Little Law Concurrency Calculator

Work out little law concurrency instantly with clear inputs, formula shown and shareable results.

About Little Law Concurrency Calculator

Little's law states L = lambda x W for any stable system, with no assumptions about arrival or service distributions. That makes it a consistency check: if observed concurrency does not match arrival rate times measured latency, one of the three measurements is wrong — usually because latency is measured at a different point than arrivals, or because the system is not actually stable.

Formula

Little's law

L = lambda x W; equivalently W = L / lambda and lambda = L / W

L: Average items in system
lambda: Arrival rate
W: Average time in system

Worked example

With the default values below, Little Law Concurrency Calculator returns Items in system (L) of 95.00. Change any input above and every figure here is recalculated in your browser.

Inputs used

Arrival rateminimum 0.001 req/s: 250 req/s
Average time in systemminimum 0.01 ms: 380 ms
Observed concurrency for comparisonminimum 0: 95

Results

Items in system (L): 95.00
Response time implied by observed concurrency: 380.0 ms
Difference between observed and predicted concurrency: 0.0%
Throughput recovered from L / W: 250.00 req/s

Step by step

1Values used
2Little's law
3Items in system (L)= 95.00
4Response time implied by observed concurrency= 380.0 ms
5Difference between observed and predicted concurrency= 0.0
6Throughput recovered from L / W= 250.00 req/s

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Does it require a steady state?

Yes, that is the only assumption. Over a window where arrivals roughly equal departures it holds exactly, regardless of the distributions involved.

How is it used for troubleshooting?

If concurrency is far above lambda x W, requests are being held somewhere your latency metric does not cover — often a queue ahead of the instrumented code.