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Margin of Error Calculator

Math Calculators

Confidence interval & sample size

Quick Answer

Margin of Error Calculator: Confidence interval & sample size. Margin of Error Calculator uses standard math formulas to compute accurate results instantly.

ME = Z × √(p(1−p)/n)
±3.0990321%
Interval: 46.900968% ~ 53.099032%

Margin of error scale

Precise <1%
Good 1-3%
Fair 3-5%
Rough 5-10%
Poor >10%

3.0990321%

Z1.96
SE 标准误0.015811388
√n31.622777
Halve ME needs n ×4

Calculation steps

  1. 1SE = √(p(1−p)/n) = √(0.5×0.5/1000) = √0.00025 = 0.015811388
  2. 2ME = Z × SE = 1.96 × 0.015811388 = 0.030990321 = ±3.0990321%
  3. 3Interpretation: in 95% of repeated samples, the true proportion falls within ±3.0990321% of 50%.

Sample size quick table (95%, p=0.5)

Target MEnTypical use
±1%9,604National elections
±2%2,401Formal surveys
±3%1,067Common polls
±5%385Market research
±10%97Quick pulse check
💡 Counterintuitive fact: for large populations, the margin of error depends almost ONLY on sample size n, not population size — a poll of 1,067 people gives ±3% whether surveying a city of 1 million or a country of 1.4 billion. Population correction (FPC) only matters when n exceeds ~5% of the population.

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How to Use

  1. Enter values or expressions: type directly into the Margin of Error 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

  • Margin of Error 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: Confidence interval & sample size.
  • Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Margin of Error Calculator formula

Margin of Error Calculator uses standard math formulas to compute accurate results instantly.

FAQ

How do I use the Margin of Error Calculator?
Open the page and fill in the input fields — results update automatically. Confidence interval & sample size.
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. Margin of Error Calculator[EB/OL]. https://www.yijiansuan.com/en/c/math/margin-error

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