How many people do you need to answer calls?

Take the calls arriving in your busiest half hour, multiply by how long each one takes, and divide by thirty minutes. That number is how many people would be busy every second of it with nothing to spare, and you always need more than that. How many more is the whole question.

A hundred calls of three minutes in half an hour works out at ten. Ten people is the floor. Fourteen is what it actually takes to answer eight callers in ten within twenty seconds, and twenty is what you put on the rota to keep fourteen of them free. This article is where those three numbers come from, because the gap between ten and twenty is the part that surprises people.

Twice the calls does not need twice the people, and this is the thing that makes phone staffing counter-intuitive rather than merely tedious.

Calls do not arrive politely spaced. They arrive at random, which means they clump, and a clump is what makes people wait. If four calls happen to land in the same two minutes and you have three people free, somebody waits regardless of how quiet the rest of the hour was. The bigger your team, the better it absorbs those clumps: ten people cover each other's clumps in a way three people cannot. That is why a larger operation can run closer to the edge, and why a team of four cannot.

The arithmetic that describes this is older than the phone system you are running it on. In 1917 a Danish engineer at the Copenhagen Telephone Company, A. K. Erlang, worked out how many circuits an exchange needed so that callers were rarely blocked. Swap circuits for people and calls for the same calls, and it is exactly the same problem. The version used for a queue where callers wait rather than being turned away is called Erlang C, and Westbay Engineers has published a free calculator for it for years.

Offered load is the calls arriving multiplied by how long each takes, divided by the length of the period. It is measured in erlangs, and one erlang is one conversation's worth of work, continuously.

100 calls x 180 seconds / 1800 seconds = 10 erlangs

The "how long each takes" figure is not just talk time. It is talk plus whatever stops the next call arriving: writing a note, updating a record, finishing a form. That is average handling time, and leaving the after-call work out of it is the most common way to under-staff a phone line, because it is invisible on a phone bill and very visible to whoever is doing it.

Ten erlangs means ten people would be occupied every second. Staff exactly ten and the queue never empties: work arrives precisely as fast as it can be finished, the wait grows without limit, and no amount of patience fixes it. So ten is a floor, not an answer.

Say the promise is that eight callers in ten get answered within twenty seconds. Working up from the floor, and matching the worked example Call Centre Helper publishes for the same numbers:

Thirteen people miss the target by less than half a percentage point and produce a seventeen-second average wait. Fourteen clears it comfortably at 88.8%. There is no thirteen-and-a-half.

Notice how fast the wait collapses across those four rows: 123 seconds, then 40, then 17, then 8. That is the shape of the thing, and it is why the answer to "can we cope with one fewer this week" is so often no in a way that feels disproportionate.

An average wait of 7.8 seconds sounds like nothing. It is also not what most waiting callers experience, because it averages in every caller answered instantly.

At fourteen people, 82.6% of callers never wait at all. The 17.4% who do wait, wait an average of 45 seconds, nearly six times the headline figure. Both numbers are true. Only one of them describes what somebody on hold is living through, and a tool that shows you eight seconds when the people who wait are waiting forty-five has told you something accurate and useless.

Quote the average when you are comparing weeks. Quote the second number when you are deciding whether the wait is acceptable, and see what happens to the calls nobody reaches when it is not.

Nobody is on the phones for every minute they are paid for. Breaks, training, team meetings, holidays, sick days and the rest are real, and the share of paid time they account for is shrinkage. Thirty percent is a common figure for a phone team and it is worth measuring rather than assuming.

14 people free / (1 - 0.30) = 20 people on the rota

Twenty. The gap between fourteen and twenty is not padding, and it is not inefficiency: it is the arithmetic of the fact that a person on their break is not answering a phone.

The important part is the direction. Shrinkage never changes how many people must be free. Fourteen is fourteen whether shrinkage is zero or forty percent. What changes is how many people you employ to keep fourteen of them free at that moment. Mixing this up in either direction is the most common way a staffing figure goes wrong: apply shrinkage first and you size the requirement against a headcount that was never going to be on the phones.

Occupancy is the share of a free person's time actually spent on calls. At fourteen people carrying ten erlangs it is 71.4%.

It reads like a number you would want higher. It is not. Occupancy has to stay below 100% by a real margin for the queue to empty at all, and above roughly 85% a team has no recovery time between calls, because the next one is always already waiting. What happens next is not a queueing problem, it is a turnover problem, and it arrives a few months later.

Occupancy and shrinkage are easy to confuse and do different jobs at different points. Occupancy is a property of the people who are free, and capping it can push the headcount up on its own. Shrinkage is applied at the very end and only converts "must be free" into "on the rota".

Erlang C assumes nobody hangs up. Real callers give up, which shortens the queue for everybody still on it, so a real team usually needs slightly fewer people than the model says. The answer is cautious rather than optimistic, which is the right direction for a first estimate and the wrong thing to forget when the numbers look expensive.

It also assumes a steady average arrival rate across the period, so a five-minute rush inside a half hour is invisible to it, so use a shorter period if your day has spikes. It assumes anybody free can take any call, so it does not describe routing where only some people can take a given call. And it assumes one person handles one call at a time, so it does not describe somebody also working three chats.

Finally, a requirement per interval is not a rota. Feed it a whole day and you get an independent calculation for each half hour, with no shift lengths and no breaks placed anywhere. That is the raw material for building a schedule, not a schedule.

The Erlang C calculator does all of the above in your browser. Put in a busy half hour, choose the promise you actually make, and it returns the people who must be free, the people to put on the rota, the two wait figures, and what one more person would change. It also tells you which constraint set the number, which is the answer to "why did adding shrinkage change nothing".

Nothing you type is sent anywhere, and the published worked examples it is checked against are cited on the page with the dates they were read. If the answer is that you need another person on the phones, what a seat costs is the other half of that decision.

Knowing the number is one half. What happens to the callers who do wait, where the call goes, who is offered it and what they hear meanwhile, is the other, and no amount of software reduces the figure above. That part is how a waiting call reaches somebody.