Margin of Error Calculator

Proportion Mean

Confidence Level (%)

Common choices are 90, 95, or 99.

Sample Size (n)

The sample size you actually have (or are planning to use).

Expected Proportion (%)

Your best guess of the true proportion. Leave blank to use 50% — the most conservative assumption, which gives the widest (safest) margin of error.

Population Size (optional)

Only matters if your population is small relative to your sample.

About This Tool

What Is Margin of Error?

Margin of error tells you how far your sample estimate might realistically be from the true population value. A smaller margin of error means a more precise estimate — but requires a larger sample to achieve.

When to Use It

Reporting the precision of a survey result you've already collected
Checking whether a planned sample size will give you acceptable precision
The mirror image of the Sample Size calculator — that one asks "how many do I need for a target margin of error," this one asks "what margin of error do I actually get with this sample size"

The Formulas

\( E = Z\sqrt{\dfrac{p(1-p)}{n}} \) (proportion) \( E = Z\dfrac{\sigma}{\sqrt{n}} \) (mean)

Worked Example

You surveyed 400 people on a yes/no question, with no prior estimate of the true proportion, at 95% confidence.

\( Z = 1.96, \ p = 0.5, \ n = 400 \)
\( E = 1.96\sqrt{0.5 \times 0.5/400} \approx 0.049 \)
Your margin of error is about ±4.9% — if 60% of your sample said "yes," the true population proportion is likely between about 55.1% and 64.9%.

Your Results

Margin of Error

What This Means

Perfect for students, researchers, and professionals looking to build real statistical skills.

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