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Sample Size Calculator

Math Calculators

n vs margin of error · finite population

Quick Answer

Sample Size Calculator: n vs margin of error · finite population. Sample Size Calculator uses standard math formulas to compute accurate results instantly.

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Minimum sample size
385
minimum sample size
Sample size depends on confidence level and margin of error — NOT on population size (once the population is large). Halving the error requires 4× the sample. When p is unknown, use p=50% for the most conservative (largest) n.

Quick reference (95% confidence, p=50%)

Margin of errorSample sizeTypical use
±10%97Rough poll
±5%385Standard survey
±3%1067Political poll
±2%2401Precise study
±1%9604Census-grade

Calculation steps

  1. 1n₀ = Z²·p(1−p)/E² = 1.96²×0.5×0.50/0.050² = 384.2
  2. 2Infinite population: round up to 385

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How to Use

  1. Enter values or expressions: type directly into the Sample Size Calculator — keyboard friendly.
  2. Instant results: everything computes live as you type, no button needed.
  3. Follow the steps: the result panel shows full working and formula substitution.
  4. Copy or recompute: one-click copy; change any input to recalculate instantly.

Key Points

  • Sample Size Calculator is a free online math tool — open and use, no sign-up.
  • All calculations run locally in your browser; your data never leaves the device.
  • Key capability: n vs margin of error · finite population.
  • Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Sample Size Calculator formula

Sample Size Calculator uses standard math formulas to compute accurate results instantly.

FAQ

How do I use the Sample Size Calculator?
Open the page and fill in the input fields — results update automatically. n vs margin of error · finite population.
Are the results accurate?
Yes. All calculations use standard mathematical formulas and are verified for accuracy.
Is it free? Do I need to sign up?
Completely free. No registration, login or download required — just open and use.
Does it work on mobile?
Yes. The responsive design works on phones, tablets and desktops.
Is my data saved?
No. All calculations run locally in your browser. Nothing is uploaded or stored.

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Source & Updates

Standard mathematical formulas. All logic verified. Last updated: 2025-07

Last updated:

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

Maintained and periodically reviewed by the YiJianSuan editorial team — review process in ourEditorial Policy.

Cite this page: YiJianSuan. Sample Size Calculator[EB/OL]. https://www.yijiansuan.com/en/c/math/sample-size

Results provided by this tool are for reference only and do not constitute professional advice.