How to Calculate Confidence Levels

By Michael Keenan; Updated April 24, 2017
A calculator can help compute confidence intervals.

A confidence level refers to the probability that a confidence interval will contain a given data point. For example, if you conduct a poll that shows 56 percent of people support candidate A with an error of plus or minus 3 percent and you have a confidence level of 95 percent, there is a 95 percent probability that the true proportion for candidate A's support is between 53 and 59 percent. To find the confidence level, you need to know the proportions, sample size and confidence interval.

Square the confidence interval. For example, if your confidence interval is plus or minus 0.03, square 0.03 to get 0.0009.

Multiply the confidence interval squared by the sample size. For example, if your survey consisted of 500 people, multiply 500 by 0.009 to get 0.45.

Multiply the percentage picking option A by the percentage picking option B. For example, if in your survey, 56 percent picked candidate A and 44 percent picked candidate B, multiply 0.56 by 0.44 to get 0.2464.

Divide the Step 2 result by the Step 3 result to find the z-score. In this example, divide 0.45 by 0.2464 to get 1.83.

Convert the z-score to a confidence level using a table z-score table and multiplying by two. In this example, use the z-score table to find "1.8" in the left-hand column and "0.03" on the top row and that row and column intersect at 0.4664. Multiplying 0.4664 by 2 gives you a confidence level of 0.9328, or 93.28 percent.

About the Author

Mark Kennan is a writer based in the Kansas City area, specializing in personal finance and business topics. He has been writing since 2009 and has been published by "Quicken," "TurboTax," and "The Motley Fool."