Margin Of Error Calculator

Form

Results

MOA

0%

Table of Contents

1

What is Margin Of Error?

Margin of error estimates the sampling uncertainty around a proportion at a chosen confidence level.

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How to Use This Calculator

  1. Enter or select Confidence Level, Probability, Sample size(n), Population size.
  2. Check the unit beside each measurement. For a percentage or rate, use the scale and time period stated in the form.
  3. Choose Calculate, then compare the output with the formula and example below. If you change a value or option, calculate again to update the result.
3

Formula Used

e=z√(p(1−p)/n), with finite-population correction when applicable.
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Variables Explained

InputWhat it means
Confidence LevelThe coverage level used to choose the normal-distribution critical value.
ProbabilityUse the measured or stated value for this item, with the unit or category shown beside the field.
Sample size(n)Number of observations or responses in the sample, rather than the population size.
Population sizeTotal number of eligible members in the population being studied.
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Worked Example

At 95% confidence with p=0.5 and n=400, e≈4.9 percentage points before correction.

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Why Use This Calculator?

Report a sampling-uncertainty band alongside a survey proportion.

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Common Mistakes

    • Confidence level is not the chance that a particular respondent is correct; the sampling assumptions still matter.
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Frequently Asked Questions

Does a calculated statistic prove a conclusion?

A statistic describes the supplied data under stated assumptions. Sampling design, missing observations and the suitability of the model still determine what can reasonably be concluded.

Should I include every observation?

Use the observations required by your study design and state any exclusion rule. Removing values only because they change the answer can bias the analysis.

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Sources & References

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