PPolySim OS

Little's Law

One simple equation governs every queue on Earth: work-in-progress equals throughput times lead time. Factories, hospitals, and software backlogs all obey it.

Little's LawLive

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Little's Law is deceptively simple and astonishingly general: the average work-in-progress equals throughput times lead time. It holds for any stable queue — a factory, a hospital, a software backlog, a checkout line — regardless of the details. It means the only ways to cut lead time are to raise throughput or reduce work-in-progress, the core insight of lean and agile.

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Data Inspector

Work in progress20.0 units
Throughput5/hr
Lead time4 hr

Governing equation

Reading this result: At 5/hr throughput and a 4 hr lead time, about 20 items sit in progress at once — so the only ways to cut lead time are to raise throughput or shrink work-in-progress; you cannot move one without the others following.

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How it works

Little's Law states that the average amount of work-in-progress in a stable system equals its throughput multiplied by the average lead time. It holds for any queue regardless of its internal details — a production line, an emergency room, a support ticket queue. The implication is powerful: to shorten lead time you must either raise throughput or cut work-in-progress, the core lever of lean and agile.

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The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.

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Frequently asked questions

Is this Little's law calculator tool really free?
Yes. Little's Law runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
Can I save or share my simulation?
Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.