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Sample Size Calculator

Calculate the minimum sample size needed for a survey or study at a given confidence level and margin of error.

Result

Required Sample Size
385

About the Sample Size Calculator

This calculator determines the minimum number of respondents a survey needs to estimate a population proportion within a chosen margin of error and confidence level. It is the standard tool for planning a poll, customer survey, or research study before data collection begins, so you know how many people to reach in advance.

How It Works

You select a confidence level, set a target margin of error as a percentage, and provide an estimated proportion (defaulting to 50%, the most conservative assumption when the true value is unknown). If you know the total population size, you can enter it to shrink the required sample using a finite population correction; leaving it at zero treats the population as effectively unlimited. The result is the smallest whole number of respondents needed to hit your precision target.

n0 = z^2 x p x (1-p) / e^2, where z is the confidence level's z-score, p is the estimated proportion, and e is the margin of error. If population size N is greater than zero: n = n0 / (1 + (n0-1)/N). Otherwise n = n0. The required sample size is n rounded up to the next whole number.

Formula & Methodology

By hand, square the z-score, multiply by p(1-p), and divide by e squared to get n0. For a 95% confidence level (z = 1.96), 50% proportion, and 5% margin of error, that is 1.96^2 x 0.25 / 0.05^2 = 0.9604 / 0.0025 = 384.16, which rounds up to 385, the figure many surveys cite as a rule of thumb. If a finite population is known, apply the correction term afterward to reduce n0 further, since sampling a large share of a small population needs fewer people than an unlimited population would.

Examples

Unknown population survey

At 95% confidence, a 5% margin of error, and 50% estimated proportion with no population entered, n0 works out to 384.16, so the calculator returns a required sample size of 385 respondents.

Known population of 2,000

Using the same 384.16 uncorrected figure but entering a population of 2,000 applies the finite population correction: n = 384.16 / (1 + 383.16/2000) = 384.16 / 1.19158 = 322.46, rounding up to 323 respondents, fewer than the unlimited-population case.

Advantages

  • Prevents both under-sampling, which leaves results too imprecise to trust, and over-sampling, which wastes time and budget on data collection beyond what precision requires.
  • Builds in the finite population correction automatically, so researchers surveying a known, bounded group do not have to apply that adjustment by hand.
  • Defaults to the conservative 50% proportion assumption, giving a safe planning number even before any pilot data exists.

Common Mistakes

  • Assuming a fixed number like 385 or 1,000 always applies, when the required size actually shifts with the chosen margin of error, confidence level, and proportion.
  • Entering the total population size when the true intent is a proportion estimate for a much larger group, which unnecessarily shrinks the calculated sample size.
  • Confusing margin of error with confidence level; a tighter margin of error at the same confidence level requires a much larger sample, since e appears squared in the denominator.

Edge Cases to Watch For

  • Margin of error must be greater than zero; a zero value triggers an error since it would require an infinite sample.
  • Leaving population size at zero skips the finite population correction entirely and treats the population as unlimited.
  • p(1-p) is maximized at p = 50%, so using 50% when the true proportion is unknown produces the largest, most conservative sample size.
  • The finite population correction only meaningfully reduces the sample when the population is small relative to n0; for large populations the corrected and uncorrected values converge.

Common Use Cases

  • Market researchers planning how many customers to survey before launching a satisfaction or preference study.
  • Academic and applied researchers determining respondent counts needed for a thesis, grant proposal, or funded study.
  • Political pollsters and public opinion firms sizing samples to hit a target margin of error for a published poll.
Written & fact-checked by the Calculateus TeamLast updated August 5, 2026How we verify our formulas

Frequently asked questions

Why use 50% as the estimated proportion if I don't know it?

The term p(1-p) in the formula is maximized at p = 50%, which produces the largest (most conservative) required sample size - using 50% when the true proportion is unknown guarantees your sample is large enough regardless of the actual value.

Related calculators

Confidence Interval CalculatorCalculate the confidence interval for a sample mean.Margin of Error CalculatorCalculate the margin of error for a survey result given sample size and confidence level.Correlation Coefficient CalculatorCalculate the Pearson correlation coefficient between two paired sets of numbers.Percentile Rank CalculatorFind what percentile a value falls at within a dataset.

Conclusion

Getting the sample size right before fieldwork begins avoids both wasted respondent recruitment and underpowered results. This calculator turns the standard proportion sample-size formula, plus an optional finite population adjustment, into a quick planning figure.