Call Center Staffing (Erlang C) & Service Level Calculator
Calculate agent staffing needs to meet service level agreements. Enter values for instant results with step-by-step formulas.
Formula
Agents = ErlangC_Solve(Traffic, SLA)
We calculate 'Traffic Intensity' (Erlangs) based on call volume and duration. Then, we use the Erlang C probability formula to find the minimum number of agents required to ensure X% of calls are answered within Y seconds, while keeping agent occupancy at sustainable levels.
Worked Examples
Example 1: Standard SLA
Problem:100 calls/hr, 5 min AHT. Target 80/20.
Solution:Traffic = 8.33 Erlangs. Need ~11-12 agents.
Result:12 Agents
Example 2: High Volume
Problem:500 calls/hr, 3 min AHT. Target 90/10.
Solution:Traffic = 25 Erlangs. Need ~30 agents.
Result:30 Agents
Frequently Asked Questions
What is Erlang C?
A mathematical formula derived by A.K. Erlang in 1917 to determine the number of telephone circuits needed. In call centers, it calculates staffing based on queuing theory (assuming calls wait in a queue).
What is Shrinkage?
Time agents are paid but not available to take calls (Breaks, Meetings, Training, Vacation). Erlang C calculates *seated* bodies. You must add ~30% Shrinkage to get the hiring number.
Why can't I just match agents to hours?
Randomness. Calls don't arrive evenly. You need 'surplus' staff to handle random spikes, otherwise queues explode.
How do I lower staffing needs?
Reduce AHT (better training/tools) or Reduce Volume (Deflection/Self-Serve).
Background & Theory
The Trade-off Triangle
- Service Level (Customer): Fast answers.
- Cost (Business): Few agents.
- Occupancy (Agent): Reasonable workload.
You cannot maximize all three. High Service Level requires more staff (High Cost) and results in lower Occupancy (Bored Agents).
Key Variables
- Interval: Staffing is usually calculated in 15 or 30-minute intervals, not daily averages.
- Wrap Time: Don't forget the time an agent spends typing notes after the call hangs up. That counts as AHT.
Practical Tips
- Use Shrinkage: This calculator outputs "Butts in Seats." Divide by (1 - Shrinkage%) to find "Heads to Hire."
- Route to Skills: Segregate complex calls from simple ones to stabilize AHT.
History
The Copenhagen Telephone Company
In 1909, Agner Krarup Erlang, a Danish mathematician, went to work for the telephone company. He wanted to solve a physics problem: How many trunk lines do we need so people don't get busy signals?
The Birth of Queueing Theory
He published his formulas in 1917. Erlang C assumed that people would wait in a queue if the line was busy. This math became the foundation of modern teletraffic engineering and later, call centers.
The WFM Revolution
Before computers, managers used "Erlang Tables" (books of pre-calculated numbers). In the 1980s, Workforce Management (WFM) software automated this, allowing for complex scheduling including skills-based routing (e.g., English vs Spanish agents). Despite AI, Erlang C remains the core engine of almost every staffing calculator today.
Common Misconceptions
- Myth: 10 hours of work requires 10 agents. Reality: Due to random arrival times, you might need 12 or 13 agents to ensure no one waits too long.
- Myth: 100% Occupancy is efficient. Reality: 100% occupancy means infinite queue times and instant burnout. 80-85% is the sweet spot.