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.
Convert From Percentage to Decimal
Divide by the Decimal
Find the First Number of the Odds Ratio
Substitute Into the Odds Ratio
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:
40 ÷ 100 = 0.4
Divide 1 by the percentage expressed as a decimal. In this example, this gives you:
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.