Odds ratio and risk ratio from a 2×2 table
Enter the four counts of a 2×2 table to get the odds ratio, risk ratio and risk difference with confidence intervals.
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- Odds ratio (confidence interval)
- Risk ratio (confidence interval)
- Risk difference (confidence interval)
- Risk in the exposed group
- Risk in the unexposed group
How it is calculated
The intervals are calculated on the logarithmic scale (Woolf for the odds ratio, Katz for the risk ratio) and converted back; the risk difference uses the usual normal approximation.
Counts must be whole numbers. If any cell is zero, 0.5 is added to all four cells and the tool says so.
OR = (a × d) / (b × c); SE(ln OR) = √(1/a + 1/b + 1/c + 1/d)RR = [a / (a + b)] / [c / (c + d)]; SE(ln RR) = √(1/a − 1/(a + b) + 1/c − 1/(c + d))RD = a / (a + b) − c / (c + d)
Worked example: Counts 20, 80, 10 and 90: odds ratio 2.25 (0.99 to 5.09), risk ratio 2.00 (0.99 to 4.05).
Sources
These calculators support research; they do not replace the advice of a statistician or a clinician.
Questions
Which of the three should I report?
In a case-control study only the odds ratio is valid. In a cohort study or a trial the risk ratio and the risk difference are also meaningful, and are easier to interpret.