Erlang B Calculator (Trunks, Lines & Blocking)

Erlang B answers the classic telephone-engineering question: with this much traffic, how many lines do I need so that only a small share of callers hear a busy signal? It applies to PBX trunks, SIP channels, radio channels, modem pools and any group of servers where a request that finds every line busy is lost rather than queued. This calculator works in all three directions — blocking from lines, lines from a target, and the traffic a group can carry — and shows how blocking changes line by line.

How to use this tool

1. Choose what to find.
2. Enter the busy-hour traffic in Erlangs, or the number of calls in the busiest hour and their average length.
3. Enter the number of lines, the target blocking (grade of service), or both, depending on the mode.
4. Read the answer and compare neighbouring line counts in the table.

Formula

B(E, N) = (E^N ÷ N!) ÷ Σₖ₌₀ᴺ (E^k ÷ k!) computed as B₀ = 1, Bₖ = E·Bₖ₋₁ ÷ (k + E·Bₖ₋₁)

E is the offered traffic in Erlangs (calls per hour × average call length in hours; one Erlang keeps one line busy all the time) and N the number of lines. The recursion gives the same value as the factorial formula without overflowing for large N. Carried traffic = E × (1 − B); occupancy = carried ÷ N. Capacity is found by bisection, since B grows with E.

Example

300 calls in the busy hour lasting 2 minutes each make 300 × 2 ÷ 60 = 10 Erlangs. With 15 lines, B(10, 15) = 0.0365: 3.65% of calls are blocked. To get down to 1%, 17 lines are not quite enough (1.29%), so you need 18 lines, which block 0.71%. Those 18 lines could carry up to 10.44 Erlangs at 1%.