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⚖️ Little's Law Calculator

Apply L = λW to size queues, thread pools, connection pools, and concurrent requests. Solve for the variable you don't know.

Inputs

Solve for:
items
Average number of items in the system (queue length, threads busy, open connections).
Arrival rate — how many items enter per unit time (requests per second, orders per minute).
Average time each item spends in the system (latency, service time, sojourn time).
Presets:

Result

L = λ × W
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About Little's Law

Little's Law states that in any stable system:

L = λ × W

  • L — average number of items in the system
  • λ — long-run average arrival rate
  • W — average time an item spends in the system

Practical uses

  • Thread pool sizing: If your service handles 500 rps at 50 ms average latency, you need ≥ 25 concurrent workers.
  • Queue depth: Given producer rate and service time, compute average depth.
  • Connection pools: DB connections needed = QPS × query time.

Assumes the system is stable (arrivals ≤ processing capacity). For unstable or bursty systems, use percentile-based sizing or queueing models (M/M/c).