Work out how many agents need to be on the phones at the same time for your hourly call volume and service level target, using the Erlang C model. It runs in your browser: no sign-up, and your values are never sent anywhere.
Agents needed on the phones at the same time
12
Target: 80% of calls answered within 20 seconds
This is an estimate for a single one-hour interval. Erlang C assumes callers never hang up while waiting, so the result usually errs on the cautious side.
Take the number of offered calls hour by hour from your ACD or phone system reports. Because the load changes during the day, calculating each hour separately is more realistic than dividing a daily average. Starting with the busiest hour shows when you need the most agents.
Add hold time and after-call work, such as notes and record updates, to the talk time. If you enter talk time alone, the requirement comes out too low.
The target says what share of calls should be answered within how many seconds. A common example is 80/20: eighty percent of calls answered within twenty seconds. Set it from your customers' expectations and the commitments you have made.
The calculator applies the Erlang C queueing model, long used in contact center planning. It turns the call volume into traffic intensity in Erlangs, then adds agents one at a time until the service level target is met and returns the smallest number that meets it. Each step also shows the same calculation with the example values.
A = calls per hour × average handle time (sec) ÷ 3,600
The total hours of work the calls bring in one hour. One Erlang is one line kept busy for a full hour. You need more agents than this value, otherwise the queue keeps growing.
With the example values100 × 300 ÷ 3,600 = 8.33 Erlangs
N starts at the first whole number above A and goes up by one until the target is met
The values below are calculated for each N. The first N whose service level reaches the target is the result.
With the example valuesN = 12 (11 agents give 74.9%, target 80%)
P = (Aᴺ ÷ N! × N ÷ (N − A)) ÷ (Σ Aᵏ ÷ k! [k = 0 … N − 1] + Aᴺ ÷ N! × N ÷ (N − A))
The chance that a call finds every agent busy and joins the queue. To avoid overflow with large numbers, the formula is not evaluated directly but built step by step from the Erlang B probability; the result is the same.
With the example valuesP = 0.176 (17.6%)
SL = 1 − P × e^(−(N − A) × target time ÷ handle time)
The expected share of calls answered within the target time. Calls that never wait and calls that wait less than the target both count.
With the example values1 − 0.176 × e^(−(12 − 8.33) × 20 ÷ 300) = 86.2%
ASA = P × handle time ÷ (N − A)
The average wait across all calls, including those answered straight away.
With the example values0.176 × 300 ÷ (12 − 8.33) = 14.4 sec
occupancy = A ÷ N
The share of agents' time on the phones spent handling calls. The higher it gets, the less time agents have to recover between calls.
With the example values8.33 ÷ 12 = 69.4%
scheduled = N ÷ (1 − shrinkage), rounded up
Turns the agents needed on the phones into the number of people to put on the schedule, so breaks, training and leave are covered.
With the example values12 ÷ (1 − 0.3) = 17.1 → 18
Erlang C is a model and rests on these assumptions:
The calculator gives the agent requirement for one queue and one hour. The following are not part of the result:
Erlang C is a queueing model based on the work of the Danish engineer Agner Krarup Erlang on telephone traffic. For a given call volume and number of agents it gives the probability that a caller has to wait; the service level and average wait are calculated from that probability. Contact centers have long used it to estimate how many agents they need.
Convert the calls in the interval to an hourly rate: 60 calls in half an hour and 30 calls in fifteen minutes both equal 120 calls per hour. The average handle time and the service level target stay the same. The result is the number of agents needed on the phones during that interval.
Shrinkage is the share of paid time agents cannot take calls: breaks, training, meetings, leave and absence. Erlang C gives the agents needed on the phones; shrinkage turns that into the number of people to schedule. Work out your own figure from your shift and leave records; the starting value in the field is only an example.
Erlang C assumes that callers never hang up while waiting, that calls arrive at random but at a steady rate, and that every agent can take every call. In reality some callers hang up, so the result often errs on the cautious side and may show slightly more agents than you need. If you have sudden call spikes or skills-based routing, treat the result as a starting point and compare it with the service level you actually achieve.
A voice agent can resolve part of your calls, such as appointments, order status or common questions, before they reach an agent. In that case, enter only the calls that are passed to agents. When the voice agent collects the caller's details first, the handle time of transferred calls can change too; you can calculate both scenarios and compare them.
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