📡 Free Telecom Traffic Engineering Tool

Erlang Calculator

Calculate trunk lines and agent staffing using Erlang B and Erlang C traffic engineering formulas.

Trusted by telecom engineers and call center managers worldwide · Based on ITU-T E.501

Erlang Calculator

Calculate trunk lines and agent staffing using Erlang B and Erlang C traffic engineering formulas.

1 – 100,000
1 – 7,200 seconds

Enter your call volume and duration above, then click Calculate to size your trunks or agents.

Based on ITU-T Recommendation E.501 —·Updated Mar 2026·Free, no signup
Common Questions

Frequently Asked Questions

Erlang B models a loss system where blocked calls are simply rejected or cleared — this is used for dimensioning trunk lines in telephone networks. Erlang C models a queuing system where callers wait in a queue until an agent becomes available — this is the standard model for call center staffing. Choose Erlang B when callers receive a busy signal, and Erlang C when callers are placed on hold.

An Erlang is the unit of telecommunications traffic intensity. One Erlang equals one circuit (or trunk line) occupied continuously for one hour. It is calculated as: Traffic (Erlangs) = (Calls per hour × Average call duration in seconds) / 3600. For example, 600 calls per hour with an average duration of 180 seconds produces 30 Erlangs of traffic.

For trunk line dimensioning with Erlang B, a common target is P.02 (2% blocking probability), meaning only 2% of call attempts are blocked. For call centers using Erlang C, typical targets are 80/20 (80% of calls answered within 20 seconds) or 90/10. The right target depends on your industry, customer expectations, and cost constraints.

If your traffic intensity is 30 Erlangs, you need more than 30 agents because calls arrive randomly — sometimes multiple calls arrive simultaneously. The Erlang formulas account for this statistical variation. Having exactly 30 agents for 30 Erlangs of traffic would result in nearly 100% occupancy and extremely long wait times for callers.

The Erlang C formula assumes calls arrive following a Poisson distribution and call durations follow an exponential distribution. While real-world call patterns may deviate from these assumptions (e.g., daily traffic peaks, non-random arrivals), Erlang C remains the industry standard for initial staffing estimates. Most workforce management platforms use Erlang C as their core engine, supplemented by historical data adjustments.

Agent occupancy is the percentage of time agents spend actively handling calls versus waiting. It is calculated as traffic intensity divided by the number of agents. High occupancy (above 85-90%) leads to agent burnout and degraded service levels. Conversely, very low occupancy means overstaffing. Optimal occupancy typically ranges from 70-85% depending on the service level target.

Yes, Erlang B is widely used for SIP trunk planning. While SIP trunks are virtual rather than physical circuits, the mathematical model still applies. Input your expected concurrent call volume and the calculator determines how many SIP channels you need to maintain your target grade of service. Many VoIP providers use Erlang B calculations for capacity planning.

Erlang C calculates the number of agents needed on the phones. In practice, you must add shrinkage — the percentage of scheduled time agents are unavailable (breaks, training, meetings, absenteeism). Typical shrinkage is 25-35%. If Erlang C recommends 40 agents, with 30% shrinkage you need to schedule approximately 57 agents (40 / 0.70) to ensure 40 are available.

In an Erlang B system, calls that arrive when all trunks are busy receive a busy signal and are lost — the caller must retry. This is called blocking. In an Erlang C system, excess calls are queued and callers wait. If the queue grows unchecked, average wait times increase exponentially. Monitoring real-time traffic against your Erlang calculations helps prevent service degradation during peak periods.

Agner Krarup Erlang (1878-1929) was a Danish mathematician and engineer who pioneered the field of traffic engineering and queuing theory while working at the Copenhagen Telephone Exchange. He published his foundational paper on blocking probabilities in 1917. The unit of telecommunications traffic (the Erlang) and the Erlang programming language are both named in his honor.

What Is the Erlang Calculator?

The Erlang calculator is a free tool for dimensioning telephone circuits and call center agent staffing using the classical traffic engineering formulas developed by Danish mathematician Agner Krarup Erlang in 1917. It supports two models: Erlang B for trunk line planning (loss systems where blocked calls are cleared) and Erlang C for call center staffing (queuing systems where callers wait on hold).

Telecom engineers use it to size SIP trunks, PRI lines, T1/E1 circuits, and cloud PBX channels. Call center managers rely on it to calculate how many agents are needed to hit a service level target — the classic 80/20 rule (80% of calls answered within 20 seconds) is modeled directly using Erlang C. VoIP architects use it to validate that their hosted telephony platform can handle peak concurrent calls without degradation.

Unlike generic calculators, this tool implements the iterative Erlang B formula for numerical stability and follows ITU-T E.501 standards for traffic estimation. The calculations are the same ones used by professional workforce management platforms and telecom equipment vendors — made freely accessible here without sign-ups or paywalls. Try the Erlang C calculator above or read our methodology page for details on the formulas.

