Erlang C Phone Staffing Calculator
Enter the calls in your busiest hour, how long each one takes and how fast you want them answered. See how many people need to be on the phone, how long callers wait, and what one more or one fewer changes.
Last updated November 12, 2026 · Free · Nothing stored
Start from an example peak
Example numbers, not benchmarks. Swap in your own below.
People on the phone at the peak
2people answering
Fewest that answer 80% within 20 seconds. Schedule 3 people once 15% shrinkage is added.
- Traffic
- 0.75 Erlangs
- Calls × handle time ÷ interval
- Answered within 20 s
- 82.7%
- Target 80%
- Callers who wait at all
- 20.5%
- Erlang C probability
- Average speed of answer
- 25 sec
- Across every call
- Occupancy
- 37.5%
- Time on calls
- People to schedule
- 3
- With 15% shrinkage
With 2 people on the phone you answer about 82.7% of calls within 20 seconds; about 3.1 callers an hour wait longer. With 1, that drops to 27.5% and about 13.1 an hour wait longer. What those unanswered calls cost.
One more or one fewer
| People | In 20 s | Avg answer | Busy |
|---|---|---|---|
| 1 | 27.5% | 7:30 min | 75% |
| 2Fewest | 82.7% | 25 sec | 37.5% |
| 3 | 96.7% | 2.9 sec | 25% |
| 4 | 99.5% | 0.4 sec | 18.8% |
| 5 | 99.9% | <0.1 sec | 15% |
Green meets your 80% target. Erlang C assumes nobody hangs up while waiting.
Show the math with your numbers
- Traffic A = 18 calls × 150 s ÷ 3600 s = 0.75 Erlangs
- Erlang C with N = 2: chance a caller waits = 0.2045
- Service level = 1 − 0.2045 × e−(2 − 0.75) × 20 ÷ 150 = 82.7%
- Average answer = 0.2045 × 150 s ÷ (2 − 0.75) = 25 sec
- Occupancy = 0.75 ÷ 2 = 37.5%
- To schedule = 2 ÷ (1 − 15%), rounded up = 3
The link holds only these numbers. Nothing is sent to us. Pricing a person for those hours? Front desk cost calculator.
How many people do you need to answer the phones?
Work out your traffic in Erlangs (calls × average handle time ÷ the interval), then use Erlang C to find the fewest people whose service level meets your target. A salon taking 18 calls in its busiest hour at 2½ minutes each has 0.75 Erlangs. One person answers only 27.5% of calls within 20 seconds; 2 answer 82.7%. Add shrinkage to get the number to schedule.
The math is the Erlang C queueing formula from Agner Krarup Erlang's 1917 work on telephone traffic, computed with the Erlang B recursion so it stays exact at hundreds of Erlangs. It reproduces Call Centre Helper's published Erlang C worked example: 100 calls in 30 minutes at 180 seconds needs 14 agents for 88.8% answered within 20 seconds and a 7.8 sec average speed of answer. The business examples are placeholders, not industry averages.
What is an Erlang?
An Erlang is one hour of phone time per hour: one line or one person kept busy for the whole period. It measures how much talking arrives, not how many calls. Thirty two-minute calls in an hour and ten six-minute calls are both 1 Erlang.
The unit is named after Agner Krarup Erlang, the Danish mathematician and engineer at the Copenhagen Telephone Company whose 1917 paper set out the formulas for lost calls and waiting time that still carry his name.
Traffic is the starting point, but it is not the answer. With exactly as many people as Erlangs, everyone is busy all the time and the queue never clears, so you always need more people than Erlangs. How many more depends on how fast you want to answer.
Traffic intensity
A =calls in the interval × average handle timelength of the interval
Salon Saturday peak, example
18 calls × 2:30 (150 s) ÷ 3,600 s = 0.75 Erlangs. Less than one person’s worth of talking, yet one person answers only 27.5% of calls within 20 seconds, because calls bunch up. It takes 2 to reach 82.7%.
