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Margin of Error Calculator
Find out how much your survey result can move once you read it back onto the whole population. Enter your population size, the responses you collected, and a confidence level, and the band updates as you type.
Your inputs
Everyone the result is meant to speak for, not only the people you contacted.
How often the true answer would land inside the band if you ran the survey again. 95% is the usual choice.
Completed responses you actually collected. Partial and abandoned answers do not count.
Nothing you type here leaves your device.
Key terms
Population size
Total number of people in the population you are researching. If you survey your organization, population size is the total number of employees.
Confidence level
A percentage that indicates how sure you can be that a certain amount of the population will select an answer. A 95% confidence level, for example, means that the outcomes between x and y are 95% certain.
Sample size
A value that tells how many people you need to interview to get results that will represent the target population as accurately as possible.
This band covers sampling error only, and assumes a simple random sample with a 50/50 population proportion. Question wording, who chose to answer, and who stayed silent all sit outside it.
How accurate is your survey result?
Surveying is a balancing act: you question a smaller group and use their answers to describe a much larger one. The margin of error puts a number on what that shortcut costs you. A 60% "yes" with a 5% margin means 55% to 65% of the wider population would agree, so a rival option sitting at 58% is not behind at all.
01
Count what you collected
Take your completed responses and the population they came from. Both go into the box above.
02
Read the band
Add and subtract the result from any percentage in your findings to see how far it could really sit.
03
Report it alongside
Quote the margin next to your headline number. Without it, nobody reading your report can tell how firm that number is.
Free, private, and built for research
Most calculators of this kind want your email before they will show a number, and many run the arithmetic on someone else's server. This one does neither.
01
Runs in your browser
No API call sits behind this page. Your response counts and study parameters stay on your machine.
02
No account, no email wall
Change an input, read the number, close the tab. Nothing is logged and nothing is asked of you.
03
Working you can check
The formula is printed above and the same inputs always return the same figure, so you can defend it in a method section.
The margin of error formula
Nothing here is invented for this page. It is the textbook confidence interval for a proportion, so you can check any number the calculator gives you.
- z is the z-score for your confidence level: 1.28 at 80%, 1.65 at 90%, 1.96 at 95%, 2.58 at 99%.
- p is the population proportion, held at 0.5 here because a 50/50 split produces the widest band and never flatters your result.
- n is your sample size, and the square root under it is why quadrupling your responses only halves the margin.
- The finite population correction then narrows the band using your population size N, which matters when you have surveyed a large share of a small group.
Who reaches for a margin of error calculator
Anyone who has to say out loud how much a result can be trusted.
01
Researchers
Report the confidence interval next to every headline figure, the way a reviewer expects to see it.
02
Product teams
Check whether two options really differ before a preference survey decides your roadmap.
03
Marketing and CX
Know whether this quarter's score genuinely moved or simply wobbled inside the band.
04
HR and people teams
Say how far an engagement result could sit from the mood of the whole company.
05
Students and academics
Produce the confidence interval your write-up has to state and justify.
06
Agencies
Show a client what their sample actually bought them in precision, before they read too much into it.
Tighter results start with better data.
BlockSurvey encrypts responses end to end, so people answer honestly and the data behind your numbers is never sold, mined, or used to train a model.
Work the other direction
Explore more →
Margin of error and sample size are two readings of the same equation.
Frequently Asked Questions
- It is the band around your survey result, written in percentage points. If 60% of respondents said yes and your margin of error is 5%, the true figure for the whole population sits somewhere between 55% and 65%. The narrower the band, the more precisely your sample speaks for everyone you did not survey.