How to Use This Erlang Calculator

Step 1: Choose Erlang B or Erlang C+
Start by selecting your calculation mode. Use Erlang B when you're dimensioning physical or virtual trunk lines — situations where a caller who can't get through receives a busy signal and must call back. This is the right model for PSTN trunks, SIP channels, T1/E1 circuits, and PRI lines. Use Erlang C when callers are placed in a queue and wait for the next available agent. This is the standard model for inbound contact centers, help desks, and any environment where abandoning callers is not acceptable. Getting this choice right matters: the two formulas produce very different results for the same traffic load.
Step 2: Enter Your Call Volume (Calls Per Hour)+
Enter the number of calls arriving during your busiest hour — not your daily average. Traffic engineering is always sized for peak load. If your PBX CDR reports show 480 calls between 10 AM and 11 AM on a Monday, enter 480. If you only have daily totals, divide by the number of active hours and multiply by a peak factor of 1.3–1.5. Undersizing because you used average traffic instead of busy-hour traffic is one of the most common planning mistakes. For call centers, use the peak 30-minute interval doubled (two half-hours = one hour equivalent).
Step 3: Enter Average Call Duration (Seconds)+
For Erlang B (trunks), enter the average call duration in seconds including ring time and any post-call processing on the network side. For Erlang C (agents), this should be your Average Handle Time (AHT) — the sum of average talk time, hold time, and after-call wrap-up work. A typical B2B support call might be 3 minutes talk + 30 seconds hold + 45 seconds wrap-up = 255 seconds AHT. Including wrap-up is critical: agents who are in after-call work cannot take new calls, so omitting it underestimates the staffing requirement by 15–25% in most contact centers.
Step 4: Set Your Grade of Service Target+
For Erlang B, the Grade of Service (GoS) is the maximum acceptable blocking probability — the percentage of call attempts that will receive a busy signal. ITU-T recommends P.02 (2%) for general telephony and P.01 (1%) for more critical applications. Emergency services often plan to P.001 (0.1%). For Erlang C, the service level target is usually expressed as X% of calls answered within Y seconds. The standard 80/20 target means 80% of calls answered within 20 seconds. Enter 20% as the "wait probability" (the inverse of 80%) and 20 seconds as the target answer time. Healthcare and financial services typically require 90/15 or better.
Step 5: Interpret Your Results+
The calculator returns traffic intensity in Erlangs (calls per hour × duration in seconds ÷ 3600), required lines or agents, blocking/wait probability, average wait time, service level percentage, and occupancy rate. Pay special attention to occupancy in Erlang C mode — if it exceeds 85%, your queue becomes unstable and wait times grow exponentially with any traffic spike. For trunk planning, verify the blocking probability is at or below your GoS target. If the required lines seem high, consider trunk pooling across multiple sites or DISA overflow routing to reduce the per-site requirement.

How We Calculate Your Results

Traffic Intensity: The Foundation of Erlang Math+
Everything starts with traffic intensity, measured in Erlangs. One Erlang equals one circuit occupied continuously for one hour. The formula is simple: A = (λ × h) / 3600, where λ is calls per hour and h is average call duration in seconds. If you handle 360 calls per hour with an average duration of 300 seconds (5 minutes), your traffic intensity is (360 × 300) / 3600 = 30 Erlangs. This means your network carries the equivalent of 30 circuits occupied full-time — but since calls arrive randomly (not evenly spaced), you always need more than 30 channels to serve 30 Erlangs without excessive blocking or queuing.
The Erlang B Formula — Sizing Trunk Lines+
The Erlang B formula calculates the probability that all N trunks are simultaneously busy when a call arrives. We use the iterative form for numerical stability: B(N,A) = (A × B(N-1,A)) / (N + A × B(N-1,A)), starting with B(0,A) = 1. The calculator iterates N upward from ⌈A⌉ until the blocking probability B(N,A) falls at or below your target Grade of Service. For example, 30 Erlangs of traffic at a P.02 (2%) blocking target requires 38 trunk lines — 27% more than the bare traffic intensity. This overhead accounts for statistical bunching of arrivals and is fundamental to reliable network planning.
The Erlang C Formula — Sizing Call Center Agents+
Erlang C calculates the probability that an arriving call must wait because all agents are busy: C(N,A) = [B(N,A) × N/(N-A)] / [1 - (A/N)(1 - B(N,A))] where B(N,A) is the Erlang B value for the same parameters. Service level is then computed as SL = 1 - C(N,A) × e^(-(N-A)(t/Ts)), where t is the target answer time and Ts is average handle time. The calculator finds the minimum agent count N where SL meets your target. For 30 Erlangs with an 80/20 service level target, you'd typically need around 36–38 agents — the exact number depends on your AHT. Running fewer than ⌈A⌉ + 1 agents causes the queue to grow without bound.
Why Trust This Calculation?+
These formulas are the global standard for telecom traffic engineering. The Erlang B model was formalized in Agner Krarup Erlang's 1917 paper "Solution of some Problems in the Theory of Probabilities of Significance in Automatic Telephone Exchanges," and is codified in ITU-T Recommendation E.501 (Estimation of Traffic Offered in the Network). Erlang C is documented in E.501 and the ITU-T E.500 series. The iterative B(N,A) computation we use avoids the factorial overflow that affects direct formula implementations at high traffic loads. Our results match those produced by professional WFM platforms including NICE, Genesys, and Verint — the same math, freely accessible here.

