Erlang B — trunk capacity calculator
How many phone trunks or SIP channels does your contact centre need? Enter your hourly call volume, average call duration, and maximum acceptable blocking probability. Results update as you move the sliders.
Inputs
Offered load
5.000 Erlangs
= 100 calls/hr × 180s ÷ 3 600
Results
Trunks required
11
blocking ≤ 1%
Actual blocking
0.83%
at 11 trunks
Trunks vs blocking probability
| Trunks | Blocking | |
|---|---|---|
| 8 | 7.0% | ✗ |
| 9 | 3.7% | ✗ |
| 10 | 1.8% | ✗ |
| 11minimum | 0.83% | ✓ |
| 12 | 0.34% | ✓ |
| 13 | 0.13% | ✓ |
| 14 | 0.047% | ✓ |
Model: Erlang B models a loss system — callers who find all trunks busy are immediately blocked and do not queue or retry. Assumes Poisson arrivals and exponentially distributed call durations at steady state. If callers do retry after a busy signal the effective offered load rises (use an iterative Erlang B or the Engset formula for small caller populations). Erlang B is the standard for PBX trunk sizing, PSTN circuit engineering, and SIP trunk provisioning.
How this calculator works
What is Erlang B?
Erlang B calculates the blocking probability for a group of N trunks carrying A Erlangs of offered traffic. A caller who finds all N trunks busy is blocked — they receive a busy signal and are lost from the system. This is called a loss system, as opposed to a queue system (Erlang C). The formula is computed using a numerically stable recurrence that avoids factorial overflow.
What is offered load (Erlangs)?
Offered load A = (calls per hour × average call duration in seconds) ÷ 3 600. One Erlang means one circuit occupied continuously. 10 calls per hour each lasting 6 minutes = 1 Erlang. The offered load is the “weight” the trunk group must carry; Erlang B tells you how many circuits are needed to keep the blocking probability below your target.
Erlang B vs Erlang C
Erlang C models an inbound call queue— callers wait if agents are busy. Use it to answer “how many agents?”. Erlang B models a circuit or trunk group — callers are lostif all circuits are occupied. Use it to answer “how many SIP channels or PSTN trunks?”. Applying Erlang C to trunk sizing will underestimate lines needed because it assumes queuing capacity that does not exist.
What blocking target should I use?
The traditional PSTN grade of service is P.01 — 1% blocking. Many contact centres use 0.5% for inbound queues to avoid nuisance busy signals. Outbound trunk groups used for predictive dialling can tolerate 2–5% because the dialler retries automatically. Internal tie lines and voicemail trunks are typically sized at 1–2%.
What Erlang B does not model
Erlang B assumes blocked callers do not retry. In practice many callers redial after a busy signal. If retry rates are high:
- Iterative offered-load method:Start with Erlang B, estimate how many blocked callers retry (add them to next interval’s offered load), and iterate until stable. Typically 2–4 iterations suffice.
- Engset formula: Use when the total caller population is small (fewer than ~50 sources) and the assumption of infinite sources breaks down.
- Agent staffing: Trunk sizing and agent staffing are separate problems. Use the Erlang C calculator to size your agent pool, then size trunks to match.
Need agent staffing, forecasts, and schedules too?
Trunk sizing is one piece. Turnella connects it to an Erlang C staffing model, a shift schedule, and a labour cost tracker that updates as your call volume changes.