Sample Size Calculator

How many survey responses you need for a given confidence level and margin of error

Required sample size
385

Using 50% expected proportion gives the most conservative (largest) sample size — safe to use whenever you don't already have a good estimate.

Frequently Asked Questions

Why does using 50% as the expected proportion give the largest sample size?
Because the underlying formula's p×(1−p) term is maximized at p=50%, so using it whenever you don't have a better prior estimate guarantees your sample size is large enough regardless of the true (unknown) proportion — it's the conservative, safe default.
When does population size matter?
Only when your population is relatively small and you're sampling a meaningful fraction of it. For large or effectively unlimited populations, leave it blank — the finite population correction has almost no effect.
Is my data sent anywhere?
No. Everything is calculated locally in your browser.

Determining how many survey responses are needed for a given confidence level and margin of error is the planning-stage counterpart to the Confidence Interval Calculator — rather than analyzing an already-collected sample, this calculator answers the upstream question of how large a sample needs to be before data collection even begins.

Why required sample size depends on confidence level and margin of error together

A larger sample size generally produces a narrower confidence interval (more precision) for the same confidence level — but the specific sample size needed to achieve a target margin of error depends on both the desired confidence level and how tight that margin of error needs to be, with tighter (smaller) margins of error and higher confidence levels both independently pushing the required sample size upward. This relationship isn't linear — cutting the target margin of error in half doesn't just double the required sample size, it roughly quadruples it, since sample size requirements scale with the square of the margin of error, not directly with it. This is exactly why survey designers often have to make a practical tradeoff between achievable sample size and desired precision, rather than simply specifying an arbitrarily tight margin of error.

A worked example

Halving the target margin of error for a survey (making the results twice as precise) doesn't require twice as many respondents — it requires roughly four times as many, since the underlying formula's sample-size requirement scales with the square of the precision improvement, not linearly with it, which is exactly why very high-precision surveys become disproportionately expensive to run as the required margin of error shrinks.

How this connects to your other statistical calculations

Once a survey is actually run using a properly calculated sample size, the Confidence Interval Calculator analyzes the resulting data — the two calculators are companion tools for the planning and analysis stages of the same underlying statistical process, using the same confidence-level and margin-of-error concepts from opposite directions.

Common mistakes

Requesting an arbitrarily tight margin of error without considering the resulting sample-size requirement is a common planning mistake — because required sample size scales with the square of the precision target, a seemingly modest tightening of the desired margin of error can push the required sample size to an impractically large number, and checking this tradeoff before committing to a target precision avoids an unrealistic survey design.

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