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 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 by the Decimal
Divide 1 by the percentage expressed as a decimal. In this example, this gives you:
1 ÷ 0.4 = 2.5
Find the First Number of the Odds Ratio
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 Into the Odds Ratio
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.