Cycle Time ⇄ Throughput (Little's Law)

The engineering

Little's Law ties the three numbers that define any production line or queue: the average work-in-process equals throughput times cycle time. Fix any two and the third is forced — there is no dodging it, no matter how the line is scheduled. Reach for it whenever someone claims they can cut cycle time without touching WIP or capacity.

The gotcha is units: throughput and cycle time must share a time base, and all three must be steady-state averages, not instantaneous peaks. A rule of thumb that falls straight out of the law — if you want faster flow at fixed capacity, the only lever is less WIP. Adding takt lets you check whether the line's throughput actually keeps up with customer pull.

Where this math comes from

The relation was folklore in operations circles for decades before John D. C. Little gave it a rigorous proof in 1961, showing L = λW holds for essentially any queuing discipline in steady state. It was one of those results everyone used and nobody had nailed down, and Little's proof made it a theorem rather than an assumption.

Wallace Hopp and Mark Spearman put it at the center of factory physics in their 1996 book, reframing Little's Law in the plant vocabulary of WIP, throughput, and cycle time. That framing — plus the CONWIP control ideas that came with it — is why the law now shows up on lean shop floors as routinely as it does in textbooks.

1. 1954Operations researchersL = λW circulates as an unproven but widely used queuing identity.
2. 1961John D. C. LittlePublishes the general proof of L = λW for steady-state queues.
3. 1996Hopp & SpearmanRecast the law as WIP = TH · CT, the backbone of Factory Physics.

See the full timeline of the math behind every calculator →

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