Little's Law
Enter any two values to calculate the third. Use this to explore how changes in throughput, inventory, or flow time affect each other.
Also known as: Little's Theorem, Little's Formula, L = λW
Little’s Law (John Little, 1961) connects three core measures of any process: how much is in the system (inventory), how fast units come out (throughput), and how long each unit stays (flow time). Given any two, you can calculate the third.
The law is a mathematical proof, it holds regardless of arrival patterns, processing distributions, or number of steps. It applies to manufacturing lines, hospital ERs, airport security lines, call centres, and software development pipelines.
Formula
Inventory = Throughput × Flow Time
Rearranged: Flow Time = Inventory / Throughput
Rearranged: Throughput = Inventory / Flow Time
Example 1
An insurance company processes 10,000 claims per year (200/week over 50 weeks). Average flow time is 3 weeks. Average inventory = 200 × 3 = 600 claims in the process at any time.
Example 2
A care facility has 1,000 patients. 5 patients leave per month and are replaced. Flow time = 1,000 / 5 = 200 months (16.7 years).
Example 3 — SLA monitoring
A contact centre has a service level agreement (SLA) requiring an average response time of 5 days. Using a rolling 3-month average, throughput is 40 tickets resolved per day.
On Monday morning, there are 250 open tickets in the queue.
Flow time = 250 / 40 = 6.25 days.
The team is off track — at the current throughput, each ticket will take over 6 days on average, exceeding the SLA. To hit the 5-day target, either the queue needs to drop below 200 (5 × 40) or throughput needs to increase above 50/day (250 / 5).
This shows Little’s Law as a daily operational tool: check your inventory each morning, divide by your known throughput, and you have an immediate read on whether you’ll meet your target flow time.
Why It Matters
Little’s Law gives you visibility into a dimension you might not be measuring. If you know your throughput and how many items are “in progress,” you can calculate the average flow time without tracking individual items. It’s especially powerful for identifying hidden inventory, if Little’s Law says your flow time should be X but customers report Y, there’s delay you haven’t accounted for.