Erlang B Calculator
Calculate call center traffic capacity and blocking probability with this free tool. Get accurate results and download our Excel template.
Calculation Results
Complete Guide to Erlang B Calculator: Excel Free Download & Usage
The Erlang B formula is a fundamental tool in telecommunication engineering and call center management, used to calculate the probability that a call will be blocked when all servers (or channels) are busy. This guide provides everything you need to understand, use, and implement the Erlang B calculator, including a free Excel template download.
What is Erlang B?
Erlang B is a traffic engineering formula developed by Danish mathematician Agner Krarup Erlang. It calculates the probability of call blocking in a system with:
- A fixed number of channels/servers
- No call waiting (blocked calls are cleared)
- Random call arrivals following a Poisson process
- Exponentially distributed call durations
Key Applications of Erlang B
- Call Centers: Determine staffing requirements based on expected call volume
- Telecom Networks: Calculate required circuit capacity for voice traffic
- Wireless Systems: Dimension cell tower capacity for mobile networks
- Cloud Computing: Estimate server requirements for handling requests
The Erlang B Formula
The blocking probability (B) is calculated using:
B(N,A) = (AN/N!) / [Σi=0N(Ai/i!)]
Where:
- A = Total offered traffic in Erlangs
- N = Number of channels/servers
- B(N,A) = Blocking probability
| Traffic (Erlangs) | Channels | Blocking Probability (1%) | Blocking Probability (2%) | Blocking Probability (5%) |
|---|---|---|---|---|
| 5 | 8 | 0.012 | 0.025 | 0.078 |
| 10 | 15 | 0.011 | 0.023 | 0.072 |
| 20 | 28 | 0.010 | 0.021 | 0.065 |
| 30 | 40 | 0.009 | 0.019 | 0.060 |
| 50 | 63 | 0.008 | 0.017 | 0.054 |
How to Use Our Erlang B Calculator
- Enter Traffic Intensity: Input your expected traffic in Erlangs (call volume × average call duration in hours)
- Specify Channels: Enter the number of available channels/agents
- Set Target Blocking: Define your acceptable blocking probability (typically 1-5%)
- Call Duration: Provide average call duration in seconds
- Calculate: Click the button to get instant results
- Download Excel: Get our free template for offline calculations
Practical Example Calculation
Let’s consider a call center expecting:
- 300 calls per hour
- Average call duration of 3 minutes (0.05 hours)
- Target blocking probability of 2%
Step 1: Calculate traffic intensity (A) = 300 calls × 0.05 hours = 15 Erlangs
Step 2: Using our calculator with A=15 and B=0.02, we find N=22 channels required
Step 3: This means you need 22 agents to handle 300 calls/hour with only 2% being blocked
Erlang B vs Erlang C
| Feature | Erlang B | Erlang C |
|---|---|---|
| Call Handling | Blocked calls cleared | Calls wait in queue |
| Primary Use | Circuit-switched networks | Call centers with queues |
| Key Metric | Blocking probability | Average wait time |
| Formula Complexity | Simpler calculation | More complex |
| Typical Applications | Telecom trunk sizing | Call center staffing |
Advanced Considerations
While the basic Erlang B calculator provides valuable insights, real-world applications often require additional factors:
- Non-Poisson Arrival Rates: Modern systems may have bursty traffic patterns
- Non-Exponential Service Times: Some calls may have fixed or variable durations
- Agent Skill Levels: Not all agents handle calls at the same efficiency
- Multi-Channel Contacts: Email, chat, and social media interactions
- Peak Hour Variations: Traffic often varies by time of day/week
For these scenarios, simulation modeling or more advanced queuing theory models like Erlang C or the M/M/c/K queue may be more appropriate. The National Institute of Standards and Technology (NIST) provides excellent resources on advanced queuing theory applications.
Implementing Erlang B in Excel
Our free downloadable Excel template includes:
- Pre-built Erlang B calculation worksheet
- Dynamic charts showing blocking probability curves
- Sensitivity analysis tools
- Example scenarios for common use cases
- Documentation with formula explanations
The template uses Excel’s iterative calculation features to solve the Erlang B formula numerically, as there’s no closed-form solution. For very large values (N > 1000), we recommend using specialized software like MATLAB or programming languages with arbitrary-precision arithmetic.
Common Mistakes to Avoid
- Unit Confusion: Always ensure traffic is in Erlangs (calls × duration in hours)
- Overestimating Capacity: Remember Erlang B assumes no queueing – blocked calls are lost
- Ignoring Peak Hours: Design for your busiest period, not average traffic
- Mixing Models: Don’t use Erlang B for systems with queues (use Erlang C instead)
- Rounding Errors: For large N, use high-precision calculations to avoid significant errors
Alternative Tools and Software
While our Excel template provides excellent functionality, several specialized tools exist:
- Traffic Engineering Tools: Commercial software like Avaya’s IEX or Cisco’s Unified Contact Center
- Open Source: R packages like ‘queuecomputer’ or Python’s ‘scipy.stats’
- Online Calculators: Web-based tools from telecom equipment vendors
- Simulation Software: AnyLogic or Simul8 for complex scenarios
Future Developments in Traffic Modeling
Emerging technologies are changing traffic engineering:
- Machine Learning: Predictive models for dynamic staffing
- 5G Networks: New traffic patterns with ultra-low latency requirements
- IoT Devices: Massive numbers of small, frequent transactions
- Cloud Contact Centers: Elastic capacity with pay-as-you-go models
- AI Assistants: Changing call duration and frequency patterns
Researchers at Stanford University are developing next-generation queuing models that incorporate these new variables.
Frequently Asked Questions
What’s the difference between Erlang and erlang?
“Erlang” (capital E) refers to the unit of telecommunication traffic. “erlang” (lowercase) is a programming language used for building concurrent, distributed systems (ironically often used to build telecom systems that handle Erlangs of traffic!).
Can I use Erlang B for email or chat support?
Erlang B assumes immediate service or blocking, which doesn’t perfectly match asynchronous channels like email. For these, consider:
- M/M/c queues for chat with response time targets
- Little’s Law for workflow balancing
- Custom simulation models for complex multi-channel support
How accurate is the Erlang B model?
For traditional voice systems with random arrivals and exponential service times, Erlang B is extremely accurate (typically within 1-2% of real-world results). Accuracy decreases when:
- Call arrivals aren’t random (e.g., scheduled callbacks)
- Call durations aren’t exponential (e.g., fixed-length calls)
- Agents have varying skill levels
- There’s significant call abandonment
What blocking probability should I target?
Industry standards vary by application:
- Emergency Services (911): 0.001% or lower
- Premium Customer Support: 0.5-1%
- General Business: 1-3%
- Internal Helpdesks: 3-5%
- High-Volume Sales: 5-10%
How do I convert calls per hour to Erlangs?
Use this formula: Erlangs = (Calls per hour × Average call duration in seconds) / 3600
Example: 500 calls/hour × 180 seconds = 90,000 call-seconds per hour = 25 Erlangs