Erlang Traffic Engineering: A Practical Guide

Understanding Traffic Intensity and Erlangs

An Erlang is a dimensionless unit representing the continuous use of one circuit for one hour. It's named after Agner Krarup Erlang (1878–1929), who developed the mathematical framework for telephone traffic while working at the Copenhagen Telephone Exchange. The unit bridges the gap between discrete calls and continuous capacity: if 600 calls per hour each last 180 seconds, the traffic intensity is 30 Erlangs — meaning 30 circuits are needed just to carry the load with zero spare capacity.

In practice, you always need more circuits than your traffic intensity suggests. Random call arrival (modeled as a Poisson process) means calls can bunch together. If 30 calls arrive in a 60-second window instead of one per 2 seconds, you need enough channels to handle that burst. The amount of overhead required depends on your Grade of Service target — stricter targets require proportionally more excess capacity.

Erlang B vs Erlang C: Choosing the Right Model

Erlang B is a loss model. When all trunks are busy, new calls are blocked — they receive a busy signal and are lost. This is how PSTN networks, most PBX trunk groups, SIP trunks, and satellite links work. It's the correct model for any system where overflow calls go elsewhere or are rejected outright.

Erlang C is a queuing model. When all agents are busy, new callers wait in a queue. Calls are never lost — they just wait. This matches virtually every inbound call center, ACD (Automatic Call Distributor) environment, or help desk. The key output is service level: what percentage of callers reach an agent within your target answer time. Our detailed comparison guide walks through when each model applies with real examples.

Grade of Service Standards Across Industries

Different industries operate to different Grade of Service standards. General business telephony typically plans to P.02 (2% blocking). Carrier-grade networks and wholesale trunks often use P.01 (1%) or stricter. Emergency services (E911, PSAP) plan to P.001 (0.1%) because a blocked emergency call can be life-threatening — standards like NENA (National Emergency Number Association) guidelines require extreme redundancy. For call centers, the ICMI (International Customer Management Institute) industry benchmark is 80/20 for general customer service, while healthcare and financial services often target 90/15.

Planning for Peak Load: Busy Hour Traffic

Every telecom system has a busy hour — the 60-minute period with the highest call volume. ITU-T E.501 defines the busy hour as the one-hour interval with the maximum traffic intensity across the measurement period. Always size your trunks and agents for the busy hour, not for average load. A typical office sees its busy hour between 10–11 AM or 2–3 PM. Call centers in retail often see their daily busy hour shift to evenings and weekends.

For seasonal businesses, plan for your peak season's busy hour. A tax preparation service that handles 200 calls on a normal January day might handle 800 on April 14th. Erlang calculations should be run against that peak scenario. Our peak hour traffic planning guide covers how to extract busy-hour data from PBX reports and CDR records, and how to model seasonal variation.

Who Should Use This Erlang Calculator?

This tool is built for anyone who needs to plan telephone circuit capacity or call center agent staffing. Common use cases include:

  • Telecom engineers sizing SIP trunk groups, PRI circuits, T1/E1 lines, or ISDN BRI channels for corporate PBX systems.
  • Call center managers and workforce planners calculating the minimum agent headcount needed to hit an 80/20 or 90/15 service level target across different shifts.
  • VoIP architects validating cloud PBX and hosted telephony platform capacity — SIP trunks follow Erlang B math even though they're virtual circuits.
  • IT managers evaluating unified communications deployments and verifying that their UCaaS provider's channel limits won't cause call blocking during peak hours.
  • Network operations teams at carriers and ISPs planning route capacity, interconnect trunks, and overflow routing between switching centers.
  • Students and academics studying telecommunications, queuing theory, or operations research who need a reliable reference implementation of the Erlang formulas.

The calculator handles everything from a small 10-person office needing 4–6 SIP trunks to enterprise contact centers carrying thousands of Erlangs. No account required — just enter your numbers and get results. For deeper reading on call center staffing methodology, our Erlang C staffing guide and 80/20 service level explainer are good starting points.

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