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Education & Statistics

Margin of Error Calculator

Calculate the margin of error for a survey proportion at a chosen confidence level, with optional finite population correction.

Your inputs

50 % gives the largest (most conservative) margin.

Results

Margin of error

3.099 percentage points

Range for the proportion
46.9 % to 53.1 %
z critical value
1.959964

✓Exact calculation — rounded only for display

Notes for this result

  • Covers random sampling error only — not non-response, wording or coverage bias.

What this calculator does

Polls report results “± a few points”. That margin of error depends mostly on sample size.

Formula and method

MOE = z × √(p(1 − p) ÷ n) × √((N − n) ÷ (N − 1)) when the population N is given

Worked example

Calculated by this tool with its default inputs:

Inputs

  • Sample size: 1000
  • Observed proportion: 50 %
  • Confidence level: 95 %
  • Population size (optional, for finite population correction):

Results

  • Margin of error: 3.099 percentage points
  • Range for the proportion: 46.9 % to 53.1 %
  • z critical value: 1.959964

How to read the results

Quadrupling the sample size roughly halves the margin of error.

Assumptions and limitations

  • Covers random sampling error only, not bias.

Questions

Why does 50 % give the largest margin?

p(1 − p) is largest at p = 0.5.

Methodology and verification

Result type
Exact mathematical calculation (rounded only for display)
Formula version
1.0
Automated verification
3 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
Editorial review
Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.

Privacy

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