Animated Confidence Interval Calculator
The calculator found below will compute the margin of error and confidence interval given the population size, sample size, sample percentage, and confidence level.
If you want to print your calculations, you must use the Simple Confidence Interval Calculator. This calculator cannot be printed using your browser's print command.
You may use this calculator to determine, out of a general population (whose number is the population size) of people, the range of the population who would choose a particular answer for a survey question. It is usually not possible to survey everyone in the entire group, so only some (whose number is the sample size) are interviewed and the population range is unknown. A certain percentage (the sample percentage) of the sample group picks the answer. If the sample group truly represents the whole population, then the population range who would have picked the answer is then known, with a certain confidence level, to be within a certain range (the confidence interval) centered about the sample percentage. The width of that range is twice the margin of error, so a larger margin of error means a wider confidence interval.
To use this calculator, enter numbers into the boxes above the Calculate button, then click on the Calculate button to see the results underneath. To make the relationships between these quantities easier to understand, the confidence interval is displayed graphically, and animated. The margin of error and confidence interval results may be displayed as percentages, or as whole numbers. The probable range of the population is shown as a range below the sample percentage (red region), and a range above the sample percentage (green region).
Further information about the calculations within this calculator may be found at confidence interval calculations.
Observations
- This confidence interval calculator does not require an estimate of the population percentage, but the sample size calculator does require the population percentage. Confidence interval calculators are used after the population is sampled, at which point the sample percentage is available for use as an estimate of the population percentage.
- The population size has less and less of an effect on the margin of error as it increases above the sample size. As the population size is increased past about 100 times the sample size, the margin of error stops growing and remains constant.
- The margin of error is largest when the sample percentage is 50%, and decreases as the sample percentage moves away from 50% in either direction, so the margin of error at 50% can be considered the "worst case" value.