Margin of Error Calculator
Estimate a survey margin of error for a proportion at 95% confidence.
Margin of error formula
At 95% confidence, margin of error ≈ 1.96 × √(p(1−p)/n). A 50% proportion gives the most conservative estimate.
What Margin of Error Means
Margin of error estimates how far a sample result may be from the corresponding population value at a chosen confidence level. It is commonly used with survey percentages and sample means.
Margin of Error Example
If a survey reports 52% support with a margin of error of 3 percentage points, a simple confidence interval would run from about 49% to 55%, assuming the stated confidence method and sampling assumptions apply.
What Changes the Margin of Error?
Larger samples usually reduce the margin of error, while higher confidence levels increase it. Greater variability in the data can also increase uncertainty.
Frequently Asked Questions
Does margin of error include every source of survey error?
No. It mainly reflects sampling uncertainty and does not automatically include bias, wording effects or nonresponse.
Does doubling sample size halve the margin of error?
No. Because uncertainty changes with the square root of sample size, a much larger increase is usually needed.
Is a smaller margin of error always better?
It provides more statistical precision, but study quality still depends on sampling and measurement methods.
Margin of Error and Confidence Level
Margin of error reflects sampling uncertainty under a stated confidence level and statistical model. Larger samples generally reduce it, while higher confidence levels increase it. The calculation does not account for nonresponse, coverage problems, biased sampling or measurement error.
Methodology, Assumptions and Interpretation
A common survey margin-of-error formula combines a critical value with the standard error of an estimated proportion. The familiar maximum-error shortcut assumes simple random sampling and often p=0.5; weighting, clustering and nonresponse can make real survey uncertainty larger.