Erlang C Calculator
The Erlang C queueing model: for a given arrival rate, service time and number of servers (or agents), the chance a request waits, how long it waits on average, the utilization — and how many servers you need to hit a target.
Requests arriving at random at λ per second, each taking S seconds, present an offered load of A = λS erlangs.
How the erlang c calculator works
Requests arriving at random at λ per second, each taking S seconds, present an offered load of A = λS erlangs. With c servers and A < c the queue is stable; Erlang C gives the probability that an arrival finds every server busy and must wait, and the average wait follows as that probability × S ÷ (c − A). It is the model behind call-center staffing and server-pool sizing, and it shows why running at 95% utilization means long queues.
Formula: A = λ S; P_wait = (Aᶜ ÷ c!) ÷ ((Aᶜ ÷ c!) + (1 − A/c) Σₖ₌₀ᶜ⁻¹ Aᵏ ÷ k!); W = P_wait × S ÷ (c − A)
Worked examples
| Inputs | Probability of waiting | Note |
|---|---|---|
| 100 calls/min, 180 s handling, 320 agents | 17.6 % | 300 erlangs; 24% wait |
| Same load with 310 agents | 45.6 % | over half wait |
| A small helpdesk: 10/hour, 15 min, 4 staff | 32 % | 2.5 erlangs; 20% wait |
FAQFrequently asked questions
What is an erlang?
One erlang is one server continuously busy: the offered load is the average number of servers that would be occupied if none had to wait. 300 erlangs of calls need more than 300 agents — how many more depends on the wait you will accept.
Why does utilization above 85% hurt so much?
Because the wait grows as 1 ÷ (c − A): the gap between servers and load is what absorbs randomness. Going from 85% to 95% utilization roughly triples the average wait; the last few percent of efficiency cost most of the service level.
What are the model’s assumptions?
Random (Poisson) arrivals, exponential service times, a single queue served in order, infinite patience and no abandonment. Real callers hang up, which makes Erlang C pessimistic; Erlang A adds abandonment.
How do I use it for web servers?
Requests per second as λ, mean response time as S, worker threads or instances as c. A target such as "95% served within 500 ms" translates directly to the target fields.
Where these figures come from
- IEC 80000-13 — Information science and technology (quantities and units) — the decimal (kB, MB) versus binary (KiB, MiB) prefixes used throughout
- RFC 4632 — Classless Inter-domain Routing (CIDR) — the address-plan arithmetic behind the subnet calculator
- RFC 1918 — Address Allocation for Private Internets — the private ranges the subnet calculator recognises
- NIST SP 800-63B — Digital Identity Guidelines, Authentication — length over composition rules; the basis of the password guidance here
- NIST SP 800-57 Part 1 — Recommendation for Key Management — key-strength comparisons used by the key-space calculator
- NIST — Digital Identity Guidelines (SP 800-63) — US federal authentication standard
Last checked: September 2026. Units follow the SI decimal convention (IEC 80000-13 defines the binary alternatives); network and security figures cite the defining standard.