A·B(n-1,A)) to avoid overflow from large factorials.
Formulas
Erlang B blocking probability
B(N,A) = (A^N / N!) / Σ(A^k / k!, for k = 0 to N)
- A
- Offered traffic in Erlangs
- N
- Number of circuits/trunks
Recursive form (numerically stable)
B(0,A) = 1; B(n,A) = A·B(n-1,A) / (n + A·B(n-1,A))
Worked example
With the default values below, Erlang B returns Call Blocking Probability of 3.6497%. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Offered Traffic (A)accepts 0.01–10,000 Erlangs
- 10 Erlangs
- Number of Circuits (N)accepts 1–2,000
- 15
Results
- Call Blocking Probability
- 3.6497%
- Carried Traffic
- 9.635 Erlangs
- Lost (Blocked) Traffic
- 0.365 Erlangs
- Circuits Needed for ≤1% Blocking
- 18
Step by step
- 1Values used
- 2Erlang B blocking probability
- 3Recursive form (numerically stable)
- 4Call Blocking Probability= 3.6497
- 5Carried Traffic= 9.635 Erlangs
- 6Lost (Blocked) Traffic= 0.365 Erlangs
- 7Circuits Needed for ≤1% Blocking= 18
Assumptions and limits
- The result is derived only from the 2 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 4 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 does 'Erlang' mean as a traffic unit?
One Erlang represents one circuit being continuously occupied for the full measurement period. Traffic of 10 Erlangs could mean, for example, 10 circuits each busy 100% of the time, or 20 circuits each busy 50% of the time — it's a measure of intensity, not a count of calls.
What does 'lost calls cleared' mean in the Erlang B model?
It's the core assumption behind Erlang B: a blocked caller simply hangs up and does not retry or wait in a queue. This makes Erlang B appropriate for trunk sizing where blocked calls truly disappear, as opposed to Erlang C, which models callers waiting in a queue.
What blocking probability is typically acceptable?
1% (0.01) is a common target grade-of-service for many carrier-grade trunk groups, meaning no more than 1 in 100 calls is blocked during the busy hour. Critical applications might target 0.1% or lower; less critical internal trunks sometimes tolerate 2-5%.
How is this different from Erlang C?
Erlang B assumes blocked calls are lost entirely (no queuing) — appropriate for circuit-switched trunk sizing. Erlang C instead assumes blocked callers wait in a queue until an agent/circuit frees up, which is the standard model for call center staffing. See the Erlang C calculator for that case.