Economic Order Quantity Calculator
The formula
What the eoq tells you
The order size that trades ordering cost against carrying cost at their intersection — inventory theory’s founding formula.
Calculation: EOQ = √(2 × demand × order cost ÷ holding cost). Enter your inputs and every substitution is shown below the result.
Reading the result
Its real gift is the asymmetry lesson: being somewhat wrong is cheap, so pallet quantities and MOQs can override the number without pain.
Rules of thumb: Compare against current order size: 10× apart signals a policy, not a math, problem
Limitations and best practice
Assumptions (steady demand, one item, no discounts) fail exactly when EOQ would help most — treat as a starting point under real constraints.
This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Frequently asked questions
With quantity discounts, use EOQ how?
Does EOQ make sense with MRP / JIT?
Source & methodology
Harris 1913 / Wilson EOQ model.
Economic Order Quantity: the number, the method and the caveats
You are here because you need a specific number, and you want to see how it was produced before you rely on it. Searchers land on an Economic Order Quantity page for three reasons — to plan, to compare options, and to check that somebody else’s arithmetic is honest. This tool serves all three, and everything after the calculator explains the model instead of hiding it.
The useful way to hold Economic Order Quantity is as a ratio with a story attached: EOQ = √(2 × demand × order cost ÷ holding cost) says how the parts combine, and the 878.3 units figure above is simply that sentence written in numbers. Everything that follows unpacks one clause of the sentence at a time.
The number itself is the easy part. What takes judgement is knowing which inputs are facts in your situation and which are guesses wearing a decimal point — a distinction this page makes explicit for every field above.
Nothing below is stock text pasted around a number: the worked example computes EOQ (per order) = 878.3 units from this tool’s own defaults, and the sensitivity section ranks the inputs that move the result — Holding cost per unit / year first, at ≈5.4 % of the headline for a ten-percent error either way in that input — which is the thread the rest of this guide pulls on.
The Economic Order Quantity formula, explained
One formula, published in full: EOQ = √(2 × demand × order cost ÷ holding cost). Anything you can read, you can reproduce in a spreadsheet, and that reproducibility is the whole point of printing it rather than hiding it behind a button.
Annual demand (units) (example value 12,000) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. Count from the record, not the estimate; whole-number inputs are cheap to verify and expensive to get wrong.
Cost per order placed ($) (example value 225) is a quantity rather than a category — precision here is cheap and worth having. Keep every money input in the same currency; mixing systems quietly corrupts the comparison.
Holding cost per unit / year ($) (example value 7) is a plain measured quantity — the unit shown in the label is the unit the formula expects. Use the figure exactly as the source document states it, not a rounded memory of it — an omitted line is the classic silent error.
A fully worked Economic Order Quantity example
Rather than describe the calculation, here it is end to end — every substitution in order, starting from the inputs above. Starting figures: Annual demand (units), Cost per order placed ($), Holding cost per unit / year ($). The endpoint of that chain is 878.3 units of EOQ (per order), sitting in the “≈ 13.7 orders/year — one every 18 working days” band.
- EOQ = √(2 × 12,000 × $225 ÷ $7.00) = 878
- The U-curve is flat near the optimum — twice the EOQ costs about a quarter more, which is why real constraints win
Annual ordering cost at EOQ — $3,074. Compare it against the main result of 878.3 units before drawing conclusions.
Annual holding cost at EOQ — $3,074. Compare it against the main result of 878.3 units before drawing conclusions.
Total relevant cost — $6,148. This is the number experienced users quote when the headline alone would mislead.
Overwrite any input above and every line of this example updates with it — the substitution is live, not a screenshot of somebody else’s numbers.
The Economic Order Quantity corridor: your result across a realistic band
Read this table as the practical error bar on the headline figure. It answers the question people actually have after seeing a single number: how wrong could this be if the main input is off by ten or twenty percent?
| Holding cost per unit / year setting | EOQ (per order) |
|---|---|
| 80 % of the example value | 982.0 units |
| 90 % of the example value | 925.8 units |
| example inputs | 878.3 units |
| 110 % of the example value | 837.4 units |
| 120 % of the example value | 801.8 units |
The corridor runs from 801.8 units to 982.0 units across that band — which is the range worth planning inside rather than the single 878.3 units point estimate. Reproduce it in the form above by editing Holding cost per unit / year alone; the substitution steps will follow your figures exactly.
What actually moves your Economic Order Quantity
This list was computed for this specific engine just now: each numeric input was nudged ±10 % while every other field held its example value, and the EOQ (per order) was recalculated from scratch. Read it as a map of where Economic Order Quantity is fragile — drawn for the example inputs, which is the map you want when deciding what to measure carefully.
