Erlang B Calculator

Calculator Inputs

Use offered traffic directly, or derive it from busy-hour attempts and average call duration. The form shifts to three columns on large screens.

Offered traffic (Erlangs)

Optional when attempts and duration are available.

Total channels

Reserve channels

These channels stay unavailable for traffic loading.

Mean call duration (minutes)

Call attempts per hour

Used to derive traffic when Erlangs are not entered.

Target blocking (%)

Forecast traffic growth (%)

Revenue per carried call

Optional financial estimate for carried calls.

Example Data Table

These sample cases help validate blocking behavior as traffic intensity and channel count change.

Scenario	Offered traffic	Channels	Blocking probability	Carried traffic	Utilization
Scenario 1	8.00 Erlangs	12	5.1406%	7.5887 Erlangs	63.24%
Scenario 2	10.00 Erlangs	15	3.6497%	9.6350 Erlangs	64.23%
Scenario 3	12.50 Erlangs	18	3.4079%	12.0740 Erlangs	67.08%
Scenario 4	15.00 Erlangs	20	4.5593%	14.3161 Erlangs	71.58%
Scenario 5	20.00 Erlangs	26	3.7195%	19.2561 Erlangs	74.06%

Formula Used

Erlang B blocking formula:
B(N, A) = (A^N / N!) ÷ Σ_k=0^N(A^k / k!)

Recursive form for stable computation:
B(0, A) = 1, and B(n, A) = [A × B(n−1, A)] ÷ [n + A × B(n−1, A)]

Traffic from attempts and duration:
Offered Traffic A = Call Attempts per Hour × Mean Duration ÷ 60

Derived engineering metrics:
Carried Traffic = A × (1 − B), Lost Traffic = A × B, Utilization = Carried Traffic ÷ Usable Channels

This model assumes blocked calls clear immediately and do not retry within the same busy hour. That makes it ideal for classic trunk sizing studies.

How to Use This Calculator

Enter offered traffic directly in Erlangs, or leave it blank and provide busy-hour call attempts with mean call duration.
Set the total channel count and any reserve channels you want excluded from service calculations.
Choose a target blocking percentage that matches your grade-of-service requirement.
Add optional forecast growth and revenue per carried call for planning analysis.
Press the calculate button to display blocking, carried traffic, headroom, and recommended channels above the form.
Use the CSV and PDF buttons to export the detailed result summary for design records or stakeholder review.

Frequently Asked Questions

1. What does Erlang B measure?

Erlang B estimates the probability that a call is blocked because every channel is already busy. It is widely used for trunk group and circuit capacity studies.

2. When should I use offered traffic directly?

Use direct Erlang input when your traffic model already provides busy-hour intensity. That is common in telecom forecasts, switch reports, and historical capacity studies.

3. Why include reserve channels?

Reserve channels let you keep part of the capacity unavailable for maintenance, resilience, or operational policy. The calculator sizes blocking using only the usable channels.

4. What is grade of service?

Grade of service is the accepted blocking level for a system. For example, one percent blocking means about one blocked attempt out of every hundred offered attempts.

5. Does Erlang B include queued calls?

No. Erlang B assumes blocked calls clear immediately instead of waiting. If callers queue or retry after delay, a different traffic model may fit better.

6. Why do forecast channels increase quickly?

Blocking rises nonlinearly as traffic approaches available capacity. A small demand increase can require several extra channels to maintain the same service target.

7. What does maximum traffic at target block mean?

It shows the highest offered traffic your current usable channels can support while still meeting the chosen blocking objective. It is a practical headroom indicator.

8. Can I use this for call center staffing?

Not directly. Erlang B is for blocked-loss systems without waiting. Queue-based staffing and service-level problems usually require Erlang C or more detailed models.