Margin of Error Calculator

What this margin of error calculator measures

The calculator estimates the margin of error for a survey proportion. It uses the conservative assumption p = 0.5, which produces the largest standard error when the expected response split is unknown, and applies a finite population correction when the sample is a meaningful share of the population.

Enter:

• Population size (N): the full group your sample should represent
• Sample size (n): valid completed responses, not invitations sent
• Confidence level: the repeated-sampling confidence level used to choose the z-score

The output is expressed in percentage points. If 60% of respondents choose an answer with a ±4% margin of error, the corresponding interval is 56% to 64% under the model assumptions.

Margin of error formula for a proportion

For a large or effectively unlimited population:

MOE = z × √(p(1 − p) / n)

For a finite population, multiply by:

√((N − n) / (N − 1))

The calculator uses p = 0.5. Common two-sided z-scores are approximately 1.645 for 90%, 1.96 for 95%, and 2.576 for 99% confidence.

How to reduce margin of error

Increasing the completed sample size reduces random sampling error. The improvement follows a square-root relationship, so halving the margin of error requires roughly four times as many responses before finite-population effects.

Use the survey sample size calculator to work backwards from a target margin. Then use the response rate calculator to estimate how many invitations the fieldwork may require.

Important limitations

Margin of error describes random sampling uncertainty under a probability-sampling model. It does not measure or correct:

• leading or ambiguous questions
• non-response bias
• coverage gaps in the invitation list
• customers choosing whether to participate
• duplicate, fraudulent, or invalid responses
• weighting and complex sample designs

Many ecommerce surveys use convenience samples rather than probability samples. The calculation can still be a useful planning reference, but it should not be presented as proof that all sources of error fall inside the interval.

For continued survey design and analysis, see the survey methodology hub or connect responses to Shopify order context with UserLoop.

Source: NIST/SEMATECH e-Handbook of Statistical Methods.

Reviewed 15 July 2026 by the UserLoop editorial team.