How to Convert a Percent to an Odds Ratio

By Mark Kennan

Percentages measure the successful attempts per 100 tries. For example, a 20 percent chance of success means you will succeed 20 times out of 100. Odds ratios are reported as the number of failures per success. For example, an odds ratio of 4-to-1 means that four failures occur for each success, or one success per five attempts. If you have two probabilities, one measured as a percentage and the other as an odds ratio, you may have to convert to compare the relative probabilities.

Step 1

Divide the percentage by 100 to convert from a percentage to a decimal. For example, if you have 40 percent, divide 40 by 100 to get 0.4.

Step 2

Divide 1 by the percentage expressed as a decimal. In this example, divide 1 by 0.4 to get 2.5.

Step 3

Subtract 1 from the result to find the first number of the odds ratio. In this example, subtract 1 from 2.5 to get 1.5.

Step 4

Substitute the result in for X in the odds ratio X-to-1. In this example, substitute in 1.5 to find that 40 percent converts to an odds ratio of 1.5-to-1.

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."