Erlang C calculator.
Size a contact centre from first principles: enter call volume, average handle time and a target service level to get the required agents, occupancy and average speed of answer. A separate helper turns calls-per-second and average duration into concurrent channels.
Contact-centre staffing (Erlang C)
Example: 300 calls in 60 minutes at 180 s handle time is 15 Erlangs of offered load. Target 80% answered within 20 s is the classic 80/20 service level.
Concurrent calls (CPS × ACD)
Concurrent calls ≈ CPS × ACD (in seconds). At 5 cps and a 90-second average, roughly 450 simultaneous channels are in use. This is the same offered-load idea as an Erlang, expressed for voice-channel or trunk capacity planning; size real capacity with headroom for peaks.
The short answer
What does the Erlang C calculator do?
It works out how many agents a contact centre needs to hit a service level. First it converts your call volume and average handle time into offered load in Erlangs. Then it applies the Erlang C queueing formula — which assumes callers wait rather than get blocked — to find the smallest number of agents whose probability of waiting is low enough to meet your target, and reports the resulting occupancy and average speed of answer.
- Offered load A (Erlangs) = arrival rate × AHT
- Erlang B: B(n,A) = A·B(n−1,A) / (n + A·B(n−1,A)), B(0,A)=1
- Erlang C: C = N·B / (N − A·(1 − B))
- Service level = 1 − C·e^(−(N−A)·t / AHT)
- ASA = C·AHT / (N − A) · · · Occupancy = A / N
Assumptions and limitations
Erlang C assumes random (Poisson) call arrivals, exponentially distributed handle times, no caller abandonment, unlimited queue patience and a steady state across the interval. Real centres see callers hang up and traffic spikes, so Erlang C tends to over-estimate waiting time and therefore staffing. It also does not include shrinkage — breaks, training, absence — so add your own shrinkage factor and headroom on top. Treat the output as a planning baseline, not an exact forecast.
Frequently asked questions
What is the Erlang C formula used for?
Erlang C models a queue where calls that find every agent busy wait rather than being blocked. It is the standard formula for contact-centre staffing: given the offered traffic and the number of agents it gives the probability a call has to wait, from which you derive service level, average speed of answer and occupancy.
What is an Erlang?
An Erlang is a dimensionless unit of traffic intensity equal to one resource in continuous use for the whole measurement period. Offered load in Erlangs is the call arrival rate multiplied by the average handle time in the same time unit — 300 calls per hour at 180 seconds each is 15 Erlangs.
What service level should I target?
A common benchmark is 80/20 — answering 80% of calls within 20 seconds — but the right target depends on your business and budget. This calculator lets you set both the percentage and the answer-time threshold so you can size to your own SLA.
What is occupancy and why does it matter?
Occupancy is the fraction of time agents spend actually handling calls (offered load ÷ agents). High occupancy looks efficient but above roughly 90% leaves no slack for variability and drives burnout and attrition, so planners deliberately staff for lower occupancy.
How do I get concurrent calls from CPS?
Concurrent calls equal the call arrival rate times the average call duration in the same unit: concurrent = CPS × ACD (seconds). At 5 calls per second and a 90-second average you need about 450 simultaneous channels. It is the same offered-load idea expressed for capacity planning.
Why does this differ from my workforce-management tool?
Most WFM tools add shrinkage (breaks, training, absence), abandonment models, multi-skill routing and per-interval forecasting on top of raw Erlang C. This calculator gives the underlying Erlang C figure so you can sanity-check those tools; expect a full WFM system to recommend somewhat higher headcount once shrinkage is included.
Does Erlang C apply to chat or messaging?
Not directly. Erlang C assumes one agent handles one contact at a time. Chat and messaging agents handle several concurrent conversations, so you need a modified model that accounts for concurrency. Use Erlang C for voice, and adjust for the average number of simultaneous sessions in digital channels.
Building a voice or OTP flow?
BroadNet runs programmable voice, IVR and Voice OTP on carrier-grade infrastructure across 200+ countries. Talk to our team about capacity and routing.