The Erlang C formula
Erlang C gives the probability that a caller has to wait, for N people answering A Erlangs of traffic. It assumes calls arrive at random (a Poisson process), call lengths vary at random around the average, and every caller waits until answered. From that probability come the service level, the average speed of answer and occupancy.
Probability a caller waits
Pwait =ANN!·NN − AN−1Σk=0Akk!+ ANN!·NN − A
- Service level (answered within t seconds)
- 1 − Pwait × e−(N − A) × t ÷ AHT
- Average speed of answer
- Pwait × AHT ÷ (N − A)
- Occupancy
- A ÷ N
A is traffic in Erlangs, N the number of people answering, AHT the average handle time in seconds. The formula only works when N is greater than A. The calculator works it out from the Erlang B recursion instead of raw factorials, so it stays exact at 500 Erlangs and beyond.
Worked example
The inputs from Call Centre Helper’s Erlang C example: 100 calls in 30 minutes, a 180-second handle time, a target of 80% within 20 seconds.
- A = 100 calls × 180 s ÷ 1,800 s = 10 Erlangs
- Start just above traffic, at 11 people, and add one at a time:
| People | Waits | In 20 s | Avg answer |
|---|---|---|---|
| 11 | 0.6821 | 39% | 2:03 min |
| 12 | 0.4494 | 64% | 40 sec |
| 13 | 0.2853 | 79.6% | 17 sec |
| 14 | 0.1741 | 88.8% | 7.8 sec |
14 people is the first to clear 80%. Occupancy is 71.4%, under the 85% cap, and with 30% shrinkage you schedule 20 people. The calculator matches the published figures; load the “Small call center” example to see it.
How many people answer the phone at the peak, by business
Example peaks for each kind of business, run through the same formula. The call counts and handle times are placeholders to show the shape of each peak, not industry averages. Load one, then replace the numbers with a busy slot from your own call log.
| Example | Calls | Handle time | Erlangs | On the phone | Answered in target | Schedule | Load |
|---|---|---|---|---|---|---|---|
| Salon Saturday peak18 calls in the busiest hour | 18 / hr | 2:30 | 0.75 | 2 | 82.7% in 20 s | 3 (15% shrink) | |
| Restaurant dinner rushTakeout and reservations | 35 / hr | 2:00 | 1.17 | 3 | 90.3% in 20 s | 4 (10% shrink) | |
| Dental Monday morningWeekend backlog, 8 to 9 a.m. | 28 / hr | 4:00 | 1.87 | 4 | 89.1% in 30 s | 5 (20% shrink) | |
| Home-services storm dayLeaks, no heat, emergencies | 45 / hr | 5:00 | 3.75 | 6 | 80.4% in 20 s | 8 (15% shrink) | |
| Small call center100 calls per half hour | 100 / 30 min | 3:00 | 10.00 | 14 | 88.8% in 20 s | 20 (30% shrink) |
Erlang C vs Erlang B vs Erlang A
All three start from the same traffic in Erlangs. They differ in what happens to a caller who cannot be answered straight away. Erlang A, the model with impatient callers, was set out for call centers by Garnett, Mandelbaum and Reiman in “Designing a Call Center with Impatient Customers” (2002).
Erlang C
Callers wait in a queue until someone answers.
Staffing a phone line or contact center with hold music or a ring-until-answered line. This calculator.
Erlang B
A caller who finds every line busy is lost and does not wait.
Sizing phone lines or trunks: how many simultaneous calls the system must carry so few callers get a busy signal.
Erlang A
Callers wait, but some hang up if the wait runs long.
Staffing where abandonment matters. It needs an average patience figure, and with no hang-ups it reduces to Erlang C.
Limits of Erlang C
- No hang-ups. Erlang C assumes every caller waits as long as it takes. Real callers abandon, which takes load off the queue, so Erlang C tends to recommend more people than you strictly need, and it cannot tell you how many callers you lose.
- Small volumes come out cautious. At one or two Erlangs the math rounds to whole people, and a single extra person jumps the service level a long way. Read the trade-off table rather than only the headline.
- Random arrivals. It assumes calls arrive independently. A radio ad, a storm or a marketing text sends a burst the formula does not see, so staff for the busiest short interval you actually get.
