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Math Calculators

Margin of Error Calculator

Verified formula Updated Jun 2026 Private — runs on your device

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Verified formula Private

Margin of error

3.10%

For general information only — not financial, tax, legal or medical advice. Verify before you rely on it.

How to use the Margin of Error Calculator

The Margin of Error Calculator works out your margin of error in an instant. Enter sample size, proportion and confidence level and the result updates as you type — it is free, needs no sign-up, and runs entirely in your browser so your figures stay private.

  1. Enter the sample size.
  2. Enter the proportion.
  3. Choose the confidence level.
  4. Read off your margin of error — the calculator updates automatically, with no button to press.

Formula

The Margin of Error Calculator uses the formula:

Margin of error = Confidence level × √(Proportion × (1 - Proportion) ÷ Sample size) × 100

Worked example

For example, with sample size of 1,000, proportion of 0.5 and confidence level of 95% (z = 1.96), the margin of error is 3.10%.

Inputs used
Sample size 1,000
Proportion 0.5
Confidence level 95% (z = 1.96)
Results
Margin of error 3.10%

Results are estimates for educational use, not professional advice.

Frequently asked questions

It is z × √(p(1 − p) ÷ n), where z is the confidence z-score, p the proportion and n the sample size. For 1000 responses at 95% it is about ±3.1%.

If you do not know it, use 0.5, which gives the largest, most conservative margin of error for a given sample size.

Larger samples shrink the margin, but with diminishing returns — quadrupling the sample roughly halves the margin.

It means if the survey were repeated many times, about 95% of the intervals would contain the true value.

Enter the sample size. Enter the proportion. Choose the confidence level. Read off your margin of error — the calculator updates automatically, with no button to press.

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