Margin of Error Calculator

The margin of error tells you how much the results of a survey might differ from the true opinion of the whole population you are studying. When a poll reports that 50% of respondents support a policy with a margin of error of plus or minus 4.90 percentage points, it means the true figure in the population is likely somewhere between 45.10% and 54.90%. Every survey that uses a random sample has a margin of error, because you are only measuring a portion of the population, and that sample may not perfectly represent the whole. The margin shrinks as you survey more people and widens if you use a higher confidence level or if the proportion is close to 50%, which is the point of maximum variability. The confidence level is the probability that the true value falls within the stated interval. At 95%, the standard choice, you accept a 5% chance that the true population value lies outside your interval. At 99% you are more certain but the interval is wider. This calculator uses the standard formula: MOE equals the z-score for your chosen confidence level multiplied by the square root of p times (1 minus p) divided by n, where p is the proportion and n is the sample size. For 95% confidence the z-score is 1.96, for 90% it is 1.645, and for 99% it is 2.576. Enter your sample size, sample proportion, and confidence level and you get the margin of error, the lower and upper bounds of the confidence interval, and the standard error. This tool suits students, researchers, journalists, and anyone interpreting survey or polling results. The formula assumes simple random sampling from a large population and does not apply a finite population correction.

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