What is the Erlang C formula?

Erlang C is a queueing model (M/M/c with no abandonment) used to estimate the probability a caller waits and to size agents from a service target. It uses offered load in erlangs (A), agents (N), average handle time (AHT), and a threshold T seconds to compute service level or ASA.

How do I calculate agents for 80/20 service level?

Compute offered load A = Calls × AHT ÷ interval seconds. Starting from N > A, increase N until service level SL(T) = 1 − Pw × exp(−(N − A) × T/AHT) meets or exceeds your target (e.g., 0.80 at 20 seconds).

What is shrinkage in staffing?

Shrinkage captures time agents are unavailable (training, meetings, breaks, PTO). To convert staffed agents N into FTE, divide by (1 − shrinkage). For example, with 30% shrinkage, FTE = N ÷ 0.7.

Erlang C Calculator

Ready

Calls Offered (per interval)

Total contacts in the interval

Interval Length (minutes)

Typical: 15 / 30 / 60

Average Handle Time (sec)

Talk + after‑call work

Shrinkage (% or decimal)

To convert agents to FTE

Goal Service Level ASA

Target Service Level (% or decimal)

e.g., 80% in 20s

Answer Time Threshold (sec)

Max Occupancy (optional % or decimal)

If set, we’ll add agents until occupancy ≤ cap

Notes

Primary

Agents —

FTE (incl shrink): —

Service

—

Target —

Details

Occ —

A — · Pw —

Staffing Quality

Agents: — FTE: — Occupancy: — Calls/hr: —

Enter calls, interval, and AHT. Choose a goal (service level or ASA). Results assume Erlang C (no abandonment).

Erlang C Formula and Examples

This call center staffing calculator uses the classic Erlang C model to size agents for a given service level (e.g., 80% in 20s) or ASA target. Outputs include occupancy, Erlangs, and FTE with shrinkage.

Offered Load (Erlangs)

A = Calls × AHT ÷ (Interval_sec)

If interval = 60 minutes, this is equivalent to Calls/hr × AHT ÷ 3600.

Erlang C Probability of Wait

Pw = \[ (A^N / N!) × (N / (N − A)) ] ÷ [ Σ_k=0..N−1 (A^k / k!) + (A^N / N!) × (N / (N − A)) ]

Valid when N > A (utilization ρ = A/N < 1).

Service Level and ASA

SL(T) = 1 − Pw × exp( −(N − A) × T / AHT )

ASA ≈ Pw × AHT ÷ (N − A)

Erlang C assumes no abandonment; for abandon-aware models use Erlang A (M/M/c+M).

Example — 80/20 target

Calls = 600 in 60 minutes; AHT = 300s
Target = 80% in 20s; Shrinkage = 30%

The calculator finds the smallest N > A that meets SL, reports occupancy and FTE = N ÷ (1 − shrinkage), and compares against optional max occupancy.

Occupancy

Utilization ρ = A/N. Many operations aim for 70–85% to balance efficiency and agent wellness.

Interval Choice

Use the same interval as your forecast (15/30/60 min) so calls and AHT align with staffing blocks.

Shrinkage

Convert staffed agents to FTE by dividing by (1 − shrinkage). Include PTO, training, and meetings.

Frequently Asked Questions

How do I use this Erlang C calculator?

Enter calls, interval, and AHT. Choose a goal (service level with a threshold, or ASA). Optionally cap occupancy and add shrinkage to convert agents to FTE.

What’s the difference between Service Level and ASA targets?

Service Level requires a % of calls answered within T seconds (e.g., 80% in 20s). ASA targets the average wait time in seconds. This tool finds the smallest agent count that meets your selected goal.

Does this account for abandonment?

Erlang C assumes no abandonment. If your operation has meaningful abandonment, consider Erlang A or add a separate abandonment model when planning staffing.

Improve Staffing Accuracy with Faster, Friendlier Support

Hit your service goals and protect agent wellness with better deflection and smarter workflows.

Try Suptask Free