- Holding cost per unit / year +10 % → Economic Order Quantity = 837.4 units · −10 % → 925.8 units (the EOQ (per order) shifts ≈5.4 %)
- Nudge Annual demand by ±10 % and Economic Order Quantity lands between 833.2 units and 921.2 units (sensitivity ≈5.1 %)
- Nudge Cost per order placed by ±10 % and Economic Order Quantity lands between 833.2 units and 921.2 units (sensitivity ≈5.1 %)
Holding cost per unit / year is the dominant lever here: ten percent either way moves the result by about 5.4 %, from 837.4 units to 925.8 units. Spend your verification effort there first, and Annual demand is effectively tied with it (≈5.1 % for the same nudge), so verify the pair together. The remaining fields can sit at safe defaults without materially changing the answer — knowing which is which is what separates a careful calculation from an anxious one.
Interpreting the Economic Order Quantity verdict
The value above only becomes useful the moment you know what it is being measured against. The default case lands in the “≈ 13.7 orders/year — one every 18 working days” band, and bands are deliberately wide because real situations overlap. How much of that band is luck? On Holding cost per unit / year alone ten percent either way covers 837.4 units to 925.8 units. The practical reading rules: ask what would have to change to move you one band. If the answer is “a small, plausible input difference”, the band itself is not the finding — the uncertainty is.
In Business & Entrepreneurship, Economic Order Quantity is one instrument in an orchestra: on its own it is a number, next to Annual ordering cost at EOQ and Annual holding cost at EOQ it becomes a diagnosis. The tools linked above exist so the headline never has to carry that weight alone.
Common mistakes with Economic Order Quantity (and the fix)
Assumptions (steady demand, one item, no discounts) fail exactly when EOQ would help most — treat as a starting point under real constraints. This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Reusing an Economic Order Quantity from last season. In Business & Entrepreneurship the inputs are the thing that drifts; the formula does not.
Attention is also misallocated between fields. Having measured this engine, we can say where it belongs: Holding cost per unit / year first, everything else second.
A final trap is presentation: reporting Economic Order Quantity to more decimal places than the inputs support. The tool prints what the arithmetic gives; you should quote only what your least precise field justifies.
Before you trust your Economic Order Quantity: a short checklist
- Compare the result with one independent method or published benchmark.
- Re-run the calculation with a ±10 % stress on the two most sensitive inputs.
- Put Holding cost per unit / year under a magnifier; the sensitivity table above is the reason why.
- Check that every field the formula needs actually arrived from a document, not from recollection.
- Recompute once with the dominant input deliberately set low, and see whether the decision changes.
- Repeat the ±10 % test on the inputs that matter and see whether the decision — not just the number — still holds.
A routine for decision-grade Economic Order Quantity
Using a calculator well sounds trivial, but the difference between a decision-grade figure and a throwaway one lives entirely in the routine. The routine for Economic Order Quantity takes a minute to learn and applies to every input above.
Step 1 — collect, then type. Everything this tool asks for is listed above (annual demand (units), cost per order placed ($), holding cost per unit / year ($)). Pull each figure from something you can point at — paperwork, a dashboard, a label — before touching a field. Guesswork at the input stage cannot be repaired at the interpretation stage. Repeating a calculation with the same numbers proves only that the arithmetic is reliable — which is worth knowing.
Step 2 — start from the case you can defend. Enter pessimistic-but-honest figures first; the optimistic run is a ceiling, not a plan. A conclusion that holds on conservative inputs holds everywhere. Numbers are cheap to produce and expensive to retract; the extra minute is the cheapest insurance available.
Step 3 — isolate your variables. Change one field, observe, revert. The live sensitivity list does the ranking for the default inputs; verify it against your own, because dominance shifts when the starting point shifts. Estimates improve most when the worst case is written down in ink.
Step 4 — run the scenario trio. Expected, pessimistic, optimistic. The gap between pessimistic and expected is the number to plan against; the optimistic result is useful only as a ceiling. Half of a good calculation is knowing which input you would hate to be wrong about.
Step 5 — record the context, not just the number. Note today’s date and the inputs alongside the 878.3 units output. Six months from now the context is what turns this figure into a trend. Say the answer out loud before you save it; if it sounds wrong, the model did not change, your understanding did.
Who actually uses Economic Order Quantity — and when
In Operations the figure computed here is usually the first one somebody asks to see. Having it — with the formula behind it — changes your position in the conversation from participant to reference. The input you reach for first is usually the one you measured longest ago.
Used properly this is a five-minute filter that saves weeks. Compute Economic Order Quantity, reject what fails, and only then bring in the expensive analysis for the survivors. The fastest sanity test is to guess the answer first and see how far the calculation disagrees.
