Margin of Error Calculator
Find the margin of error for a survey proportion.
Use 50% for the most conservative estimate
Results update as you type.
How it works
When a poll reports that a candidate has forty-eight percent support with a margin of error of plus or minus three points, that margin is exactly what this calculator produces. The margin of error measures how much a survey result might differ from the true value in the whole population simply because only a sample was questioned rather than everyone. It depends on three things: the sample size, the proportion answering a particular way, and the confidence level you want. This margin of error calculator lets you enter the number of respondents, an optional proportion, and a confidence level of 90, 95, or 99 percent, then returns the margin as a percentage. If you leave the proportion at fifty percent, you get the most conservative, largest margin, which is why fifty percent is the standard assumption when the true split is unknown. The single biggest lever is sample size: because the formula divides by the square root of the sample, quadrupling the number of respondents only halves the margin, which explains why national polls of around a thousand people typically carry a margin near three percent. Pollsters, market researchers, and students use this to judge how much trust a survey result deserves.
MOE = z · √(p(1 − p) / n)
The margin of error for a proportion is the critical z value for your confidence level times the standard error of the proportion, which is the square root of p times one minus p divided by the sample size. Using fifty percent for p gives the largest possible standard error, so it is the conservative default that pollsters quote. Larger samples reduce the margin in proportion to the square root of n.
Source:Survey sampling statistics
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter sample size (n) and confidence level.
- 2
Adjust the options
Adjust proportion (%) if they apply — sensible defaults are already set.
- 3
Read your result
Margin of error updates instantly as you type — no button to press.
Frequently asked questions
What is the margin of error?
The margin of error is the amount a survey estimate is expected to differ from the true population value because only a sample was measured. Reported as plus or minus a percentage, it defines a band around the result. A poll showing fifty-two percent with a three-point margin means the true value is likely between forty-nine and fifty-five percent at the stated confidence level.
Why is 50% the default proportion?
The quantity p times one minus p, which drives the margin, is largest when p is exactly fifty percent. Using fifty percent therefore produces the widest, most cautious margin of error, guaranteeing the estimate is not understated when the true proportion is unknown. This is why pollsters quote margins based on fifty percent unless they have a specific reason to use the observed proportion.
How does sample size change the margin?
Increasing the sample size shrinks the margin of error, but only in proportion to the square root of the sample. To halve the margin you must quadruple the number of respondents. This diminishing return is why polls rarely exceed a few thousand people: past a certain point the extra cost buys only a tiny improvement in precision.
Does population size matter?
For large populations, the margin of error depends almost entirely on the sample size, not on how big the population is. A sample of a thousand gives a similar margin whether the population is a hundred thousand or a hundred million. A finite population correction only becomes relevant when the sample is a substantial fraction of the whole group, which is uncommon in typical surveys.
What confidence level should I choose?
Ninety-five percent is the standard used in most published polls and research, balancing reliability against a reasonable interval width. Ninety-nine percent widens the margin because it demands more certainty, while ninety percent narrows it at the cost of a higher chance of error. Match the level to how costly a wrong conclusion would be in your particular context.