Find the cycle count sample size for a target confidence and margin of error on a finite population, plus the counts per day your cycle needs.
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Short answer
Cycle count sample size uses the finite-population proportion formula: n₀ = z² × p × (1 − p) ÷ e², then n = n₀ ÷ (1 + (n₀ − 1) ÷ N). For 8,400 records at 95% confidence, a ±3-point margin and a 5% expected error rate, count 198 records — about 2.4% of the population.
Counting everything is expensive and counting a handful proves nothing. A cycle count sample size sits between the two: count enough records to state an inventory accuracy figure with a known margin of error, and stop there.
Enter the population in scope, the confidence and precision you want, and roughly how wrong you expect the records to be. You get the sample size, what it means as a share of the population, and the daily count rate needed to get through it — alongside the rate a full wall-to-wall count would demand.
One caution before the numbers: this measures the accuracy of a population. It is not a plan for deciding which items to count, and it is not designed to find the specific records that are wrong.
Your numbers
records
Count the unit you actually count — usually SKU-location combinations, not SKUs.
points
±3 is a common operational target.
%
Last cycle's measured error rate. With no history use 50%, which gives the largest and safest sample.
days
Working days to complete one cycle.
/day
All counters combined. Measure it, don't assume it.
Result
Sample size to count
198 records
2.4% of 8,400 records, for ±3 points at 95% confidence
z-value applied1.960
Sample as share of population2.4%
Counts per day to finish the sample in 20 days10
Counts per day for 100% coverage in 20 days420
Days to cover the population at 90/day93.3 days
Days to finish the sample at 90/day2.2 days
Sample size at each confidence level, for 8,400 records and a 5.0% expected error rate. Halving the margin roughly quadruples the sample.
Counting 198 of 8,400 records — 2.4% — supports an accuracy figure of ±3 points at 95% confidence, provided the records are selected at random. That is 10 counts a day across a 20-day cycle.
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The formula
n₀ = z² × p × (1 − p) ÷ e² then n = n₀ ÷ (1 + (n₀ − 1) ÷ N)
n
Sample size after the finite-population correction — the number of records to count.
n₀
Unadjusted sample size, the answer you would need from an infinitely large population.
z
z-value for the confidence level. 1.645 at 90%, 1.960 at 95%, 2.576 at 99%.
p
Expected proportion of inaccurate records. Use last cycle's error rate, or 50% if you have no history at all.
e
Margin of error you will accept, as a proportion. ±3 points means e = 0.03.
N
Population size: the count of records in scope — SKUs, bin locations, or SKU-location combinations.
This estimates one proportion — the share of records that are wrong — from a simple random sample. It is a planning tool for a cycle-count programme, not an audit sampling plan. If the sample size is being used to support a financial statement assertion, your auditor's methodology takes precedence over this one.
Worked example
Population in scope
8,400 SKU-locations
Confidence level
95%
Margin of error
±3 points
Expected error rate
5%
Cycle length
20 working days
Counting capacity
90 records per day
Result
198 records — 2.4% of the population, 10 counts a day
n₀ = 1.960² × 0.05 × 0.95 ÷ 0.03² = 202.8. The finite-population correction divides that by 1 + (201.8 ÷ 8,400) = 1.0240, giving 198 records. Spread over a 20-day cycle that is 10 counts a day, well inside a 90-per-day capacity. Counting all 8,400 records instead would take 420 a day, or 93 working days at current capacity.
What the formula assumes
The maths is standard sample sizing for a population proportion. The assumptions behind it are the part that matters, because a cycle-count programme breaks several of them without anyone noticing.
Records are selected at random. If counters pick easy bins, or the schedule always lands on the same aisle on a Monday, the sample is not random and the margin of error is fiction.
Each record is simply right or wrong. A binary test. If you grade accuracy by value or by tolerance band, this formula sizes the wrong question.
One measurement per record, one period. Counting the same fast movers twelve times a year does not give you twelve independent observations of the population.
The population is stable during the cycle. Heavy receiving and picking traffic mid-count introduces timing differences that look like errors.
The result describes the population, not any single record. "94% ± 3 points accurate" says nothing about whether bin A-14-3 is right.
Precision is what costs money, not confidence
Margin of error sits in the denominator as a square, so halving it roughly quadruples the sample. Confidence only changes the z-value, which is a much gentler lever. The grid below uses a population of 8,400 records and a 5% expected error rate:
Margin of error
90% confidence
95% confidence
99% confidence
±1 point
1,115
1,500
2,293
±2 points
310
433
721
±3 points
141
198
337
±5 points
52
73
125
Sample sizes for N = 8,400 and an expected error rate of 5%. This is why ±1 point targets are usually abandoned within two cycles — and why ±5 points at 90% confidence is enough for a first programme, which only has to establish whether accuracy is 70% or 95%.
Stratify before you sample
A single random sample across the whole warehouse treats a $40,000 A-class item and a box of washers as equally important. Almost nobody wants that. The usual fix is to stratify: rank items by annual value with the ABC analysis calculator, size a separate sample per class, and count A items monthly against C items once or twice a year. Frequency and sample size are then two decisions instead of one — cadence per class, precision per sample.
Turning the sample into a cycle count schedule
Divide the sample by the working days in your cycle for the daily count rate, then compare it with what a counter can genuinely do. Somewhere between 40 and 100 bin counts per person-day is normal depending on how scattered and how countable the stock is; measure your own rate over a week rather than assuming one.
The population figure is the input people get wrong most often. "Number of SKUs" and "number of SKU-location combinations" can differ by a factor of five in a multi-bin warehouse, and the second one is what you actually count. With ERPray you ask for it — "how many distinct item and bin combinations have on-hand quantity above zero" — and the query is shown with the answer so the denominator in your accuracy report is defensible.
Frequently asked questions
How do you calculate cycle count sample size?
Compute n₀ = z² × p × (1 − p) ÷ e², then apply the finite-population correction n = n₀ ÷ (1 + (n₀ − 1) ÷ N). At 95% confidence (z = 1.960), a 5% expected error rate and a ±3-point margin, n₀ is 202.8; against a population of 8,400 records that reduces to 198 records to count.
What z-value should I use for 95% confidence?
1.960 for a two-sided 95% interval. Use 1.645 for 90% and 2.576 for 99%. These are the standard normal values and are the ones this calculator applies. The normal approximation gets shaky when the expected number of errors in the sample is very small, roughly under five.
What expected error rate should I assume?
Last cycle's measured error rate, if you have one. With no history, 50% is the conservative choice because p × (1 − p) is largest there, giving the biggest sample. Assuming a low error rate to keep the sample small is circular reasoning — you are assuming the answer you set out to measure.
How often should I cycle count?
Frequently enough that errors are found before they cause a shortage, which usually means by class rather than uniformly. A items monthly or on every replenishment, B items quarterly, C items once or twice a year is a common pattern. Frequency and sample size are separate decisions: one sets cadence, the other sets statistical precision.
Is cycle counting a substitute for a full physical inventory?
Operationally, often yes — a well-run cycle-count programme catches errors far sooner than an annual count. For financial reporting it depends on your auditor and jurisdiction. Many will accept cycle counting supported by documented procedures and accuracy statistics; that decision is theirs to make, not this calculator's.
Should the population be SKUs or bin locations?
Whatever unit you actually count and report accuracy on. In a multi-bin warehouse that is normally SKU-location combinations, which can be several times the SKU count. Mixing the two — sizing on SKUs and counting locations — quietly invalidates the margin of error you publish alongside the result.
This calculator needs you to find the inputs first. ERPray pulls them from your own ERP account and computes the answer live — with the exact query shown so you can check it.