Sample Size Calculator

This Sample Size Calculator helps you determine how many observations are needed to achieve statistically reliable results for surveys, polls, and research studies.

If unsure about the proportion, use 50% for maximum sample size.

Required Sample Size

Sample Size (n)
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Sample Size Calculator

A sample size calculator helps determine how many observations or respondents are required to achieve accurate and reliable results in surveys, experiments, and research studies. Choosing the correct sample size ensures that conclusions drawn from the data truly represent the population.

What Is Sample Size?

Sample size refers to the number of individuals, observations, or data points selected from a larger population. A properly calculated sample size reduces bias, minimizes error, and increases confidence in statistical findings.

Why Sample Size Is Important

  • Ensures survey and research results are statistically reliable
  • Reduces margin of error
  • Improves confidence in conclusions
  • Prevents over-sampling or under-sampling

Sample Size Formula

This calculator uses the standard statistical formula:

n = (Z² × p × (1 − p)) ÷ e²

Where:

  • n = required sample size
  • Z = Z-score based on confidence level
  • p = estimated population proportion
  • e = margin of error

Common Confidence Levels

  • 90% confidence level → Z = 1.645
  • 95% confidence level → Z = 1.96 (most common)
  • 99% confidence level → Z = 2.576

Where Sample Size Calculations Are Used

  • Market research and opinion polls
  • Academic and scientific research
  • Quality control and testing
  • Medical and social studies
  • Business analytics and forecasting

Frequently Asked Questions

A good sample size depends on the confidence level, margin of error, and population proportion. For many surveys, a sample size of around 385 is sufficient for a 95% confidence level with a 5% margin of error.
Using 50% produces the maximum required sample size. This is a safe and conservative choice when the true population proportion is unknown.
A smaller margin of error requires a larger sample size because more data is needed to achieve higher precision.
For very large populations, population size has little effect on sample size. However, for small populations, a finite population correction may be required.
Yes. This calculator uses standard statistical formulas commonly taught in academic research, statistics, and survey methodology.