Calculate the minimum sample size needed to achieve your target precision — for estimating means, detecting differences between two groups, or measuring proportions. Includes a precision vs sample size trade-off chart.
Select the study type, then fill in the inputs. All calculations use two-sided tests.
Choose your study type, enter the parameters, and press Calculate to see the minimum sample size with a precision trade-off chart.
StDev of 8 minutes, 95% confidence, ±2 minutes tolerance. Enter the lab and find the minimum sample you actually need.
Use the calculator above to find the minimum sample size needed to achieve the precision you want — for estimating a mean, detecting a difference between two groups, or measuring a proportion. The right sample size protects you from drawing false conclusions and from over-spending on data collection.
Sample size is the number of observations you need so that your estimate is precise enough, or that your hypothesis test has enough power to detect a real difference. Too small and the result is noise; too large and you waste effort and money. The right size depends on the variability of the data and the size of effect you want to detect.
For a mean: n = (Z × σ ÷ E)², where σ is the standard deviation and E is the margin of error you want. For a proportion: n = (Z² × p(1−p)) ÷ E². For comparing two groups, the formula includes both the desired statistical power and the minimum detectable difference. The calculator handles each case.
A team wants to estimate average satisfaction within ±0.2 points with 95% confidence. The standard deviation of past scores is 1.5. n = (1.96 × 1.5 ÷ 0.2)² ≈ 216 customers. Anything less and the interval is too wide to detect the changes leadership cares about.
If they accept ±0.3 precision instead, sample size drops to 97 — less than half. The calculator makes the precision-vs-cost trade-off explicit, so leadership can choose how much rigour they want to pay for before commissioning the survey.
Sample size discipline saves money on over-collection and protects against decisions made on under-powered data. It is the single most leveraged statistical choice in any improvement project.
Use this calculator before any survey, audit, capability study, A/B test or DOE. Calculating the right n in advance is far cheaper than discovering after the fact that the sample wasn’t big enough.
Sample size sits in DMAIC Measure. Combined with power analysis and effect size, it ensures the inferential workflow (hypothesis tests, CIs, DOE) actually produces reliable conclusions.
Decide what effect size matters before collecting data. Use the calculator to find n, then add a margin (10-20%) for missing data and non-response. Re-check assumptions (σ, p) once early data is in.
Pair sample size with confidence intervals, hypothesis testing and power analysis for a complete inferential design workflow.
For a mean: n = (Z × σ ÷ E)². For a proportion: n = (Z² × p(1−p)) ÷ E². For comparing two groups, include desired power and the smallest difference you need to detect.
Too small and you cannot detect real differences; too large and you waste time and money. The right size delivers the precision you need at the minimum cost.
No. Beyond a point, doubling sample size only narrows the interval by 1/√2 (~30%). The cost grows linearly while precision grows with the square root — diminishing returns set in quickly.
95% is the default for most business decisions. Use 99% for safety-critical or regulatory contexts. Use 90% only when speed and cost matter more than rigour.
Use power-based formulas that incorporate the desired statistical power (commonly 80%), the significance level (commonly 5%), and the smallest difference worth detecting (the minimum detectable effect).
Want to understand how sample size decisions affect your measurement system and conclusions? The Green Belt covers this in full.
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