How to Convert a Percent to an Odds Ratio

How to Convert a Percent to an Odds Ratio
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A percentage can be used to measure 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.

TL;DR (Too Long; Didn't Read)

To write a percentage as an odds ratio, convert the percentage to a decimal ​x​, then calculate as follows:

(1/​x​) - 1 = first number in the odds ratio, while the second number in the odds ratio is 1.

    Divide the percentage by 100 to convert from a percentage to a decimal. For example, consider that you're asked to convert a 40 percent chance of success into an odds ratio:

    \frac{40}{100} = 0.4

    Divide 1 by the percentage expressed as a decimal. In this example, this gives you:

    \frac{1}{0.4} = 2.5

    Subtract 1 from your result in Step 2 to find the first number of the odds ratio. In this example, you have:

    2.5 - 1 = 1.5

    Substitute your result from Step 3 for ​X​ in the odds ratio ​X​-to-1. In this example, the result from Step 3 is 1.5. So your original 40 percent success ratio, written as an odds ratio, is 1.5-to-1.

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