Survey Sample Size Calculator

Plan how many completed survey responses to collect before fielding. Choose a confidence level, a margin of error, an assumed support rate, and optionally the full population size to set a defensible response target for a proportion estimate.

How It Works

Formula

n_0 = \dfrac{z^2 \cdot p \cdot (1-p)}{e^2}

n = \dfrac{n_0}{1 + \dfrac{n_0 - 1}{N}}

z = \Phi^{-1}\!\left(1 - \dfrac{1-C}{2}\right)

Variables, symbols and units

$n_0$: Large-population baseline sample size
$n$: Finite-population-adjusted sample size
$z$: Two-sided normal critical value for the chosen confidence level
$p$: Assumed proportion, expressed as a decimal share
$e$: Desired margin of error, expressed as a decimal share
$N$: Total population size when the population is bounded and known

Calculation method explained

Enter the confidence level you want to defend, the margin of error you can live with, and the proportion you expect for the focal answer. The calculator first computes the large-population baseline, then optionally applies the finite-population correction when you know the total class, member, or customer count. The headline result is rounded up because you need a whole-response target, not a decimal.

This page uses the standard survey-planning formula for proportions: $n_0 = z^2 p(1-p)/e^2$ , where $p$ is the assumed proportion as a decimal and $e$ is the desired margin of error as a decimal. If you provide a bounded population size $N$ , it applies the finite-population correction $n = n_0 / (1 + (n_0 - 1) / N)$ .

The confidence level is converted to a two-sided normal critical value $z$ . The final answer is rounded up to the next whole completed response. A 50% assumed proportion is highlighted because it maximizes $p(1-p)$ and therefore produces the largest required sample under this model.

Frequently Asked Questions

What exactly does this calculator plan?

It plans how many completed survey responses you should target before fielding when your final result is a proportion such as support rate, approval rate, or share selecting one answer. It is a planning tool for survey precision, not a post-hoc explanation of uncertainty after the survey is already done.

Why is 50% the conservative default?

Because the sample-size formula depends on p(1-p), and that term is largest at p = 0.50. If you do not have a trustworthy prior estimate, 50% gives the biggest required sample and therefore the safest planning target.

When does the finite-population correction matter?

It matters when the target population is not very large relative to the sample you plan to collect, such as a class roster, a member directory, or a bounded customer list. In those cases the adjusted target can be meaningfully lower than the large-population baseline.

How is this different from the Confidence Interval Calculator, Normal Distribution Calculator, and Statistics Calculator?

Confidence Interval Calculator interprets a sample you already collected. Normal Distribution Calculator answers probability questions under a bell-curve model. Statistics Calculator summarizes an existing dataset. This page answers an earlier planning question: how many completed survey responses to aim for before you launch.

What does this not cover?

It does not do experiment power analysis, means-based studies, causal claims, weighting design, or nonresponse correction. A mathematically large sample does not fix biased sampling, bad wording, or an unrepresentative frame.

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Survey Sample Size Calculator

How It Works

Frequently Asked Questions

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