Margin of Error Calculator
Measure the expected sampling uncertainty for a population proportion or sample mean using your sample size, confidence level, and research data.
Enter Your Research Data
Select a calculation type and provide the required sample information.
Calculation features
Built for Surveys and Statistical Research
Calculate uncertainty for polls, market research, academic studies, customer surveys, and other sample-based analysis.
Simple process
How the Margin of Error Calculator Works
Get a clear statistical estimate in three straightforward steps.
1
Choose the Data Type
Select population proportion for percentages or sample mean when your research uses an average and standard deviation.
2
Enter Sample Details
Provide the sample size, confidence level, proportion or standard deviation, and optional population size.
3
Review the Result
The calculator displays the margin of error, confidence interval, standard error, interval width, and precision level.
What Is a Margin of Error?
A margin of error estimates how much a sample result may differ from the true value for the full population. It is normally displayed with a plus-or-minus symbol.
For example, a survey result of 50% with a margin of error of ±3% suggests that the corresponding population value is likely between 47% and 53%, based on the selected confidence level.
Margin of Error for a Proportion
Standard formula
MOE = z × √[p(1 − p) ÷ n]
- MOE is the calculated margin of error.
- z is the critical value for the confidence level.
- p is the sample proportion expressed as a decimal.
- n is the number of observations in the sample.
Margin of Error for a Mean
Mean-based formula
MOE = z × (standard deviation ÷ √n)
This calculation estimates uncertainty around a sample mean. It is most appropriate when the standard deviation is known or when the sample is sufficiently large for a normal approximation.
Helpful answers
Frequently Asked Questions
Learn how to interpret and use your margin of error calculation.
A margin of error between 3% and 5% is commonly used for general surveys. However, the appropriate value depends on the study purpose, budget, population, and required precision.
A 50% proportion produces the greatest possible variability and therefore the largest, most conservative margin of error for a given sample size.
Yes. Increasing the sample size normally reduces standard error and produces a narrower confidence interval. The improvement becomes smaller as the sample continues to grow.
It is commonly used when sampling without replacement and the sample represents more than about 5% of the total finite population.
No. Margin of error measures random sampling uncertainty. It does not correct poor question wording, nonresponse bias, selection bias, inaccurate answers, or data collection errors.
The confidence level expresses the degree of certainty used by the interval, while the margin of error describes how far the sample estimate may extend above or below the reported result.