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Staffing calculator

Erlang C calculator for call center staffing

Enter your busiest hour's call volume, your average handle time and the service level you aim for. You'll see how many agents you need on the phones and on the schedule, then how that changes when AI agents take part of the calls.

calls

Every call offered, including callers who hung up before an answer.

seconds

Talk, hold and after-call work, averaged per call.

%

The share of calls you aim to answer within the time below.

seconds

The answer time your service level is measured against.

%

Paid time agents can't take calls: breaks, training, meetings, absence.

%

The most of their time you want agents spending on calls.

Staffing you need

Agents on the phones
17
Agents to schedule
25
Calls answered within 20 seconds
81.0%
Average speed of answer
16.8 seconds
Occupancy
78.4%
Traffic
13.3 erlangs

With AI agents

How many agents AI frees up

%

Your estimate for the call types you'd hand to AI, not a Telvana figure.

$

Fully loaded: wages, benefits and overhead.

hours

How many hours a month your lines run at about this call volume.

Agents to schedule with AI taking 20% of calls
25 to 20
Fewer agents in the busy hour
5
Agent cost saved a month
$22,000

Agent cost only. It does not subtract what the AI agents cost. See pricing.

What the Erlang C formula calculates

Erlang C takes the calls you expect in an interval and how long each one takes, and gives the probability that a caller has to wait when a given number of agents is on the phones. From that come the share of calls answered within your target time and the average wait. The calculator adds one agent at a time until the result meets your target and stays under your occupancy ceiling.

Traffic (A)
Calls per hour x average handle time in seconds / 3,600. The unit is the erlang: one erlang is one agent kept busy for the whole hour.
Probability of waiting, C(A, N)
With N agents, (A^N / N!) x N / (N - A), divided by the sum of A^k / k! for k from 0 to N - 1 plus that same first term.
Service level
1 - C(A, N) x e^(-(N - A) x T / AHT), where T is the answer-time target in seconds.
Average speed of answer
C(A, N) x AHT / (N - A), averaged over every call.
Occupancy
A / N: the share of time each agent spends on calls.
Agents to schedule
N / (1 - shrinkage), rounded up.

A worked example

Take 200 calls in the busiest hour at a 4-minute average handle time. That is 13.3 erlangs: on average, 13.3 calls are in progress at any moment.

To answer 80% of calls within 20 seconds, you need 17 agents on the phones. They answer 81.0% within 20 seconds, with an average speed of answer of 16.8 seconds and occupancy of 78.4%. With 16 agents, only 69.0% would be answered in time.

With 30% shrinkage, keeping 17 people on the phones takes 25 on the schedule.

Where Erlang C falls short

  • Callers who hang up

    Erlang C assumes every caller waits until answered. Real callers abandon, which shortens the queue, so the formula can show more agents than you need when waits run long. Call center research, such as the review by Gans, Koole and Mandelbaum, points to models that include abandonment, such as Erlang A, for that reason.

  • One interval at a time

    The formula assumes a steady rate of calls. Run it for your busiest half hour or hour, not for a daily average, which hides the peaks.

  • Identical agents

    It treats every agent as able to take every call. If calls route to skill groups, run each group on its own.

  • Random arrivals

    Calls are assumed to arrive at random. A surge after an outage or a mailing arrives faster than the formula expects.

How AI agents change the staffing math

When AI agents answer part of the calls from start to finish, your team only has to staff for the rest. The calls they still take keep the same handle time and the same service level target.

Staffing does not fall in step with volume. In the example above, AI agents taking 20% of the calls leaves 160 an hour for people, and the agents needed on the phones go from 17 to 14. The smaller the team, the larger the share of it that is buffer for random bursts of calls, so the drop is a little less than proportional.

The calculator counts agent cost only. It does not subtract what the AI agents cost, so set that against the saving before you decide.

See the calls Telvana's AI agents take

FAQ

Staffing questions.

What is an erlang?

An erlang is a unit of telephone traffic: one erlang is one line or agent kept busy for a full hour. In a call center, traffic in erlangs is calls per hour times average handle time in hours, which is the average number of calls in progress at once.

What is the difference between Erlang B and Erlang C?

Erlang B assumes there is no queue: a call that finds every line busy is lost, so it is used to size phone lines and trunks. Erlang C assumes callers wait in a queue until an agent is free, which is why it is the one used for agent staffing.

How do I choose a service level target?

Service level is written as a pair, such as 80/20: 80% of calls answered within 20 seconds. Use the target you already report on. Then look at the average speed of answer the calculator shows, because two targets with the same percentage can feel very different to callers.

What is shrinkage?

Shrinkage is the share of paid agent time that is not available for calls: breaks, training, coaching, meetings, sick days and vacation. Erlang C gives the agents who must be on the phones; dividing by one minus shrinkage gives the number to schedule. Measure yours from your own workforce data.

Does the calculator account for callers who hang up?

No. Like any Erlang C calculator, it assumes callers wait until they are answered, so with long queues it can show more agents than you need. Treat it as a planning starting point and check it against your real abandonment and answer-time data.

Sources

Put AI agents to work in your contact center.

Book a demo. We'll walk through your call types, show you which ones Telvana can take, and let you hear it handle one.

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