Relative Risk Calculator
Compare the risk of an outcome between an exposed and unexposed group. Enter the four counts from your 2x2 table.
Learn how to calculate it yourselfEnter your values
Results update as you type.
Relative risk
- 95% CI
- 1.149 to 3.482
Calculate it yourself
Use a = 30 exposed people with the outcome, b = 70 exposed without it, c = 15 unexposed with it and d = 85 unexposed without it.
Follow this worked example, then repeat the steps with your own numbers.
Calculate outcome risk in each group
Exposed risk = a/(a + b) = 30/100 = 0.30. Unexposed risk = c/(c + d) = 15/100 = 0.15.Divide the two risks
RR = 0.30 ÷ 0.15 = 2.Calculate the standard error on the log scale
SE = √[1/30 − 1/100 + 1/15 − 1/100] = √0.08 ≈ 0.28284.Transform the confidence limits back
95% limits = exp[ln(2) ± 1.96 × SE] ≈ 1.15 to 3.48.ln is the natural logarithm and exp reverses it. A ratio of 2 means the observed outcome risk in the exposed group is twice that in the comparison group.
To match this calculator, add 0.5 to all four cells if any cell is zero. Comparisons of observed risks do not by themselves establish a causal effect.
Check your answer in the calculatorBuilt into PaperSurvey.io
Choose exposure and outcome questions to compare observed risks using the Relative risk figure in the Odds Ratio widget.
Relative risk vs odds ratio
Relative risk is the probability of the outcome in the exposed group divided by the probability in the unexposed group. A value of 1 means no difference, above 1 means higher risk with exposure and below 1 means lower risk. It is more intuitive than the odds ratio, which compares odds rather than probabilities, though the two agree closely when the outcome is rare.
How the counts map
Enter exposed-with-outcome, exposed-without-outcome, unexposed-with-outcome and unexposed-without-outcome. If any cell is zero, a Haldane-Anscombe correction of 0.5 is added to every cell so the ratio and its confidence interval stay defined. A 95% interval that excludes 1 points to a statistically significant association.
Frequently asked questions
Should I report relative risk or the odds ratio?
For cohort and experimental data where you can measure risk directly, relative risk is usually the clearer choice. Case-control studies typically report the odds ratio instead.
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