What is an Erlang calculator?
An Erlang calculator is a call center staffing tool that turns call volume, average handle time and a service level target into the number of agents you need on the phones. It runs the Erlang C formula, which assumes calls arrive at random and wait in a queue while every agent is busy, and returns the smallest agent count whose predicted service level meets your target. The calculator above then divides that count by one minus your shrinkage rate to give the number of people to schedule.
Erlang C is the queueing formula underneath: give it the workload in Erlangs and a number of agents, and it returns the probability that a caller has to wait. A call center staffing calculator is the same tool named for its job. The tool recomputes in your browser as you type, with no email gate, and the whole formula is printed below so you can check the arithmetic yourself.
Worked example: 100 calls in 30 minutes
For 100 calls in 30 minutes with a 180-second average handle time and an 80/20 target, you need 14 agents on the phones and 20 on the schedule at 30 percent shrinkage. The workload is 100 x 180 / 1800 = 10 Erlangs. Thirteen agents reach 79.6 percent, just short of the target, and 14 reach 88.8 percent, with a 17.4 percent chance that a caller waits, a 7.8-second average speed of answer and 71.4 percent occupancy. Shrinkage then turns 14 into 14 / 0.70 = 20 scheduled agents.
| Agents (N) | P(wait) | Service level in 20 s | ASA | Occupancy |
|---|---|---|---|---|
| 11 | 0.6821 | 39.0% | 122.8 s | 90.9% |
| 12 | 0.4494 | 64.0% | 40.4 s | 83.3% |
| 13 | 0.2853 | 79.6% | 17.1 s | 76.9% |
| 14 | 0.1741 | 88.8% | 7.8 s | 71.4% |
A = 10 Erlangs. Figures from this calculator, identical to the hand-worked version by Call Centre Helper, Erlang C formula worked example.
These are the calculator's default inputs, so the page loads on this answer. Call Centre Helper works the same example by hand and publishes the same four wait probabilities (0.6821, 0.4494, 0.2853 and 0.1741), the same 88.8 percent service level, the same 7.8-second ASA and the same 20 agents after 30 percent shrinkage. We also checked the calculator's recurrence against a direct evaluation of the textbook formula on about 32,000 combinations of agents and traffic up to 400 Erlangs. The two never differed by more than 2 in 10 trillion.
The table shows why the stepwise search matters. Going from 13 to 14 agents moves service level by 9 points and cuts ASA from 17.1 to 7.8 seconds. Near the target, a single agent makes a large difference to the queue.
Erlang C formula, explained
Erlang C answers one question: if calls arrive at random and queue when all agents are busy, what share of callers has to wait? Service level, ASA and the staffing answer all come from that probability. Three quantities drive it:
- A, the traffic intensity in Erlangs: calls per interval x average handle time in seconds / interval length in seconds
- N, the number of agents handling calls at the same time
- P(wait), the Erlang C probability that an arriving call queues
Read the block top to bottom. A is the workload the interval carries. Erlang C turns A and N into P(wait), the chance that a new call finds every agent busy. Calls that do queue wait AHT / (N - A) seconds on average, so ASA across all callers is P(wait) x AHT / (N - A). Service level is one minus the share of callers still holding at your target time T. The calculator starts at the first whole number above A and adds agents until service level clears your target and, if you set a cap, occupancy falls under it.
The formula needs N to be greater than A. With fewer agents than Erlangs of work, the queue grows without limit and no service level is reachable. To avoid the factorial overflow you would hit computing A^N / N! directly, the tool uses the Erlang B recurrence (B(0) = 1, then B(k) = A x B(k-1) / (k + A x B(k-1)) up to k = N) and converts the result to Erlang C at the end. That stays exact for floors of thousands of agents.
Adding shrinkage to an Erlang result
Erlang C returns agents who must be logged in and available. People on a roster also take breaks, sit in training and coaching, attend meetings, go on holiday and call in sick, and that lost share of paid time is shrinkage. To turn the Erlang answer into a schedule, divide by one minus shrinkage and round up:
Five points of shrinkage cost two seats in that example. Planners who add shrinkage as a markup (14 x 1.30 = 18.2, so 19 seats) end up one agent short in every interval, because dividing by 0.70 multiplies by 1.43, not 1.30. Call Centre Helper puts the industry standard for shrinkage at 30 percent and says most centres its team visits calculate 30 to 35 percent, while the average figure entered into its own Erlang calculator is 26.6 percent (Call Centre Helper, call centre industry standards). If you have not measured yours, the shrinkage calculator adds it up from breaks, training, meetings, holiday, absence and downtime, then hands the result back here.
