Erlang Calculator
Size voice trunks with Erlang B (blocking probability) or call-center agents with Erlang C (service level and waiting), from the traffic in Erlangs or from calls per hour and the average handle time. Everything in your browser.
How it changes with the number of lines
The highlighted row is the minimum that meets the target.
How it is calculated · Erlang B and C
1. Traffic
A (Erlangs) = calls/hour × AHT(s) / 3600.
It is the average number of circuits busy at the same time.
2. Erlang B (no queue):
the blocking probability is obtained iteratively
B = 1; for n=1..N: B = A·B / (n + A·B). We raise
N until B ≤ target.
3. Erlang C (with a queue,
requires N > A): from
EB = ErlangB(N,A),
C = EB / (1 − (A/N)·(1−EB)) is the probability of
waiting.
4. Service level
SL = 1 − C·e^(−(N−A)·t/AHT) and average wait
Wq = C·AHT / (N−A). We raise N until the
goal is met.
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How it works
The calculator sizes voice systems with the two classic teletraffic models. In trunks (Erlang B) mode it finds the minimum number of lines N such that the blocking probability B(N, A) stays under the target (typically 1 %, the P.01 grade of service), using the standard recurrence B = A·B / (n + A·B) for n from 1 to N. In agents (Erlang C) mode it finds the minimum number of agents (with N > A) that meets a call-center service-level goal, for example 80/20: answering 80 % of calls in under 20 seconds.
The offered traffic A is entered directly in Erlangs (1 Erlang = one circuit continuously busy for an hour) or derived from A = calls/hour × AHT(s) / 3600. In Erlang C, from EB = ErlangB(N, A) it computes the probability of waiting C = EB / (1 − (A/N)·(1 − EB)), the service level SL = 1 − C·e^(−(N−A)·t/AHT) and the average wait Wq = C·AHT / (N − A). A sensitivity table shows how blocking or service level changes as you add or remove lines.
Example: 10 Erlangs of voice traffic
- Trunks with a 1 % blocking target: with 17 lines blocking is 1.29 % (fails); with 18 trunks it drops to
0.71 %. Average occupancy sits near 55 % per line. - Agents with an 80/20 goal and 180 s AHT: with 13 agents the service level is 79.6 % (just misses the goal); with 14 agents it rises to
88.8 %with an average wait of 7.8 s. - Same traffic, different answers: Erlang B rejects excess calls (busy signal) while Erlang C queues them, which is why it needs more resources for a comparable goal.