erlang b calculator

Erlang B Blocking Calculator

Use this free calculator to estimate call blocking probability (Grade of Service) and trunk/channel requirements for telecom and call center capacity planning.

1) Blocking Probability from Offered Traffic and Channels


2) Required Channels for a Target Blocking Rate

What is Erlang B?

Erlang B is a classic teletraffic engineering model used to estimate the probability that an incoming call is blocked when all channels are busy. It is widely used for trunk sizing, PBX design, SIP capacity planning, and other systems where there is no queue. If a caller cannot get service immediately, that call is lost (or retries later).

In practical terms, this helps answer questions like: “How many phone lines do I need if I expect 18 Erlangs of busy-hour traffic and I only want 1% of calls blocked?”

How to Use This Erlang B Calculator

Option A: Find Blocking Probability

  • Enter offered traffic in Erlangs.
  • Enter total channels (or trunks).
  • Click Calculate Blocking to get:
    • Blocking probability
    • Carried traffic
    • Blocked traffic
    • Average channel occupancy

Option B: Find Required Channels

  • Enter offered traffic in Erlangs.
  • Enter your target blocking percentage (such as 0.5%, 1%, or 2%).
  • Click Calculate Required Channels to estimate the minimum channels needed.

The Erlang B Formula

The direct form is:

B(A, N) = (AN / N!) / ∑k=0..N (Ak / k!)

Where:

  • A = offered traffic in Erlangs
  • N = number of channels
  • B(A, N) = blocking probability

For numerical stability and speed, this calculator uses the recursive form:

B(0, A) = 1
B(n, A) = (A * B(n - 1, A)) / (n + A * B(n - 1, A))

How to Estimate Offered Traffic (Erlangs)

If you only have calls-per-hour and average call duration:

Traffic (Erlangs) = (Calls per hour * Average call duration in seconds) / 3600

Example: 900 calls/hour, average call length 120 seconds:

A = (900 * 120) / 3600 = 30 Erlangs

When to Use Erlang B vs Erlang C

Use Erlang B when:

  • There is no waiting queue.
  • Blocked calls are cleared immediately.
  • You are sizing trunks, lines, or channels.

Use Erlang C when:

  • Customers can wait in queue.
  • You need agent staffing/service level metrics.
  • You care about average speed of answer and delay probability.

Interpreting Results Correctly

A blocking rate of 1% does not mean every customer experiences poor service. It means that, statistically, around 1 out of 100 call attempts arrives when all channels are occupied. Actual user experience also depends on retry behavior, redial logic, and traffic burstiness.

Common target Grade of Service values:

  • 0.5% for premium/high-availability voice networks
  • 1% for many enterprise voice systems
  • 2% for less critical applications

Planning Tips for Real Networks

  • Size for busy hour, not daily average load.
  • Add headroom for seasonal and campaign spikes.
  • Validate assumptions against real CDR/SIP data.
  • Recalculate after major routing or policy changes.
  • Account for outages and failover scenarios (N+1 planning).

Frequently Asked Questions

Can I use decimals for traffic?

Yes. Offered traffic can be fractional (e.g., 7.35 Erlangs).

Do channels have to be integers?

Yes. Channel count is a whole number, so this tool rounds to integer requirements where needed.

What if offered traffic is zero?

If traffic is zero, no channels are required to meet a blocking target because there are no incoming calls to block.

Bottom Line

An Erlang B calculator is one of the fastest ways to make capacity decisions for voice trunks and circuit resources. With the tool above, you can quickly move from traffic estimates to concrete channel requirements and better reliability outcomes.

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