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Sample Size Calculator
Determine the minimum number of subjects required for your study or survey based on your target confidence level, margin of error, and population size.
Calculate required sample size
Results
| Z-Score | — |
|---|---|
| Population Proportion (p) | — |
| Margin of Error (E) | — |
| Required Sample Size | — |
How to Determine Sample Size
Selecting the right sample size is critical for the validity of statistical research. If the sample size is too small, you won't get statistically significant results; if it's too large, you waste resources.
The required sample size is calculated using the following variables:
- Confidence Level: The probability that the sample represents the population. Commonly set to 95%, which corresponds to a Z-score of 1.96.
- Margin of Error: The maximum acceptable difference between the sample result and the true population value (often called confidence interval).
- Population Proportion: The estimated percentage of the sample that has a particular attribute. Setting this to 50% (0.5) is the most conservative choice because it maximizes the required sample size.
- Population Size: The total number of people in the target group. If this is very large or unknown, we use the infinite population model. If it is small, we apply a finite population correction.
Formulas for Sample Size
For an infinite or large population, the sample size n₀ is calculated as:
n₀ = (Z² * p * (1 - p)) / E²
For a finite population N, the corrected sample size n is:
n = (n₀ * N) / (n₀ + N - 1)
FAQ
What is a Z-score?
A Z-score (standard score) measures how many standard deviations a value is from the mean. In sample size calculation, it represents the statistical confidence level. For example, a 95% confidence level means you are within 1.96 standard deviations of the mean.
Why does 50% proportion give the largest sample size?
The term p * (1 - p) is maximized when p = 0.5. For instance, 0.5 * 0.5 = 0.25, whereas 0.3 * 0.7 = 0.21. Since this term is in the numerator, a proportion of 50% ensures your sample is large enough regardless of what the actual proportion turns out to be.