About the Little's Law Calculator
Little's Law says that, in a stable system, the average number of items inside it equals the average rate at which items leave multiplied by the average time each item spends inside. In operations language: work in process (WIP) = throughput × lead time. Enter any two of the three values and this calculator solves for the third.
It works for almost any flow system: parts on a production line, orders in a fulfilment centre, patients in a clinic, tickets on a software team’s board, cars in a car wash or customers in a queue. Managers use it to see how much WIP they must cut to shorten lead time, or what lead time to promise given today’s backlog and throughput.
The law holds for long-run averages when the system is stable — items arrive and leave at roughly the same rate and WIP is not steadily growing or shrinking. Throughput and lead time must use the same time unit, which you choose from the menu.
With the default inputs, the answer is 100. Change any value above to recalculate instantly.
How to use the little's law calculator
- 1Choose which quantity you want to solve for.
- 2Pick the time unit you measure throughput and lead time in.
- 3Enter the two known values as long-run averages.
- 4Read the answer and the plain-English summary.
- 5Use the notes to see how reducing WIP changes lead time.
Formula and method
Little's Law (proved by John D. C. Little in 1961) links three long-run averages of any stable queueing system: L, the average number of items in the system (WIP); λ, the average arrival or completion rate (throughput); and W, the average time an item spends in the system (lead time, cycle time or flow time). Multiply throughput by lead time to get WIP, or rearrange to solve for either of the others.
The relationship does not depend on the arrival pattern, service-time distribution or processing order, which is why it is so widely used. It does require consistent units (throughput per day with lead time in days) and a system that is roughly in steady state, with no long-term build-up of WIP.
- L
- Average work in process — items in the system
- λ
- Average throughput (arrival/departure rate) per time unit
- W
- Average lead time — time each item spends in the system
Worked examples
Solve WIP: 20 orders/day for 5 days each
With 20 orders completed per day and each order taking 5 days from start to finish, the system holds 20 × 5 = 100 orders in process on average.
Solve throughput: 150 items in WIP, 10-day lead time
If 150 items are in process and each spends 10 days in the system, the process must be completing 150 ÷ 10 = 15 items per day.
Solve lead time: 240 tickets, 30 closed per week
A support queue with 240 open tickets that closes 30 per week has an average lead time of 240 ÷ 30 = 8 weeks — a new ticket should expect to wait about two months.
Frequently asked questions
What is Little's Law in simple terms?+
Little's Law states that the average number of items in a system equals the average rate items flow through it times the average time each item spends inside: WIP = throughput × lead time.
Does Little's Law work for any queue?+
It holds for long-run averages in any stable system regardless of arrival pattern or processing order. It breaks down over short periods or when WIP is steadily growing, for example during a ramp-up or a backlog that is never cleared.
How does reducing WIP shorten lead time?+
If throughput stays the same, lead time is WIP divided by throughput, so cutting WIP by a third cuts the average lead time by a third. This is the logic behind WIP limits in lean manufacturing and Kanban software teams.
What is the difference between lead time and cycle time here?+
In Little's Law W is the time an item spends inside whatever boundary you draw. If the boundary starts when work begins it is often called cycle time; if it starts when the request arrives it is lead time. Use WIP measured within the same boundary.
Do units matter?+
Yes. Throughput and lead time must use the same time unit: items per day with lead time in days, or items per hour with lead time in hours. WIP is a count of items and has no time unit.