Math & Science
Sample Size Calculator
Calculate required sample size for surveys
Formulas and edge cases are reviewed against authoritative references before publication. For methodology, editorial standards, or corrections, use the links below.
Frequently asked questions
Why use 50% proportion?
50% gives maximum variance, ensuring sample is large enough for any result.
Does population size matter?
Only for small populations. For populations over 20,000, effect is minimal.
What margin of error should I use?
5% is standard for most surveys. Lower margin requires larger sample.
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About this tool
Inputs
- Confidence Level
- Margin of Error
- Population Size
- Expected Proportion
- 90%
- 95%
- 99%
Results
- Required Sample Size
- Formula Used
- n = (Z² × p × (1-p)) / E²; For finite population: n' = n / (1 + (n-1)/N)
The Sample Size Calculator is built for anyone who needs a quick, reliable answer. Enter your numbers and let the formula do the heavy lifting. Many practical problems — from engineering to daily budgets — reduce to straightforward arithmetic once you identify the right formula. Every calculator on this page uses a well-defined formula — the same one you would find in a textbook, applied instantly. Provide confidence level, margin of error, population size, expected proportion, 90%, 95% and 99% to get started.
The tool derives required sample size, formula used and n = (z² × p × (1-p)) / e²; for finite population: n' = n / (1 + (n-1)/n) from your entries. The ability to calculate required sample size for surveys comes up more often than most people expect — in professional work, academic projects, and everyday planning. 50% gives maximum variance, ensuring sample is large enough for any result. If the result seems implausible, work backward from the answer to see where the logic breaks. Run the calculation with your best-case and worst-case assumptions to bracket the likely outcome.