Margin of Error Calculator
Calculate the margin of error on a survey proportion at any confidence level.
Why national polls stop near 1,000 respondents
At n = 1,000 the 95% margin of error is ±3.1 points. Quadrupling the sample to 4,000 only halves it to ±1.6, at four times the cost. That square-root wall, not budget alone, is why nearly every published poll lands between 800 and 1,200 people.
What this page needs from you
This page asks for sample size, sample proportion (0.5 or 50) and confidence level. From those it returns margin of error in %, together with interval lower bound, interval upper bound, z value used and sample needed to halve the error. Every figure updates as you type, and nothing you enter leaves your browser.
Significance is not the same as importance
With a large enough sample almost any difference becomes statistically significant, because significance measures how confident you can be that a difference exists at all — not how big it is or whether it matters. Effect size answers the second question, and the two should always be read together.
The formula
MoE = z · √(p(1−p) / n)
Every result on this page comes from this formula. Nothing is rounded until the final display, so figures match a spreadsheet to the cent.
How to use the Margin of Error Calculator
- Fill in each field with your own figures — the defaults are only there as an example.
- The result updates as you type, so there is no button to press.
- Check the breakdown under the main result for the supporting numbers.
- Use the copy button to take the result with you, or share the link to reload the same inputs.
Margin of Error Calculator — frequently asked questions
Is this margin of error calculator free to use?
Yes. Every calculator on the site is free, needs no sign-up, and runs entirely in your browser, so your figures never leave your device.
How accurate is the result?
The maths is exact for the formula shown on the page. Accuracy in the real world depends on your inputs and on assumptions the formula cannot see, so treat the output as a well-grounded estimate rather than a quote.
Can I use it on my phone?
Yes. The page is responsive, weighs a few kilobytes and works offline once loaded, so it behaves the same on a phone as on a desktop.
What people search for
This page answers each of these searches. They are the exact phrases visitors use to find the margin of error calculator.
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About this calculator
Written and reviewed by The Samsung Calculator editorial team. Every calculator is written against a published formula, reviewed against at least one independent reference implementation, and dated when it changes.
Last reviewed September 14, 2026 · Calculation runs client-side · No data collected · Report an error