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Glossary · Call centre operations

What is Erlang C?

  • Also called: erlang formula, erlang c calculator

Reviewed by Sujan ThapaliyaLast updated

Definition

Erlang C is the queueing formula used to work out how many agents an inbound queue needs to hit a service level, given call volume, average handle time and the target answer time. It is the arithmetic behind almost every contact-centre staffing model.
The three STIR/SHAKEN attestation levels, which underpin how erlang c behaves in practice: A asserts both that the carrier knows the customer and that the customer may use the calling number, B asserts the customer only, and C asserts neither. A shared number pool can reach B at best, which is why number ownership keeps recurring in these definitions.
Attestation is the backdrop to most caller-ID and deliverability terms, erlang c included.

In practice

How erlang c actually works

Its central and counter-intuitive result is that staffing does not scale linearly. Adding one agent to a small team improves service level dramatically; adding one to a large team barely moves it, which is why small queues are so volatile.

The formula assumes calls arrive randomly, agents are interchangeable and nobody abandons. All three assumptions are wrong in detail, which is why the output is a starting point to be adjusted for shrinkage and abandonment rather than a rota.

Shrinkage is applied after the calculation, not inside it: needing ten agents on the phone with 30% shrinkage means scheduling roughly fourteen.

Small queues are volatile: one agent changes service level far more than in a large one.
InputExampleEffect on headcount
Calls per interval100 in a half hourLinear
Average handle time4 minutesLinear
Service level target80% in 20sSteep near the top of the range
Agents required on the phone≈17Before shrinkage
Agents to schedule≈24After 30% shrinkage

Worked example

100 calls in a half hour at 4 minutes handle time, targeting 80% answered in 20 seconds, needs about 17 agents on the phone — and around 24 scheduled once 30% shrinkage is applied.

Erlang C: common questions

What does Erlang C calculate?
The number of agents required to answer a given call volume within a target time. It converts volume, handle time and a service-level target into a headcount for that interval.
Why does Erlang C ignore abandonment?
Because it models an infinitely patient queue. Real callers hang up, which means the formula slightly overstates the staffing needed — one of several reasons its output is adjusted rather than used directly.
Do I apply shrinkage inside the formula?
No, afterwards. Erlang C gives agents needed on the phone; shrinkage converts that into people to schedule.

Sources

  1. Combating Spoofed Robocalls with Caller ID Authentication — Federal Communications CommissionThe STIR/SHAKEN framework, the attestation levels carriers sign calls with, and the mandate requiring providers to authenticate caller ID.
  2. 47 U.S.C. § 227 — Restrictions on the use of telephone equipment — Cornell Legal Information InstituteThe Telephone Consumer Protection Act itself — the consent requirements, calling-hours limits, and private right of action.
  3. ITU-T Recommendation E.164 — The international public telecommunication numbering plan — International Telecommunication UnionThe international number format, the 15-digit maximum, and how country codes and national numbers compose.

See erlang c in the product

A call queue holds inbound callers in order and distributes them to whichever agent frees up next, instead of ringing one phone and failing. A callback option lets the caller keep their place and hang up, which is what actually reduces abandoned calls.

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