Margin of Error Calculator
Find the margin of error for any survey or poll, and see the range behind a reported result.
Calculate your margin of error
This free tool is for poll readers, survey makers, students and journalists who want to know how precise a result is. It needs no sign-up, and it runs entirely in your browser.
Your margin of error
Margin of error at different sample sizes
Same confidence level and proportion, with the sample size running from 100 to 10,000 people. Your sample size is highlighted.
How margin of error works
Margin of error is the range around a survey result that is likely to contain the true value, and it is one of the most quoted numbers in polling. It comes from the sample size, the confidence level and the proportion in the sample. This calculator shows the margin and the range around a reported result.
What does a margin of error of 3 percent mean?
It means that if the same survey were repeated many times, the result would fall within 3 percentage points of the true value in 95 out of 100 surveys, when the confidence level is 95 percent. A reported result of 52 percent with a margin of 3.10 percent means the true value is likely to lie between 48.90 percent and 55.10 percent.
A margin of error does not cover every possible mistake. It only covers the random variation that comes from sampling, and it says nothing about biased questions, a poor sample or people who refuse to answer.
How do you calculate margin of error?
The margin of error is the critical value times the square root of the proportion times one minus the proportion, divided by the sample size. The critical value comes from the confidence level: 1.645 for 90 percent, 1.960 for 95 percent and 2.576 for 99 percent. Worked example: a sample of 1,000 with a 95 percent confidence level and a proportion of 50 percent gives 1.960 times the square root of 0.25 divided by 1,000, which is 3.10 percent. Try it in the calculator above.
What sample size do you need for a margin of error of 3 percent?
At 95 percent confidence and a 50 percent proportion, a margin of 3 percent needs about 1,068 people. A margin of 5 percent needs about 385 people, and a margin of 2 percent needs about 2,401 people. The required sample grows fast as the margin shrinks, because the margin is divided by the sample size under a square root. Use our Sample Size Calculator to work out the exact sample for the margin you want.
Why is 50 percent the worst case for margin of error?
The margin is largest when the proportion is 50 percent, because the product of the proportion and one minus the proportion is at its maximum there. A result of 50 percent has a wider margin than a result of 10 percent or 90 percent from the same sample. That is why pollsters use 50 percent when they quote a general margin of error, and why this calculator defaults to 50 percent.
What does margin of error not tell you?
It does not tell you whether the survey asked the right people, whether the questions were fair, or whether the people who answered are like the people who did not. A poll with a margin of 2 percent can still be wrong if the sample is biased. Always check who was surveyed, how they were chosen, and how many refused to answer before you trust a result.
Margins of error at 95% confidence, 50% proportion
| Sample size | Margin of error | Typical use |
|---|---|---|
| 100 | 9.80% | Small focus groups |
| 400 | 4.90% | Local surveys |
| 1,000 | 3.10% | National polls |
| 2,000 | 2.19% | Detailed research |
| 10,000 | 0.98% | Very large studies |
Frequently asked questions
What is a good margin of error for a survey?
Most published polls aim for a margin of 3 percent to 5 percent. A margin of 3.10 percent from a sample of 1,000 is typical for a national poll. A margin above 5 percent is usually too wide to be useful for close results.
Does a larger sample always give a smaller margin?
Yes, but the benefit shrinks quickly. Doubling a sample from 1,000 to 2,000 cuts the margin from 3.10 percent to 2.19 percent, not in half. To halve the margin, you need four times as many people, because the margin falls with the square root of the sample size.
Why do some polls quote a margin of 3 percent and others 5 percent?
Because the margin depends on the sample size, the confidence level and the proportion. A poll of 1,000 people at 95 percent confidence has a margin of 3.10 percent at a 50 percent proportion, while a poll of 400 people has a margin of 4.90 percent. The margin is a property of the survey design, not of the result itself.
Can two candidates both be ahead within the margin of error?
Yes. If one candidate is at 52 percent and another at 48 percent, with a margin of 3.10 percent, the race is a statistical tie. The lead of 4 points is smaller than twice the margin, so the poll cannot say who is really ahead.
What is the difference between margin of error and confidence interval?
The margin of error is the half width of the confidence interval. A result of 52 percent with a margin of 3.10 percent has a confidence interval from 48.90 percent to 55.10 percent. Our Confidence Interval Calculator shows the same range for means as well as proportions.
Does margin of error apply to a census?
No. A census surveys everyone in the population, so there is no sampling variation and no margin of error. The margin only applies when a sample is used to estimate a value for a larger group.
Does this calculator store my data?
No. The calculator runs entirely in your browser. Nothing you type is uploaded, stored or shared.
More tools you may need
Once you know the margin, check the range with the Confidence Interval Calculator and the sample behind it with the Sample Size Calculator. For single values, use the Z-Score Calculator, the Standard Deviation Calculator and the P-Value Calculator.
