- Enter throughput rate (units per hour or per day).
- Enter lead time (average time from start to finish).
- Click Calculate to see WIP levels based on Little's Law.
Little's Law
Understanding Little's Law
Little's Law is one of the most powerful and universal principles in operations management. Proven mathematically by John Little in 1961, it states a remarkably simple relationship: the average number of items in a system (WIP) equals the average arrival rate (throughput) multiplied by the average time an item spends in the system (lead time).
This holds true for any stable system: a factory floor, a hospital emergency room, a software development pipeline, or a coffee shop queue. It requires no assumptions about arrival distributions or service patterns — only that the system is in a steady state.
The Three Rearrangements
| Solve For | Formula | When to Use |
|---|---|---|
| WIP | WIP = Throughput x Lead Time | Setting Kanban limits |
| Lead Time | LT = WIP / Throughput | Predicting delivery dates |
| Throughput | TH = WIP / Lead Time | Estimating output capacity |
Real-World Example
A production floor has 120 units of WIP and completes 40 good units per day.
If WIP is reduced to 80: LT = 80 / 40 = 2 days
If WIP is reduced to 40: LT = 40 / 40 = 1 day
Cutting WIP by two-thirds cut lead time by two-thirds — without changing throughput at all.
Why Less WIP Is Almost Always Better
Kanban + Little's Law
Kanban systems use Little's Law in reverse: set a WIP limit, and lead time is forced down. If your desired lead time is 2 days and throughput is 40/day, your Kanban WIP limit should be 80 units. Any more and lead time exceeds your target.
✅ Flow Thinking
- Set explicit WIP limits
- Measure lead time, not just output
- Stop starting, start finishing
- Pull work only when capacity opens
❌ Batch Thinking
- Pushing work in regardless of WIP
- Measuring only throughput (ignoring lead time)
- Starting new jobs while old ones stall
- Hiding problems behind large WIP buffers
🎯 Key Takeaway
Little's Law proves that the fastest way to reduce lead time is to reduce WIP. You do not need to speed up any process — just stop overloading the system. Set WIP limits, pull work instead of pushing it, and watch lead times drop.
Frequently Asked Questions
What is Little's Law?
Little's Law states that WIP = Throughput x Lead Time. This fundamental relationship holds for any stable system — manufacturing lines, hospitals, software teams, even traffic.
Why does reducing WIP reduce lead time?
From Little's Law: Lead Time = WIP / Throughput. If throughput stays constant and you reduce WIP, lead time drops proportionally. Less inventory means products move through faster.
What is the ideal WIP level?
The minimum WIP that keeps the bottleneck busy. Excess WIP creates congestion, increases lead time, hides quality problems, and ties up cash. Lean manufacturing aims to minimize WIP.
How does Little's Law apply to Kanban?
Kanban limits WIP at each stage. By capping WIP, you force lead times down (per Little's Law). If throughput drops, the low WIP makes the problem visible immediately.
Does Little's Law always work?
It works for any system in a stable state (arrivals roughly equal departures over time). It does not apply during ramp-ups, shutdowns, or major disruptions where the system is not in steady state.
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