How to set each input
Calls per interval and interval length
Use your busiest realistic interval, not a daily average. A day with 1,000 calls might peak at 120 in one half hour, and staffing to the average interval misses service level at the peak. Fifteen-minute intervals capture sharper peaks and 60-minute intervals smooth them. Count the calls over the same window you select, or you double or halve the workload by accident.
Average handle time
AHT is talk plus hold plus after-call work, divided by calls handled. Leaving wrap time out is a common reason a staffing model comes out optimistic. If your phone system gives you totals, the AHT calculator does the division and sends the answer straight into this tool. For context, Call Centre Helper reports an average AHT of 6 minutes 3 seconds across 190,702 entries into its Erlang calculator (Call Centre Helper, call centre industry standards). That figure describes what planners type in, so treat it as a rough reference and use your own data.
Service level target
The classic inbound target is 80/20: 80 percent of calls answered within 20 seconds. Call Centre Helper calls it the traditional contact centre standard and reports, from its 2019 survey, that many centres have moved toward answering 90 percent of calls in 15 seconds. Regulated and healthcare lines often run tighter targets, and low-urgency support lines run looser ones. See how service level sits next to the other core metrics in the call center KPI benchmarks.
Maximum occupancy
Occupancy is the share of logged-in time an agent spends handling contacts. On large floors Erlang C can return a headcount that runs agents at 90 percent or more. Call Centre Helper's worked example caps occupancy at 85 percent and warns that agents above that level are likely to burn out, which is why this tool lets you set a ceiling and adds agents beyond the pure Erlang C answer when the cap binds. The occupancy and shrinkage guide covers the trade-off in more detail.
Erlang C vs Erlang B vs Erlang A
Erlang C staffs a queue where callers hold until an agent frees up, which is the inbound call center case and the model the tool above runs. Erlang B sizes lines and trunks for a system with no queue: a call that arrives when everything is busy is blocked and lost. For the same traffic, Erlang C always needs at least as much capacity as Erlang B, because queued callers eventually use agent time instead of vanishing. Erlang A extends Erlang C with caller patience, so some queued callers abandon before an agent reaches them (Call Centre Helper, a beginner's guide to the Erlang A formula).
What Erlang C assumes, and where it bends
- Callers never abandon. Real callers hang up, which drains the queue, so Erlang C somewhat overstates staff when queues get long. Most planners accept that as a safety margin.
- Calls arrive independently at a steady average rate within the interval. Marketing spikes, outages and redial storms break this, so model those intervals separately with their own volumes.
- Every agent can take every call. Skills-based routing splits the pool and usually needs more agents than one big Erlang C group predicts. Running the calculator once per queue is the practical approximation.
- The interval is in a steady state, which is why you feed it interval peaks rather than daily averages.
None of this makes the model wrong as a baseline. It makes it a starting number with a known bias, transparent and reproducible, that you then adjust with observed abandonment and occupancy.
Common Erlang calculator mistakes
- Forgetting shrinkage. Erlang C returns agents who must be on the phones, not names on a roster. Staff the 14-agent answer above with 14 people at 30 percent shrinkage and about 10 of them are available in a given interval.
- Mixing interval lengths. Counting an hour of calls with the interval set to 30 minutes doubles the workload.
- Ignoring the occupancy ceiling. A plan that runs agents at 90 percent reads fine on paper and shows up later as sick days and resignations. Track that side with the attrition rate calculator.
- Using monthly averages. A month of volume divided by opening hours flattens every peak. Run the busiest interval you actually have to answer, then plan quieter intervals on their own.
From agents to budget
An Erlang answer is a headcount, and the business question is what that headcount costs. At US onshore loaded costs the gap between 14 agents on the phones and 20 on the schedule is a large budget line. A Call Force Global seat runs $12 an hour on the Staffed Desk, $13 on the Scored Desk (our dialer, call recording and 100% AI QA on calls), $14 on the Open Desk and up to $18 for regulated work. The wage inputs behind that range are in the Caribbean wage index. To turn your headcount into a monthly cost, run the nearshore cost calculator, or see how staffed teams run as an outsourced call center or an inbound call center program. For seasonal Medicare volume, the Medicare AEP staffing calculator layers enrollment assumptions on the same queueing base.
