Erlang B
Calculate call blocking probability and required trunk lines using the Erlang B formula.
Inputs
Traffic intensity = (calls per hour × avg. call duration in hours)
Call Blocking Probability
3.6497%
Carried Traffic
9.635Erlangs
Lost (Blocked) Traffic
0.365Erlangs
Circuits Needed for ≤1% Blocking
18
Step by step
Values used
Offered Traffic (A) = 10 Erlangs; Number of Circuits (N) = 15
Erlang B blocking probability
B(N,A) = (A^N / N!) / Σ(A^k / k!, for k = 0 to N)
Recursive form (numerically stable)
B(0,A) = 1; B(n,A) = A·B(n-1,A) / (n + A·B(n-1,A))
Call Blocking Probability
= 3.6497
Carried Traffic
= 9.635 Erlangs
Lost (Blocked) Traffic
= 0.365 Erlangs
Circuits Needed for ≤1% Blocking
= 18
How it works
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))
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.