Erlang Calculator
Optimize your contact center staffing by calculating Service Level, ASA, and agent requirements using the Erlang C formula.
Calls answered within target time
Service Level Projection by Agent Count
This chart visualizes how adding agents improves your Service Level.
Staffing Scenarios Table
| Agents | Service Level (%) | ASA (Sec) | Occupancy (%) |
|---|
Comparison of staffing levels relative to your current inputs.
What is an Erlang Calculator?
An Erlang Calculator is a specialized mathematical tool used primarily in call centers and telecommunications to predict staffing requirements. Named after A.K. Erlang, a Danish mathematician, the Erlang Calculator utilizes the Erlang C formula to estimate how many agents are needed to meet specific service level targets based on call volume and handle time.
Who should use it? Workforce management (WFM) professionals, call center managers, and operations analysts rely on the Erlang Calculator to balance customer experience with operational costs. A common misconception is that staffing is a simple linear calculation (calls divided by time). In reality, call arrivals are random, requiring the complex probability modeling found in an Erlang Calculator.
Erlang Calculator Formula and Mathematical Explanation
The core of this Erlang Calculator is the Erlang C formula, which calculates the probability that an incoming call will have to wait in a queue because all agents are busy.
The formula for the probability of a delay $P(W > 0)$ is:
Ec(m, u) = [ (u^m / m!) * (m / (m – u)) ] / [ Sum_{i=0}^{m-1} (u^i / i!) + (u^m / m!) * (m / (m – u)) ]
Variable Definitions
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| u (A) | Traffic Intensity | Erlangs | 1 – 500+ |
| m (N) | Number of Agents | Integer | Must be > u |
| AHT | Average Handle Time | Seconds | 120 – 600 |
| t | Target Wait Time | Seconds | 10 – 60 |
Practical Examples (Real-World Use Cases)
Example 1: Small Help Desk
In this scenario, a help desk receives 60 calls per hour with an AHT of 10 minutes (600 seconds). The traffic load is exactly 10 Erlangs. If the manager uses an Erlang Calculator and assigns 12 agents, the probability of waiting is roughly 34%, and the 20-second Service Level would be approximately 78%. Adding just one more agent (13 total) significantly boosts the Service Level to 92%.
Example 2: High Volume Insurance Center
A center receives 1,200 calls per hour with an AHT of 4 minutes (240 seconds). This results in 80 Erlangs of traffic. Using the Erlang Calculator, we find that 85 agents result in an occupancy of 94% but a poor Service Level of 56%. By increasing staff to 90 agents, the occupancy drops slightly to 89%, but the Service Level jumps to 91%, illustrating the "economies of scale" in larger centers.
How to Use This Erlang Calculator
- Enter Call Volume: Input the number of calls expected during your peak "busy hour."
- Define AHT: Enter the Average Handle Time in seconds, including talk and wrap-up time.
- Input Staffing: Provide the number of "on-chair" agents available.
- Set Target: Define your Service Level objective (e.g., 20 seconds).
- Analyze Results: Review the Service Level percentage, ASA, and Occupancy metrics instantly.
Key Factors That Affect Erlang Calculator Results
- Call Arrival Randomness: Erlang C assumes calls arrive randomly (Poisson distribution). Real-world bursts can deviate from this model.
- Agent Occupancy: Higher occupancy means higher efficiency but also higher burnout risk and longer wait times.
- Shrinkage: This Erlang Calculator assumes agents are 100% available. You must account for shrinkage (breaks, meetings, sick leave) separately.
- Patience Levels: Erlang C assumes no callers hang up (abandon). In reality, average handle time and patience affect true performance.
- Economy of Scale: Larger agent pools are mathematically more efficient than smaller pools at the same occupancy levels.
- SLA Targets: Tightening your service level agreement target from 30 to 10 seconds requires significantly more staff for the same volume.
Frequently Asked Questions (FAQ)
One Erlang is equivalent to one continuous hour of call traffic (e.g., one agent busy for 60 minutes).
If the number of agents is less than or equal to the Traffic Intensity (Erlangs), the queue will grow infinitely, and the Erlang Calculator will show 0% Service Level.
No, this uses Erlang C, which assumes an infinite queue. Erlang B is used for calculating trunk/line requirements where calls are blocked.
Most centers aim for 85-90%. Any higher often leads to agent burnout and attrition. Check our occupancy rate guide.
Small changes in average handle time have a massive impact on staffing requirements, often more than call volume changes.
Erlang C is best for "immediate" channels like voice and chat. Email often uses different logic due to longer deferral times.
Average Speed of Answer. It measures the average time a caller spends in the queue before an agent picks up.
It tends to be slightly pessimistic for very small teams (under 5 agents) but remains the industry standard for call center staffing.
Related Tools and Internal Resources
- Workforce Management Guide: Learn the fundamentals of scheduling and forecasting.
- Call Center Staffing Tools: Advanced models for complex multi-skill environments.
- SLA Guide: How to set realistic Service Level Agreements for your business.
- Occupancy Rate Calculator: Deep dive into agent productivity metrics.
- AHT Optimization: Tips to reduce handle time without sacrificing quality.
- Shrinkage Calculator: Convert Erlang results into total headcount requirements.