Erlang Calculator
Calculate key metrics for telecommunications systems using Erlang formulas. Determine traffic intensity, call blocking rates (Erlang B), or analyze call center performance including queue probability, agent occupancy, Service Level, and Average Speed of Answer (Erlang C).
Calculate Traffic Intensity (Erlangs)
Measure the total traffic volume handled by a system. Input either the call rate and average duration, OR the total call duration over a specific time period.
Input Method 1: Rate & Average Duration
OR
Input Method 2: Total Duration & Time Period
Understanding Erlang Concepts
What is an Erlang?
An Erlang is a dimensionless unit measuring telecommunications traffic intensity. It represents the continuous use of one resource or circuit for a one-hour period. For example, 1 Erlang means a resource is fully utilized (100% occupied) over the measurement period.
In this tool, traffic intensity (Erlangs) can be:
- Entered directly.
- Calculated from call rate and average duration (e.g.,
(Calls/Hour * Avg Duration Mins) / 60). - Calculated from total duration and measurement period (e.g.,
Total Call Hours / Measurement Hours). - Calculated from arrival rate and average service time (e.g.,
Arrivals/Sec * Avg Service Time Secs).
Erlang B Formula
Used for systems where blocked calls are lost (no waiting queue), the Erlang B formula calculates the probability that a call arriving when all N lines are busy will be blocked (Grade of Service).
The required Traffic Intensity (E) can be entered directly, or calculated within the tab using Arrival Rate and Average Service Time inputs.
B(E, N) = (EN / N!) / Σk=0N (Ek / k!)Where:
- E: Traffic offered (in Erlangs).
- N: Number of servers (lines/circuits).
Erlang C Formula & KPIs
Used for systems like call centers where calls wait in a queue if all agents are busy. The core formula calculates the probability that an arriving call must queue.
The required Traffic Intensity (E) can be entered directly, or calculated within the tab using Calls per Interval, Interval Length, and Average Handle Time (AHT) inputs.
C(E, N) = [ (EN / N!) * (N / (N - E)) ] / [ Σk=0N-1 (Ek / k!) + (EN / N!) * (N / (N - E)) ]Key call center metrics derived from this include:
- Probability of Waiting (C(E, N)): The likelihood any arriving call has to wait.
- Agent Occupancy: Average agent utilization (
E / N). Must be less than 100% (N > E) for a stable queue. - Service Level (SL): Percentage of calls answered within
Target Time(1 - C(E, N) * exp(-(N - E) * Target Time / AHT)). Requires AHT. - Average Speed of Answer (ASA): Average wait for queued calls (
C(E, N) * AHT / (N - E)). Requires AHT. - E: Traffic offered (in Erlangs).
- N: Number of servers (agents).
- AHT: Average Handle Time (in seconds).
Note: The Erlang C model assumes calls wait indefinitely and there's no abandonment. Real-world results may differ.