Little's Law Calculator
Relate work in process, throughput and lead time in a stable system.
In short
Relate work in process, throughput and lead time in a stable system.
Formula: WIP = Throughput × Lead time (so Lead time = WIP ÷ Throughput, and Throughput = WIP ÷ Lead time)
What this calculator does
One multiplication or one division, chosen by the user. The calculator solves for whichever of the three quantities is selected and shows which two measured averages it used.
Use it to turn What do you want to work out?, Average throughput, Average lead time, Average work in process into a checked result you can compare, copy, or rerun with different assumptions.
The page shows the formula, a numeric worked example, and the assumptions that affect this professional & industry calculation.
Inputs and what they mean
- What do you want to work out?
- — The third figure is the answer; the other two are the averages you measured..
- Average throughput
- — Average units leaving the system per hour over the window. Ignored when throughput is what you are solving for..
- Average lead time
- — Average time one unit spends inside the same boundary. Ignored when lead time is what you are solving for..
- Average work in process
- — Average number of units inside the boundary. Ignored when work in process is what you are solving for..
How to use it
- Enter your own figures — the calculator never fills in a rate, price or benchmark for you.
- Press Calculate to see the result.
- Read the formula, variables, assumptions and source below the result before you rely on it.
Formula
WIP = Throughput × Lead time (so Lead time = WIP ÷ Throughput, and Throughput = WIP ÷ Lead time).
Inputs used: What do you want to work out?, Average throughput, Average lead time, Average work in process.
Edge handling: Average throughput cannot be negative.; Average throughput must be no more than 1000000000000.; Average lead time cannot be negative.; Average lead time must be no more than 1000000000000.; Average work in process cannot be negative..
Worked example
Work in process implied by a stable line
- Start with What do you want to work out?: wip, Average throughput: 128, Average lead time: 3.5, Average work in process: 0.
- Apply the method: WIP = Throughput × Lead time (so Lead time = WIP ÷ Throughput, and Throughput = WIP ÷ Lead time).
- A line averaging 128 units an hour with a 3.5 hour lead time holds about 448 units between its start and end points.
Reading the result
The headline figure is the main answer. Any breakdown underneath shows the parts that make it up, so you can check the working and see what changes when you adjust an input.
Limitations and assumptions
- Inputs outside the supported range are rejected rather than forced into a result.
- The result depends on the values you enter for this little's law calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.
Reference: Massachusetts Institute of Technology — 2.854 Introduction to Manufacturing Systems
Last reviewed:
Common questions
Where does this formula come from?
MIT OpenCourseWare 2.854 Introduction to Manufacturing Systems — the published queueing result L = λW: for a stable system the average inventory equals the average throughput rate multiplied by the average time in system, whatever the arrival or service distributions. See the source link on this page.
What kind of calculation is this?
For a stable system observed over a long enough window, the average number of items inside it equals the average arrival or departure rate multiplied by the average time an item spends inside. Check the formula, example, and limitations on this page before using the result for a real professional & industry decision.
What are its limits?
Exact only for a stable system observed over a long enough window; for a short window, or while work in process is growing or draining, the three averages will not reconcile. It is a relationship between averages — it says nothing about the spread of individual lead times, or about why the work in process is what it is. Arithmetic over the figures entered — it cannot tell whether the measurements behind them are right. A measured result, an industry benchmark and an organisation's target are three different things; only the entered figures are used.
How do I use the Little's Law Calculator?
Enter the required values for What do you want to work out?, Average throughput, Average lead time, Average work in process. The calculator applies the formula on this page and shows the main result with any supporting breakdown so you can check the arithmetic.
What formula does the Little's Law Calculator use?
WIP = Throughput × Lead time (so Lead time = WIP ÷ Throughput, and Throughput = WIP ÷ Lead time) The visible formula section above lists the calculation path and the edge cases the page handles, so the result can be checked without relying on the form alone. Check the formula, example, and limitations on this page before using the result for a real professional & industry decision.
Can the Little's Law Calculator be used for exact decisions?
Use it as a calculation aid, not as a substitute for checking the underlying rule, contract, policy, or professional advice that applies to your situation. When a result depends on local rules, personal details, prices, or dates, enter those values yourself and confirm them before acting.
Formula, source and verification
For a stable system observed over a long enough window, the average number of items inside it equals the average arrival or departure rate multiplied by the average time an item spends inside.
The question it answers: If we know two of work in process, throughput and lead time, what is the third?
The formula
WIP = Throughput × Lead time (so Lead time = WIP ÷ Throughput, and Throughput = WIP ÷ Lead time)
- L — Average work in process
- (count). Average number of units inside the boundary being measured.
- λ — Average throughput
- (count/h). Average units leaving the boundary per hour over the same window.
- W — Average lead time
- (h). Average time one unit spends inside the boundary.
Units: Units and hours; the rate is units per hour. Any consistent pair of time units may be used as long as all three figures share them.
What kind of calculation this is
Deterministic formula. The same inputs always give the same answer. The maths is fixed and does not depend on judgement.
Method
One multiplication or one division, chosen by the user. The calculator solves for whichever of the three quantities is selected and shows which two measured averages it used.
Assumptions built into the result
- Mathematical: The system is stable over the window: units are not accumulating or draining on average.
- Mathematical: All three quantities are averages over the same window and the same boundary.
- Mathematical: Throughput and lead time use the same time unit.
Figures this calculator will never guess for you
- No industry benchmark, target lead time or target work in process is supplied or applied.
- The law is not applied to a system the user has described as growing or draining; the condition is stated, not assumed away.
- No queueing distribution, batch size or scheduling rule is inferred.
Limitations
- Exact only for a stable system observed over a long enough window; for a short window, or while work in process is growing or draining, the three averages will not reconcile.
- It is a relationship between averages — it says nothing about the spread of individual lead times, or about why the work in process is what it is.
- Arithmetic over the figures entered — it cannot tell whether the measurements behind them are right.
- A measured result, an industry benchmark and an organisation's target are three different things; only the entered figures are used.
Source and version
- Standard or reference
- Little's Law — the relationship between work in process, throughput and flow time — MIT OpenCourseWare (MIT OpenCourseWare 2.854 Introduction to Manufacturing Systems — the published queueing result L = λW: for a stable system the average inventory equals the average throughput rate multiplied by the average time in system, whatever the arrival or service distributions.)
- Published source
- Massachusetts Institute of Technology — Fall 2016
- Formula version
- Version 1
- Verification
- Reviewed against the cited source on
- How much weight the source carries
- Academic
- Applies to
- Currency
- The result is a ratio or index, so it does not depend on currency.
Cite this page
Free Calculator. (2026, September 16). Little's Law Calculator. https://freecalculator.tech/tools/littles-law-calculator
"Little's Law Calculator." Free Calculator, 16 Sept. 2026, https://freecalculator.tech/tools/littles-law-calculator.
Little's Law Calculator — Free Calculator, https://freecalculator.tech/tools/littles-law-calculator
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