Erlang C calculator for call center staffing
Enter your call volume, handle time and service level target. Get the agents an inbound queue needs, the service level and speed of answer they deliver, and how many to schedule after shrinkage.
Work out the agents you need
One interval at a time, usually your busiest half hour. The example is 100 calls in 30 minutes at a three-minute AHT, with an 80/20 target.
One interval of inbound calls
Interval length
Agents on the phones
14
Schedule 20 agents once 30% shrinkage is added.
- Traffic intensity
- 10.00 Erlangs
- Service level achievedAnswered within 20s
- 88.8%
- Average speed of answer
- 7.8s
- Calls that wait at all
- 17.4%
- Occupancy
- 71.4%
Service level at nearby head counts
| Agents | Service level | ASA | Calls that wait | Occupancy |
|---|---|---|---|---|
| 12 | 64.0% | 40s | 44.9% | 83.3% |
| 13 | 79.6% | 17s | 28.5% | 76.9% |
| 14recommended | 88.8% | 7.8s | 17.4% | 71.4% |
| 15 | 94.1% | 3.7s | 10.2% | 66.7% |
| 16 | 97.1% | 1.7s | 5.7% | 62.5% |
| 17 | 98.6% | 0.8s | 3.1% | 58.8% |
How to read this
- Traffic intensity
- The workload in Erlangs: how many agents would be busy every second if calls arrived perfectly evenly. You always need more than this.
- Agents on the phones
- The fewest agents that meet your service level and stay under the occupancy cap. These are people logged in and taking calls.
- Average speed of answer
- The mean wait across every call, including those answered at once. Most calls wait much less than this; a few wait longer.
- Agents to schedule
- Agents on the phones divided by one minus shrinkage, rounded up. This is the head count for the roster.
How the Erlang C formula works
What is Erlang C?
Erlang C is a queueing formula from the early 1900s, named after the Danish engineer A. K. Erlang. It answers a simple planning question: if calls arrive at random and wait in a queue for the next free agent, how many agents do you need so that a set share of callers are answered within a set time? It is still the standard starting point for inbound call center staffing.
How do you calculate the agents needed?
First, turn volume into workload. One Erlang is one agent busy for the whole interval.
Then, for a given number of agents N, Erlang C gives the probability that a call has to wait at all. From that you get service level, the share of calls answered within the target time T:
ASA = Pw x AHT / (N - A)
The calculator starts at the first head count above A and adds one agent at a time until the service level is met and occupancy (A / N) is under your cap. It works out Erlang B with a running ratio and converts it to Erlang C, so it never computes huge factorials and stays accurate for thousands of agents.
A worked example
100 calls arrive in 30 minutes with an AHT of 180 seconds. Traffic is 100 x 180 / 1,800 = 10 Erlangs. With 13 agents, 28.5% of calls wait and the service level is 79.6%, just short of an 80/20 target. With 14 agents, 17.4% wait, 88.8% are answered within 20 seconds, the ASA is 7.8 seconds and occupancy is 71.4%. So 14 agents are needed on the phones. With 30% shrinkage, 14 / 0.7 = 20 agents go on the schedule.
The table under the calculator shows the same queue at nearby head counts. It is the quickest way to see how steep the curve is: one agent fewer can cost nine or ten points of service level, while each agent added past the target buys less and less. Plan each interval of the day this way, because volume and AHT both change from hour to hour.
What targets are normal?
- 80/20 (80% answered within 20 seconds) is the classic inbound target. Sales lines often aim higher; back-office queues lower.
- Occupancy of 75% to 90%. A cap of 85% stops large teams from being run flat out, which shows up as burnout and absence a few weeks later.
- Shrinkage of 25% to 35%. Work out your own figure with the shrinkage calculator, and check your handle time with the AHT calculator.
Where Erlang C does not fit
Erlang C is built for inbound queues, where customers call in and wait. Outbound floors work differently. A predictive dialer places several calls per agent and paces them from answer rates, talk time and abandon limits, so there is no inbound queue for Erlang C to model. Outbound staffing is planned from dial ratios and connect rates instead.
On outbound fronting floors there is another option: AI fronter bots that run on the center's own dialer. They are priced per bot, $40 a month with unlimited calls, so capacity scales one seat at a time from a 15-bot minimum rather than through a queueing model.
Erlang C questions
An Erlang C calculator works out how many agents an inbound queue needs to answer a set share of calls within a target time. It takes call volume, interval length and average handle time, and returns agents needed, the service level achieved, average speed of answer and occupancy.
With a three-minute AHT, 100 calls in 30 minutes is 10 Erlangs of traffic. To answer 80% of calls within 20 seconds you need 14 agents on the phones, which gives about 88.8% service level and a 7.8 second ASA. With 30% shrinkage, schedule 20 agents.
Erlang B assumes a caller who finds every line busy is blocked and goes away, so it is used for sizing trunks and phone lines. Erlang C assumes callers wait in a queue until an agent is free, which is how an inbound call center works. This calculator uses Erlang B as a step to compute Erlang C.
Not really. Erlang C models customers calling in and waiting. On an outbound floor the dialer sets the pace, placing several calls per agent based on answer rates and abandon limits. Outbound staffing is planned from dial ratios, connect rates and talk time, not a queue model.
Erlang C assumes every caller waits forever and nobody hangs up. In real queues some callers abandon, which takes load off the agents, so actual service level comes in slightly higher than predicted. Most planners accept the small cushion, or use Erlang A when abandon rates are high.
How many bots would cover this?
If part of this floor is outbound fronting or verification, AI bots can take those seats on your own dialer. Fronter bots are $40 and verifier bots $50 per bot per month with unlimited calls, from 15 bots.