Call Blocking
Calculate the probability of call blocking for a given number of trunks and traffic load.
About Call Blocking
The Erlang B formula calculates the probability that an incoming call finds all trunks/channels busy and is blocked, given a fixed number of trunks (N) and offered traffic (A) in Erlangs, assuming blocked calls are lost (not queued or retried) — the standard model for circuit-switched trunk groups. It's computed recursively: B(0,A) = 1, and B(n,A) = (A × B(n-1,A)) / (n + A × B(n-1,A)) for each trunk added, which avoids the numerical overflow that computing factorials directly would cause for larger trunk counts.
Formulas
Erlang B formula
B(N,A) = (A^N / N!) / Σ(A^k / k!, k=0..N)
- N
- Number of trunks
- A
- Offered traffic in Erlangs
Recursive form (used for computation)
B(n,A) = (A × B(n-1,A)) / (n + A × B(n-1,A)), with B(0,A) = 1
Worked example
With the default values below, Call Blocking returns Call Blocking Probability of 3.650%. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Offered Trafficminimum 0 Erlangs
- 10 Erlangs
- Number of Trunks / Channelsaccepts 1–10,000
- 15
Results
- Call Blocking Probability
- 3.650%
- Carried Traffic
- 9.64 Erlangs
- Grade of Service
- Acceptable (2-5% blocking)
Step by step
- 1Values used
- 2Erlang B formula
- 3Recursive form (used for computation)
- 4Call Blocking Probability= 3.650
- 5Carried Traffic= 9.64 Erlangs
- 6Grade of Service= Acceptable (2-5% blocking)
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 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's a typical acceptable blocking probability for enterprise trunking?
1-2% (often called P.01 or P.02 grade of service) is a common target for enterprise voice trunks — meaning roughly 1-2 calls per 100 offered during the busy hour would be blocked. Emergency services and critical infrastructure often target well below 1%, while cost-sensitive or non-critical applications may tolerate 5% or higher.
Why use Erlang B instead of Erlang C?
Erlang B assumes blocked calls are simply lost (the caller hears a busy signal or fast busy and must redial) — the standard model for PSTN trunk groups. Erlang C instead assumes blocked calls queue and wait for the next available channel, which better models call center agent staffing where callers are placed on hold rather than disconnected.
How many more trunks do I need to cut blocking in half?
There's no fixed ratio — it depends on where you are on the Erlang B curve. Near saturation (blocking already high), even one additional trunk can meaningfully cut blocking; near very low blocking, the curve flattens and each additional trunk buys progressively smaller improvements. Recompute with N+1, N+2, etc. to find the exact trunk count that hits your target grade of service.