Little's law calculator
Little's law links three averages of any stable system: how many items are inside, how fast they arrive and how long each one stays. Pick the one you want, enter the other two in the units you have, and the calculator does the conversion.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Choose what to find: the number in the system L, the rate λ or the time W.
- Enter the other two quantities. The rate and the time have their own units and can differ (per hour and minutes, for example).
- The answer appears in the unit you picked, with the rate per hour and the time in minutes for comparison.
L = λ × W, so λ = L ÷ W and W = L ÷ λ. The calculator first turns the rate into items per second and the time into seconds, then converts the answer back.
Worked example
A coffee shop serves 10 customers a minute, and each one spends 3 minutes inside from the door to the counter and out. On average L = 10 × 3 = 30 people are inside, which is a rate of 600 per hour.
The other way round: a help desk has 30 open tickets and closes 120 per hour; each ticket is open for W = 30 ÷ 120 = 0.25 h = 15 min on average.
Tips
- Use averages over the same period. Mixing a busy-hour rate with a daily average time gives nonsense.
- Count the whole system or one part: the law works for the queue only (waiting time) or the queue plus service (total time), as long as L and W refer to the same part.
- The queue calculator for M/M/1 and M/M/c gives L and W from arrival and service rates, and they satisfy L = λW.
Frequently asked questions
What is Little's law?
In a stable system the average number of items inside equals the arrival rate times the average time each one spends there, L = λW. It holds for shop queues, web servers, support tickets and work in progress on a production line.
Does Little's law need a particular queue model?
No. It does not depend on the distribution of arrivals or service times, the number of servers or the order of service. It only needs long-run averages of a system that is not growing without bound.
How is it used in kanban and lean?
As cycle time = work in progress ÷ throughput. With 40 tickets in progress and 8 finished a day, each ticket takes 5 days on average; cutting work in progress to 20 halves it.
Which rate should I enter, arrivals or departures?
In a stable system they are equal on average, so either works. If the queue keeps growing, the system is not stable and the law does not describe it.