If you search for "Erlang C calculator", you will find dozens of free tools. If you search for "Erlang A", you will find far fewer, even though most real contact centres behave much more like Erlang A. This guide explains the difference in plain language, shows the numbers side by side, and tells you when each formula is the right one to use.
The short answer
Erlang C assumes every caller waits as long as it takes. Nobody hangs up.
Erlang A adds one realistic detail: callers lose patience and abandon. The "A" stands for abandonment.
That single change matters because abandoned calls free up agent time. Erlang C does not know this, so it overstates the workload and recommends more agents than you need, especially when the queue gets long.
Erlang C vs Erlang A at a glance
| Question | Erlang C | Erlang A |
|---|---|---|
| Do callers abandon? | No, they wait forever | Yes, after an average patience time |
| Extra input needed | None | Average patience (seconds) |
| Staffing result | Higher, safe side | Lower, closer to real life |
| Behaviour when understaffed | Predicts the queue grows without limit | Predicts abandonment rises and the queue stabilises |
| Best for | Quick sizing, very low abandonment | Realistic planning, peaks, tight budgets |
| Risk | Over-staffing | Wrong patience value gives wrong answer |
A worked example
To compare the two, We used the same test case in both models and solved for an 80/20 service level (80% of calls answered within 20 seconds).
| Input | Value | |
|---|---|---|
| Calls per 30 minutes | 100 | |
| Average handle time | 300 seconds | |
| Workload | about 16.7 Erlangs | |
| Average caller patience | 120 seconds | |
| Result | Erlang C | Erlang A |
| Agents required | 21 | 19 |
| Occupancy at that staffing | about 79% | about 82% |
| Abandonment | assumed zero | about 6% |
Erlang A needs 2 fewer agents (about 10%) for the same service level, because the callers who give up leave the queue and stop consuming capacity.
Does the gap grow with size?
Not as a percentage. In this model the saving is steady at about 9% to 12% of the Erlang C number, but in absolute terms it grows with scale.
For a team handling 600 calls per half hour, Erlang C asks for 108 agents and Erlang A asks for 98. That is 10 agents, which is a real hiring decision.
What happens when volume is higher than forecast
This is where the two models behave very differently. We staffed 19 agents (the Erlang A answer) and raised actual volume above the forecast.
| Actual volume | Erlang C says | Erlang A says |
|---|---|---|
| 100% of forecast | 59% | 83% |
| 105% | 42% | 79% |
| 110% | 21% | 74% |
| 120% | 0% (queue grows forever) | 64% |
Erlang C is brittle. Once the workload gets close to your agent count, it predicts a total collapse. Erlang A predicts a gradual slide, because callers hang up and the queue settles. Real queues behave much more like the second line, which is why Erlang C often looks too pessimistic when you are slightly short.
The catch: patience is the new input
Erlang A needs one extra number, average patience, and you must get it right. We staffed 18 agents based on a patience of 60 seconds and then changed the real patience:
| Real caller patience | Service level | Abandonment |
|---|---|---|
| 60 seconds (as planned) | 83% | 9.5% |
| 120 seconds | 78% | 8.2% |
| 180 seconds | 74% | 7.4% |
| 300 seconds | 69% | 6.4% |
| 600 seconds | 63% | 5.0% |
If you assume callers are impatient but they are actually loyal (for example a premium line, or people who must resolve a claim), service level can miss the target by 15 to 20 points. Patient callers stay in the queue and keep the queue long.
How to find your average patience
- Take your abandoned call report and the time each caller waited before hanging up.
- Ignore very short abandons (under 5 to 10 seconds). These are usually wrong numbers or instant hang ups.
- Use the average of the remaining wait times, or the point where half of abandoners have left.
- Calculate it per queue and per time of day. Patience is lower for sales and billing, and higher for claims and healthcare.
- Review it every quarter, because it changes when IVR messages, call-back offers or wait announcements change.
When to use which
Use Erlang C when:
- Abandonment is very low (under 2%) and the target is strict.
- You need a fast, conservative number for an RFP or a first sizing.
- You are staffing a queue that callers cannot leave, such as an internal help desk.
Use Erlang A when:
- Abandonment is meaningful (3% or more) and you can measure it.
- You are planning peaks, where waiting times are long.
- You want to avoid over-hiring, or test what happens when volume runs 5% to 10% above forecast.
- You offer callbacks or virtual hold, since those change patience (see why callbacks move workload but do not remove it).
Common mistakes
- Using Erlang A to cut staff, then ignoring the abandonment. The saving comes from callers giving up. If your business treats every abandon as a lost sale, you do not want to plan for them.
- Copying an industry patience number. Measure your own.
- Treating the result as exact. Both models assume random, independent calls. Real centres have bursts, so keep a buffer for the busiest intervals.
- Forgetting shrinkage. Both formulas give agents on the phones. Divide by (1 minus shrinkage) to get rostered headcount.
Try it yourself
Run your own numbers in the Erlang A calculator and compare with the Erlang C calculator. Use the service level calculator to see what your current roster delivers. If service level is slipping in real time, the service level recovery calculator shows what you need for the rest of the period.
Key takeaways
- Erlang C assumes nobody hangs up. Erlang A does.
- In this model Erlang A needed about 9% to 12% fewer agents for the same 80/20 target.
- Erlang A degrades gradually when volume runs high. Erlang C predicts a collapse.
- The price of Erlang A is one extra input, patience, and a wrong value can cost 15 to 20 points of service level.
- Use Erlang C as the safe ceiling, Erlang A as the realistic estimate, and measure patience from your own abandon data.
The figures come from a model with a 30 minute interval, exponential patience and the stated inputs. Check them against your own data before changing staffing.