Statistics Calculator

Sample Size Calculator

Estimate completed survey responses needed for one population proportion using confidence level, margin of error, expected proportion, and optional population size.

Free to useRuns in your browserClear formula & method

Enter your data

Sample Size inputs

Use the fields below. Results update only when you select the calculate button.

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What is a sample size calculator?

A sample-size estimate connects desired precision with confidence and the expected variability of a proportion. It answers how many completed responses a simple random survey may need under stated assumptions.

Use this page for a transparent calculation, then compare the result with the Confidence Interval Calculator when a different view of the same data would be useful.

How does this sample size calculator work?

The calculator uses the normal-approximation formula for one proportion, rounds up, and applies the finite-population correction when a population size is entered.

Before interpreting spread or position, it can help to check the center with the Probability Calculator. Every tool states its assumptions so results can be reproduced.

n₀ = z²p(1 − p) / e²   |   finite population: n = n₀ / [1 + (n₀ − 1)/N]

How to use this calculator

  1. Enter the requested numbers in the labeled fields.
  2. Review unit, sample, confidence, or test choices when shown.
  3. Select Calculate Sample Size.
  4. Read the main result, supporting facts, and method note.
  5. Use Copy, Download, or Print when you need to keep the result; select Reset to start over.

If you edit any input after calculating, the old result is marked stale and hidden until you calculate again.

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How should you interpret the result?

A smaller margin of error, higher confidence level, or expected proportion near 50% increases the recommended sample. The result counts completed usable responses, not invitations.

For another useful perspective, open the Percentile Calculator; it answers a related question without changing the values you entered here.

Assumptions and limitations

Complex survey designs, clustering, weighting, subgroup targets, nonresponse, and measurement error can require a larger sample. Study planning should consider more than a single formula.

Consider the Chi-Square Calculator for a complementary summary and the Coefficient of Variation Calculator when your question involves another statistical property. No single statistic describes every important feature of a data set.

Scope: Results are educational calculations, not a substitute for an appropriate study design, subject-matter expertise, or professional statistical review.

Frequently asked questions

A sample-size estimate connects desired precision with confidence and the expected variability of a proportion. It answers how many completed responses a simple random survey may need under stated assumptions.
Use the labeled fields in the calculator and enter finite numeric values. The page validates missing, impossible, and mismatched inputs before showing a result.
n₀ = z²p(1 − p) / e²   |   finite population: n = n₀ / [1 + (n₀ − 1)/N]
A smaller margin of error, higher confidence level, or expected proportion near 50% increases the recommended sample. The result counts completed usable responses, not invitations.
Complex survey designs, clustering, weighting, subgroup targets, nonresponse, and measurement error can require a larger sample. Study planning should consider more than a single formula.
Yes. The calculator and BMI-style result panel are responsive for phones, tablets, laptops, and desktop screens.
No. Calculations run in your browser. This page does not require an account, and the entered values are not sent to a calculation server.
No. It is an educational tool for transparent calculations and quick checks. Important research, clinical, legal, financial, or policy decisions should use an appropriate study design and qualified review.

Sources and methodology

The formulas and cautions on this page are documented so the calculation can be checked against authoritative statistical guidance.

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