Treat Economic Order Quantity like a smoke alarm rather than a painting — its value is in being tested periodically, not in being admired once. The input you reach for first is usually the one you measured longest ago.
The questions that come up most about Economic Order Quantity
What affects Economic Order Quantity the most?
Economic Order Quantity is driven above all by Holding cost per unit / year. Perturbing only that field by ten percent either way produced 837.4 units against the 878.3 units baseline — a ≈5.4 % response, while Annual demand manages ≈5.1 %.
Do annual demand and holding cost per unit / year matter equally?
Effectively. Measured on this engine they land at ≈5.4 % and ≈5.1 % for the same ten-percent nudge, so the honest advice is to get both right; chasing precision in only one of them buys almost nothing.
What is a typical Economic Order Quantity?
With the example inputs on this page the result is 878.3 units, labelled “≈ 13.7 orders/year — one every 18 working days”. “Typical” varies with situation, which is why every result here ships with its verdict band and its sensitivity list: they turn one figure into a range you can locate yourself inside.
How do I calculate Economic Order Quantity by hand?
EOQ = √(2 × demand × order cost ÷ holding cost) is the entire method. Work the inputs in that order — EOQ = √(2 × 12,000 × $225 ÷ $7.00) = 878 — and you will reach 878.3 units on the default figures, the same number this tool prints.
What happens to Economic Order Quantity if holding cost per unit / year changes by 10 %?
Try it in the form above and the printed substitution will follow you; the pre-computed answer for the defaults is 837.4 units to 925.8 units across the ten-percent probe, i.e. ≈5.4 % sensitivity on the EOQ (per order).
Is the Economic Order Quantity result of 878.3 units good or bad?
The tool answers “what”, not “whether”: 878.3 units carries the verdict “≈ 13.7 orders/year — one every 18 working days” for the default case, which is a starting interpretation rather than a verdict on your situation. Re-run with your own figures and compare the bands.
Is Economic Order Quantity accurate?
The arithmetic is exact: EOQ = √(2 × demand × order cost ÷ holding cost) is evaluated with full floating-point precision and every substitution is printed in the worked example. What limits accuracy is input quality and the model’s assumptions, so treat the 878.3 units result as the correct answer to the question you typed — and check the assumptions section before acting on it.
How do I calculate Economic Order Quantity manually?
Write down the inputs, then follow the printed steps in order — EOQ = √(2 × demand × order cost ÷ holding cost). A spreadsheet replicates it with two or three cells. The manual route is worth doing once to build intuition; after that the calculator saves time and eliminates transcription slips.
With quantity discounts, use EOQ how?
Compute EOQ at each price break, discard infeasible sizes, then compare total annual cost including the price — the classic all-units procedure.
Does EOQ make sense with MRP / JIT?
As a diagnostic yes: how far actual batches sit above EOQ reveals the setup-cost economics you have not yet attacked.
Do I need an account to use this Economic Order Quantity calculator?
No, and no data leaves the tab. The engine runs in the page itself, which is why the worked example, the bands and the sensitivity ranking all respond instantly to your keystrokes.
The vocabulary of Economic Order Quantity
- Annual ordering cost at EOQ
- $3,074 in the default Economic Order Quantity calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Annual holding cost at EOQ
- $3,074 for the Economic Order Quantity worked case; it sits next to the main result because it carries context the headline leaves out.
- Total relevant cost
- $6,148 in the default Economic Order Quantity calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- EOQ (per order)
- The primary output of this tool: 878.3 units for the default inputs, computed exactly from EOQ = √(2 × demand × order cost ÷ holding cost).
- Worked example
- The step-by-step substitution printed above, so the arithmetic can be re-derived by hand or in a spreadsheet.
- Verdict band
- The plain-language label — here “≈ 13.7 orders/year — one every 18 working days” — mapping the computed figure onto experience-based ranges for Business & Entrepreneurship.
- Sensitivity (±10 %)
- How far the Economic Order Quantity moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
Methodology, sources and limits
The model is published arithmetic implemented exactly as written: EOQ = √(2 × demand × order cost ÷ holding cost). Source of record: Harris 1913 / Wilson EOQ model. Any other implementation of this model should return the same figure for the same inputs. If one does not, the difference is in its assumptions — which this page prints and that one probably does not.
Treat the output as a precise answer to the question you typed: exact arithmetic, transparent formula, published source, no hidden rounding. The design constraint was set by usefulness rather than by comfort: an estimate you can interrogate beats an answer you have to trust.
After the number: what to do with it
Save the number together with its inputs and today’s date; an Economic Order Quantity figure without context is unusable the moment an input changes.
This page was written for people who need one trustworthy number before their next decision, and the promise is that nothing above required trust. Bookmark the tool, re-run it whenever an input moves by more than a few percent, and keep the date with the number.