Risk Ratio Calculator
A risk ratio calculator compares the probability of an outcome between two groups, giving the relative risk. Enter the events and totals for each arm, choose a confidence level, and read the risk ratio, the risk in each group, and the confidence interval right away.
Enter the number of events and the total number of people in each arm. Group 1 is the exposed or treatment arm; Group 2 is the comparison group.
How to use the risk ratio calculator
You need the number of events and the total number of people in each of the two groups. With those four numbers the calculator works out the risk in each arm and divides one by the other.
- 1. Enter the first group. Type the events and the total number of people in the group of interest, usually the treated or exposed arm.
- 2. Enter the comparison group. Add the events and total for the control or unexposed group.
- 3. Choose a confidence level. Select 90, 95, or 99 percent, with 95 percent the usual choice.
- 4. Read the result. You get the relative risk, the absolute risk in each arm, the confidence interval, and a p-value. A zero in an event cell triggers a 0.5 correction so the ratio stays defined.
A worked example
Suppose 15 of 100 treated patients had the outcome and 25 of 100 control patients had it. The risk is 0.15 in the treated arm and 0.25 in the control arm, so the relative risk is 0.15 divided by 0.25, which equals 0.60. In plain terms the treatment is associated with a 40 percent lower risk of the outcome.
The confidence interval is built on the log scale, where the standard error of the log relative risk is about 0.29. The 95 percent interval back-transforms to roughly 0.34 to 1.07. Because the upper bound just edges past 1, this 40 percent reduction is not quite statistically significant: the sample is too small to rule out chance. It is a useful reminder that a sizeable relative effect and statistical significance are two different things.
Relative risk versus the odds ratio
Relative risk is the more intuitive of the two main ratio measures because it speaks the language of probability: a relative risk of 2 means twice the chance, full stop. The odds ratio compares odds rather than probabilities, so the two agree only when the outcome is rare and diverge sharply when it is common. Cohort studies and randomised trials can estimate risk directly and therefore favour the risk ratio, while case-control studies and logistic regression are stuck with the odds ratio. The guide to odds ratio versus relative risk covers when to use each.
From the same data you can also derive how many people you would need to treat to prevent one event. The number needed to treat calculator turns the risk difference into that clinically useful figure, and the explainer on relative versus absolute risk reduction shows why a large relative reduction can still mean a small absolute benefit. To pool relative risks across studies, use the tool that pools across studies.
Common mistakes to avoid
- Reporting only the relative reduction. A 40 percent lower relative risk sounds dramatic, but if the baseline risk is tiny the absolute benefit may be negligible. Always pair the relative risk with the risk in each arm.
- Using a risk ratio from a case-control study. Case-control designs cannot estimate risk directly, so the odds ratio is the correct measure there. Reserve the risk ratio for cohort studies and randomised trials.
- Confusing a large effect with significance. As the worked example shows, a relative risk of 0.60 can still have an interval that crosses 1. Judge significance by the interval, not by how far the estimate sits from 1.
- Reversing the reference group. A relative risk of 0.6 in one direction is 1.67 in the other. Fix which group is the comparison before you read the result.
Need the relative risks pooled across studies?
One comparison is a start. If you need every trial extracted, the right model chosen, and a results section that holds up in peer review, a methodologist can take the analysis from here.
Get help with your analysisFrequently asked questions
How do you calculate risk ratio?
The risk ratio, also called relative risk, is the risk of the outcome in one group divided by the risk in the other. Risk in each group is simply the number of events divided by the number of people, so with events and totals for both arms you compute risk one, compute risk two, and divide the first by the second. This calculator does that and builds the confidence interval on the natural-log scale, because the log relative risk is closer to normally distributed, then back-transforms the bounds. A zero in the event column triggers a 0.5 correction so the ratio stays defined.
What does a risk ratio of 1.25 mean?
A risk ratio of 1.25 means the outcome is 25 percent more likely in the first group than in the comparison group. Unlike the odds ratio, this maps directly onto probability, so a 1.25 relative risk really does mean a quarter more events per person at risk. Check the confidence interval before drawing conclusions: if it includes 1, the apparent increase may be due to chance, and a wide interval signals that the sample is too small to be sure.
What is a good risk ratio?
There is no universally good value, because the answer depends on whether the outcome is desirable or harmful. For a harmful outcome under a new treatment, a risk ratio below 1 is good because it means the treatment lowers risk; for a beneficial outcome, a value above 1 is what you want. A risk ratio of exactly 1 means no difference between the groups. What makes any value trustworthy is a confidence interval that excludes 1 and is narrow enough to be informative.
What is a normal risk ratio?
A risk ratio of 1 is the reference point of no association: the outcome is equally likely in both groups. Values close to 1, with confidence intervals that span it, indicate little or no effect. Departures from 1 in either direction measure the strength of the association, with values well above or below 1 representing strong effects. Because relative risk is a ratio, the scale is multiplicative, so 0.5 and 2.0 represent effects of equal magnitude in opposite directions.
What does a relative risk of 0.5 mean?
A relative risk of 0.5 means the outcome is half as likely in the first group as in the comparison group, a 50 percent reduction in risk. For a harmful outcome that is a strong protective effect. To express any relative risk below 1 as a percentage reduction, subtract it from 1 and multiply by 100, so 0.5 becomes a 50 percent lower risk. Confirm the confidence interval stays below 1 before treating the reduction as established.
What is the difference between risk ratio and risk difference?
The risk ratio divides one risk by the other and is a relative measure, while the risk difference subtracts one risk from the other and is an absolute measure. A risk ratio of 0.5 always means half the risk, whether the baseline is 2 percent or 40 percent, but the risk difference captures how many fewer events that represents per hundred people. Both matter: the relative measure travels well across populations, and the absolute measure tells you the real-world impact.