- One queue, interchangeable people. Everyone answering can take any call. If only one person can book a certain service, model that line separately.
- Shrinkage is your estimate. The people-to-schedule figure is only as good as the share of time you enter for breaks, clients and other work.
Covering the peak without overstaffing the day
01
Staff the peak, not the day
Run the calculator for your busiest hour or half hour, then cover that slot first. A quiet Tuesday afternoon needs far fewer people than Saturday at ten.
Cost a front-desk person →02
Put a price on the calls you still miss
The callers who wait past your target are the ones most likely to hang up and book elsewhere. Count what those calls are worth before deciding how many to cover.
Missed-call revenue calculator →03
Send overflow somewhere instead of voicemail
Busy and no-answer forwarding passes a call to a second phone or service when everyone on site is tied up.
How call forwarding works →04
Let an AI receptionist take the peak
An AI receptionist picks up the calls your team cannot get to, answers questions and books into your calendar, including after close. Your people keep the calls that need a person.
See the AI receptionist →
How to work out phone staffing with Erlang C
01
Count calls in your busiest slot
From your phone or VoIP call log, take the calls that rang in the busiest hour, half hour or 15 minutes of a normal week, and your average handle time including wrap-up.
02
Set the answer target
Choose the share of calls to answer and the time limit, such as 80% within 20 seconds. Add an occupancy cap if you use one, and your shrinkage for breaks and other work.
03
Read people needed and the trade-off
The result shows the fewest people that meet the target, the share answered, the chance a caller waits, the average speed of answer and occupancy, plus a table for a few more or fewer people and how many to schedule.
Common questions
How do you calculate Erlang C?
First find traffic in Erlangs: calls in the interval × average handle time ÷ the interval length. Start with one more person than that, compute the Erlang C probability of waiting, turn it into a service level, and add people until you meet the target. With 100 calls in 30 minutes at 3 minutes each, traffic is 10 Erlangs and it takes 14 people to answer 88.8% within 20 seconds.
How many people do I need to answer the phones at a small business?
Fewer than a call center, but usually more than the average suggests, because calls bunch up. In the salon example, 18 calls an hour at 2½ minutes is under one person's worth of talking, yet one person answers only 27.5% within 20 seconds and about 13 callers an hour wait longer. 2 people answer 82.7%.
What does an 80/20 service level mean?
It means 80% of calls answered within 20 seconds. A service level always has two parts, a share of calls and a time limit. 80/20 is the target in Call Centre Helper's worked example, but it is a choice: a business where a missed caller books elsewhere may want a higher share or a shorter time.
What is the difference between Erlang B and Erlang C?
Erlang B assumes a caller who finds everyone busy is lost, so it is used to size phone lines and trunks. Erlang C assumes the caller waits in a queue until answered, so it is used to staff the people answering. Erlang A adds callers who hang up while waiting.
Does Erlang C account for callers hanging up?
No. Erlang C assumes every caller waits as long as it takes. In reality some hang up, which takes load off the queue, so Erlang C tends to recommend slightly more people than you need and cannot tell you how many callers you lose. Erlang A models abandonment if you know how long callers will wait.
What is shrinkage and how does it change the number of people?
Shrinkage is the share of paid time someone is not free to answer: breaks, clients in the chair, checkout, training. Divide the people needed on the phone by one minus shrinkage and round up. In the call-center example, 14 on the phone with 30% shrinkage means scheduling 20.
Why does one person make such a big difference?
Because waiting rises steeply as people get close to fully busy. In the call-center example, 13 people answer 79.6% within 20 seconds with an average wait of 17 sec; 14 answer 88.8% with 7.8 sec. With no more people than Erlangs, the queue never clears at all.
Is Erlang C accurate for very small call volumes?
It is a sound guide, but read it with care. At one or two Erlangs every answer is a whole person, so the step from one to two people moves the service level a long way, and real callers who hang up make it cautious. In the salon example, 0.75 Erlangs still takes 2 people to reach 82.7%. Use the trade-off table to choose.
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