About the Margin of Error Calculator
When a poll says that 52 percent of people support something, give or take 3 points, the 3 points is the margin of error. It describes how far the true value for the whole population could plausibly be from the result in your sample, at a chosen confidence level. This calculator finds the margin of error for a survey percentage using the sample size, the result and the confidence level, with an optional correction for small populations. It can also work out the margin for an average from a standard deviation. It shows the critical value used and the range in which the true value probably lies.
Updated October 2026
How to use the Margin of Error Calculator
- 1Choose whether you measure a percentage or an average.
- 2Choose a confidence level: 90, 95 or 99 percent, or type your own.
- 3Enter the sample size and the result, or the standard deviation.
- 4Optional: enter the total population for a finite correction.
- 5Read the margin of error and the likely range.
Worked example
A survey of 1,000 customers finds 62 percent satisfied. With 95 percent confidence, the critical value is 1.96. The margin is 1.96 × the square root of 0.62 × 0.38 ÷ 1,000, which is 3.0 points. So the true satisfaction in all customers is probably between 59 and 65 percent. If you only had 100 responses, the margin would be about 9.5 points, and the range from 52 to 72 percent would be much less useful.
What shrinks the margin
- A larger sample: quadruple it to halve the margin.
- A lower confidence level, at the price of less certainty.
- A result far from 50 percent (a 10 percent result has a smaller margin).
- For averages, less spread in the data.
- A small population with a high sampling share.
Using it well
Choose the sample size before the survey, using the Sample Size Calculator, so that the margin is small enough for the decisions you want to make. When comparing two results, remember that the difference needs to be larger than the combined margins before you call it real. If the confidence ranges overlap a lot, the data may not support a clear difference.
Related tools
The Standard Error Calculator shows the quantity behind the margin, the Confidence Interval Calculator works from raw data, the Sample Size Calculator plans a survey and the Z-Score Calculator explains critical values.
Features
- Percentage or average
- Any confidence level
- Finite population correction
- Shows the critical z value
- Gives the likely range
- Instant, private results
Frequently asked questions
What is the margin of error?
It is the amount added and subtracted from a sample result to give a range in which the true population value is likely to fall. A result of 52 percent with a margin of error of 3 points suggests the true value is between 49 and 55 percent.
How do I calculate it for a survey percentage?
Multiply the critical value (1.96 for 95 percent confidence) by the square root of p times (1 − p) divided by the sample size. For 50 percent and 1,000 people that is 1.96 × 0.0158 = 3.1 percentage points.
Why do pollsters often quote about 3 percent?
With about 1,000 respondents and a result near 50 percent, the 95 percent margin of error is just over 3 points. That sample size gives a good balance between cost and accuracy.
What does the confidence level mean?
If you repeated the survey many times and built a range each time, about 95 percent of such ranges would contain the true value. A higher confidence level gives a wider margin.
When does the population size matter?
Only when the sample is a sizeable share of the population, say more than 5 percent. Surveying 500 of 1,000 students has a smaller margin than surveying 500 of 10 million voters. Enter the population to apply the correction.
Does a small margin of error mean the survey is good?
No. The margin covers random sampling error only. A biased sample, poor question wording or low response rates cause other errors that the margin of error does not include.