Little's Law Calculator (Concurrency, Throughput, Latency)
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Little's Law Calculator (Concurrency, Throughput, Latency) by TheCalcTools
How the Little's Law Calculator (Concurrency, Throughput, Latency) works
Little’s law says that in a stable system the average number of items inside equals the arrival rate times the average time each spends there: L = λW. It holds for any queue, regardless of arrival patterns.
Use it to size thread pools and connection pools (concurrency = requests per second × latency), or to estimate wait times from queue length.
The formula
Worked example
Using the default values shown in the calculator:
| Find | Items in the system (concurrency) |
|---|---|
| Throughput (per second) | 500 |
| Time in the system (seconds) | 0.12 |
| Items in the system | 60 |
- 500 requests a second at 120 ms each means 60.00 in flight on average.
Result:
| Items in the system (L) | 60.00 |
|---|---|
| Throughput λ (per second) | 500.00 |
| Time in the system W (seconds) | 0.1200 |
| Throughput per minute | 30,000 |
Frequently asked questions
How many concurrent connections for 500 requests/s at 120 ms?
500 × 0.12 = 60 on average; add headroom for peaks.
Sources and further reading
- Wikipedia: Little's law
- Little JDC (1961). A proof for the queuing formula L = λW. Operations Research 9(3):383-387
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.