Sample Size Calculator
This calculator helps you determine the minimum sample size needed for your research study to achieve a desired level of confidence and precision.
When to Use This Calculator
Use this calculator when you need to determine how many participants or observations you need to collect in order to make statistically valid inferences about a population.
Key Parameters
- Confidence Level: The probability that your sample accurately reflects the population. Common choices are 90%, 95%, and 99%.
- Margin of Error: The maximum likely distance between your sample statistic and the true population parameter. Smaller margins require larger samples.
- Population Size: For finite populations, entering this value adjusts the sample size downward using the finite population correction.
- Estimated Proportion: Your best estimate of the true proportion. Use 0.5 (50%) for the most conservative (largest) sample size.
Formula
For infinite populations:
n = (Z² × p × (1-p)) / E²
For finite populations:
n = (Z² × p × (1-p) × N) / (E² × (N-1) + Z² × p × (1-p))
Where Z is the Z-score for your confidence level, p is the estimated proportion, E is the margin of error, and N is the population size.
Common Z-Scores
| Confidence Level | Z-Score |
|---|---|
| 90% | 1.645 |
| 95% | 1.96 |
| 99% | 2.576 |
