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Margin of Error Calculator for Polls and Surveys

This free margin of error calculator shows how accurate your survey result is. Enter the sample size, confidence level and the percentage you found, and read the plus or minus margin and the range.

By Debmedia Technologies LLP · Kolkata, India · Updated

What Is It and When Do You Need It?

The margin of error tells you how much to trust a poll. If 52% of 1,000 people say yes with a margin of 3.1%, the true share is probably between 48.9% and 55.1%. News stories often quote it, but few explain it.

Enter your numbers and see the margin and the range.

How to Use This Tool

  1. Enter the sample size.
  2. Choose the confidence level.
  3. Enter the percentage that answered yes.
  4. Press Calculate.

How the Calculation Works

The standard error is √(p × (1 − p) ÷ n). It is multiplied by the z-score of the confidence level to give the margin. With a population N, it is scaled by the finite population factor √((N − n) ÷ (N − 1)). The confidence interval is the result plus and minus the margin.

Worked Example

With 1,000 people, 95% confidence and a result of 50%, the margin is about 3.1 points, so the range is 46.9% to 53.1%.

Common Uses

  • Reading polls and surveys.
  • Reporting your own results.
  • Judging if a difference is real.
  • Planning sample sizes.

Tips and Common Mistakes

  • Margins are largest at 50%.
  • Compare ranges, not single numbers.
  • Sampling bias is not included.

Next, you may need the sample size calculator, confidence interval calculator, normal distribution calculator, binomial calculator.

Everything runs in your browser. Nothing you type is uploaded, stored or sent to any outside service.

Frequently Asked Questions

The plus or minus amount around a survey result that shows how much it could differ from the true value in the whole population.
MOE = z × √(p × (1 − p) ÷ n), where z is the z-score for the confidence level, p the proportion and n the sample size.
The margin shrinks with the square root of the sample size. To halve the margin you need four times as many responses.
No. The margin only covers random sampling error, not bias from who was asked or how.

Disclaimer: results are calculated in your browser from the numbers you enter. Check important results before you rely on them for money, health, safety or legal decisions.