How to Convert a Percent to an Odds Ratio


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.

  • 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.

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

  • 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.

  • 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.


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