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Formula verified · Deterministic calculation

Sample Size Calculator

Choose a supported confidence level and enter the desired margin of error and expected proportion to estimate the required sample size.

Required sample size385
Unrounded sample size384.145882069
Margin of error0.05
Expected proportion0.5
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Result methodology

Normal-approximation proportion sample size, rounded upward without finite-population correction.

Solution steps
  1. z* = 1.95996398454
  2. n = z*²p(1-p)/E² = 384.1458820693913
  3. Round up = 385

How this calculator works

The normal-approximation formula is n=z*²p(1−p)/E², and the result is rounded upward.

Formula

n=z*²p(1−p)/E²

Estimates sample size for a proportion using a normal approximation and no finite-population correction.

Worked example

95% with 5% margin is a verified test case used by the calculation engine.

Assumptions and limitations

  • The calculation estimates sample size for a proportion.
  • No finite-population correction or design effect is applied.
  • Use p=0.5 when a conservative maximum-variance assumption is appropriate.

Methodology & sources

This calculator uses deterministic, versioned calculation logic. The formula and verified examples above are part of the calculation definition used by CalcuMint.

  • CalcuMint deterministic statistics engine

Frequently asked questions

Why is the sample size rounded up?

A fractional participant cannot satisfy the target, so the calculated requirement is rounded upward.

Does this account for a finite population?

No. This version does not apply finite-population correction.

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