FAQ
What is an Erlang calculator?
An Erlang calculator is a call center staffing tool that tells you how many agents you need to answer a given call volume within a service level target. It applies the Erlang C formula, which treats calls as arriving at random and queueing when every agent is busy, to four inputs: calls per interval, average handle time, target service level and target answer time. The output is the smallest agent count whose predicted service level clears the target. You then divide that count by one minus your shrinkage rate to get the number of people to put on the schedule.
What is an Erlang?
An Erlang is the unit of telecommunications traffic intensity, named after the Danish mathematician A. K. Erlang. One Erlang equals one hour of continuous call workload inside a one-hour window. In staffing terms, traffic intensity in Erlangs equals calls per interval multiplied by average handle time, divided by the interval length. At 100 calls in 30 minutes and 180 seconds each, you carry 100 x 180 / 1800 = 10 Erlangs of workload, so you need at least 11 agents before any queueing math is applied.
What is the Erlang C formula?
The Erlang C formula computes the probability that an arriving call has to wait in queue, given N agents and a traffic intensity of A Erlangs. It assumes calls arrive randomly, queue if all agents are busy, and never abandon. From the wait probability you derive the two planning outputs: service level, the share of calls answered within a target time, and average speed of answer. A staffing calculator inverts the formula by searching for the smallest N whose predicted service level meets your target, for example 80 percent of calls answered in 20 seconds.
What is the difference between Erlang B and Erlang C?
Erlang B models systems with no queue: if every line or agent is busy, the new call is blocked and lost. It is used for sizing trunks and phone lines. Erlang C models systems with a queue: if every agent is busy, the call waits. It is used for staffing call centers, where callers hold rather than being dropped. Erlang C always requires at least as many servers as Erlang B for the same traffic, because queued callers keep occupying capacity until they are served.
How many agents do I need for 100 calls an hour?
Twelve agents on the phones and 18 on the schedule, under these assumptions: 100 calls arriving in a 60-minute interval, a 300-second average handle time, a target of 80 percent of calls answered in 20 seconds, 30 percent shrinkage and an 85 percent occupancy cap. Traffic intensity is 100 x 300 / 3600 = 8.3 Erlangs. Eleven agents deliver only a 74.9 percent service level, while 12 deliver 86.2 percent, with a 14.4-second average speed of answer and 69.4 percent occupancy. Change any assumption, handle time most of all, and the answer moves, so run your own numbers in the calculator.
How do I add shrinkage to an Erlang C result?
Divide the Erlang C agent count by one minus your shrinkage rate and round up. Fourteen agents at 30 percent shrinkage becomes 14 / 0.70 = 20 people on the schedule. Multiplying by 1.30 instead gives 18.2, which rounds to 19 and leaves you one agent short in every interval.
What shrinkage percentage should I use?
Measure your own: divide the paid hours agents spend unavailable for calls by total paid hours over a few representative weeks. As a sense check, Call Centre Helper puts the industry standard at 30 percent and says most centres its team visits calculate 30 to 35 percent, while the average entered into its Erlang calculator is 26.6 percent. Using a figure 10 points below your real shrinkage understaffs every interval, which shows up as missed service level and rising occupancy.
What is a call center staffing calculator?
A call center staffing calculator is a tool that converts forecast contact volume into the number of agents to put on the schedule. Most, including this one, use Erlang C for the queueing step, then apply an occupancy cap and divide by one minus shrinkage. The inputs are calls per interval, average handle time, the service level target, shrinkage and maximum occupancy.
What are the limitations of the Erlang C model?
Erlang C assumes callers never abandon, arrivals are random and independent, every agent handles every call type, and handle times follow one distribution. Real floors break all four assumptions to some degree. Because abandonment is ignored, Erlang C overstates required staff when queues are long and callers hang up. Because it is a single-skill model, it cannot represent skills-based routing directly. It remains the standard planning baseline because it is transparent and errs on the safe side, so treat its output as the starting headcount and adjust with observed abandonment and occupancy data.
Keep going
Work out the inputs first with the AHT calculator and the shrinkage calculator, then score the KPIs this plan will produce in the KPI benchmark tool. Track churn with the attrition rate calculator and price it with the turnover cost calculator. Every free tool is on the tools hub.