What is margin of error?

Margin of error (MoE) is the maximum expected difference between the observed survey result and the true population value, at a given confidence level. A 95% confidence level with ±3% MoE means you can be 95% confident the true value lies within 3 percentage points of your result.

Why use 50% as the default proportion?

When you do not know the true proportion, 50% (p = 0.5) produces the largest — most conservative — margin of error. This is standard practice in polling because it guarantees the actual MoE will be no wider than calculated.

What is the finite population correction?

When your sample is a large fraction of a small population, the standard formula overestimates uncertainty. The finite population correction factor (FPC) shrinks the MoE proportionally. It only has a noticeable effect when the sample exceeds about 5% of the population.

What confidence level should I choose?

95% is the standard for most survey research and academic work. Use 99% when you need very high certainty (e.g., medical or safety research). Use 90% when a smaller sample must still yield a usable result and a slightly wider error is acceptable.

Does a larger sample always reduce margin of error?

Yes, but with diminishing returns. Doubling your sample size reduces the MoE by a factor of roughly √2 (about 29%), not 50%. Beyond ~1,000 respondents the gains become small for typical proportions.

Margin Of Error Calculator

Enter your confidence level, sample size, and population proportion to instantly calculate the margin of error for any survey or poll.

Survey Parameters

Confidence Level

Sample Size (number of respondents)

Population Proportion (%)

Use 50% for the most conservative estimate.

Population Size (optional, for FPC)

Enter only if your sample exceeds ~5% of the total population.

Fill in the parameters on the left and click Calculate.

Copied!

Summary

The Margin of Error Calculator computes the statistical margin of error for survey or poll results using the standard formula based on a Z-score, sample size, and population proportion. It works with finite population correction when your sample is a meaningful fraction of the total population. Results include the confidence interval so you can see the full range your true population value likely falls within.

How it works

Select a confidence level (90%, 95%, or 99%) — this determines the Z-score used in the formula.
Enter your sample size — the number of people surveyed.
Enter the population proportion as a percentage (default 50% gives the largest, most conservative margin).
Optionally enter a finite population size to apply the finite population correction factor.
The tool computes the margin of error and displays the full confidence interval around your proportion.

Use cases

Evaluate the reliability of opinion poll results before publishing.
Determine how many respondents you need for an acceptable margin of error.
Report survey findings with statistically valid confidence intervals.
Compare margins of error across surveys with different sample sizes.
Validate academic or market research data quality.
Understand the uncertainty in A/B test or experiment proportions.

Frequently Asked Questions

Last updated: 2026-06-04 · Reviewed by Nham Vu