Quality & Statistics
Sample Size Calculator
The sample size needed for surveys, quality inspections, and experiments — for proportions or means, with finite population correction.
n = Z²·p(1−p) ÷ E²Use 50% if unknown (maximizes sample size)
Why sample size matters
Too small a sample gives unreliable conclusions. Too large wastes time and money. The right sample size balances statistical confidence with practical resource constraints.
- Ensures statistically valid conclusions
- Optimizes inspection costs
- Required for AQL sampling plans
- Drives experiment design
Sample size formulas
For proportions
n = Z² × p × (1 − p) ÷ E²For means
n = Z² × σ² ÷ E²Finite population correction
n_adj = n ÷ (1 + (n − 1) ÷ N)Z is the z-score for the confidence level, E the margin of error, σ the standard deviation, and N the population size.
Z-score by confidence level
| Confidence | Z-score | α | Common use |
|---|---|---|---|
| 80% | 1.282 | 0.20 | Preliminary studies |
| 90% | 1.645 | 0.10 | General screening |
| 95% | 1.960 | 0.05 | Standard (most common) |
| 99% | 2.576 | 0.01 | High-confidence |
| 99.9% | 3.291 | 0.001 | Critical applications |
Frequently asked questions
What proportion should I use if I don’t know the expected defect rate?
Use 50% (p = 0.5), which gives the maximum (most conservative) sample size. As the true proportion moves away from 50% in either direction, the required sample size decreases.
When should I use finite population correction?
Apply finite population correction when the sample is more than 5% of the total population. For large populations (over 100,000), the correction has negligible effect.
How do I estimate standard deviation for means?
Options: (1) use data from a pilot study, (2) use historical process data, (3) estimate it as range ÷ 4 if you can estimate the range, or (4) use a conservative estimate and adjust after initial data collection.