Math & Trig
Little's Law (WIP, Throughput, Cycle Time) and Takt Time formulas
Size Kanban WIP caps with Little's Law (WIP = Throughput * CycleTime) and balance production lines using Takt Time and workstation efficiency.
Little's Law for Kanban queues and Takt Time for customer-paced lines
Little’s Law relates average WIP, throughput and time in a consistently defined stable system. At throughput 24/day and time 3.5 days, average WIP is 84.
Work content divided by takt gives a theoretical minimum station count; actual task allocation may require more stations.
| Lean Operations Formula | Calculation | Result |
|---|---|---|
| Little's Law WIP | 24 units/day * 3.5 days | 84 units in WIP |
| Takt Time (Heartbeat Pace) | 420 net min / 140 daily demand | 3.00 min / unit |
| Minimum Workstations | =ROUNDUP(10.5 task min / 3.0 Takt, 0) | 4 stations |
| Line Balance Efficiency % | =10.5 / (4 * 3.0) | 87.5% (0.875) |
Takt Time, workstation count, and Little's Law formulas
Subtract breaks and planned meetings from shift minutes before computing Takt Time.
=LET(takt, C2 / D2, stations, ROUNDUP(E2 / takt, 0), ROUND(E2 / (stations * takt), 4))Little's Law implied Cycle Time (W = WIP / Throughput)
WIP/throughput gives the implied average time when the assumed throughput is maintained.
=ROUND(A2 / B2, 2)Additional worked calculation
Using the initial example inputs:
=ROUND(C2 / D2, 2)Additional worked calculation
Using the initial example inputs:
=ROUNDUP(E2 / (C2 / D2), 0)Inputs and interpretation
Little’s Law relates long-run averages under a stable system definition and consistent time units. Reducing WIP does not guarantee unchanged throughput. Takt time requires positive demand and available time. Rounded work-content/takt is a theoretical lower bound on stations; precedence, indivisible tasks and variability may require more. The displayed efficiency assumes feasible allocation.
Try the example
Use the original values or change them to test your understanding.