A risk ratio (also called relative risk) is calculated by dividing the risk of an outcome in an exposed group by the risk of that outcome in an unexposed group. The formula is straightforward once your data is organized into a simple table, but interpreting the result correctly requires understanding what the number actually tells you.
The Formula
Risk ratio uses a 2×2 contingency table where exposure status runs along the rows and outcome status runs across the columns. The four cells are labeled by convention:
- A = exposed and developed the outcome
- B = exposed and did not develop the outcome
- C = unexposed and developed the outcome
- D = unexposed and did not develop the outcome
The risk in the exposed group is A divided by (A + B), which is the total number of exposed people. The risk in the unexposed group is C divided by (C + D). The risk ratio is simply one divided by the other:
RR = (A / (A + B)) / (C / (C + D))
A Worked Example
Suppose you’re studying whether a workplace chemical is linked to a lung condition. You follow 200 workers exposed to the chemical and 400 workers who are not exposed over five years. Among the exposed workers, 30 develop the condition. Among the unexposed workers, 15 develop it.
Risk in exposed group = 30 / 200 = 0.15 (15%). Risk in unexposed group = 15 / 400 = 0.0375 (3.75%). The risk ratio is 0.15 / 0.0375 = 4.0. Workers exposed to the chemical were four times as likely to develop the lung condition as those who were not exposed.
What the Number Means
A risk ratio of exactly 1.0 means the exposure made no difference: both groups had the same risk. A risk ratio greater than 1.0 means the exposed group had a higher risk of the outcome, suggesting the exposure increases risk. A risk ratio below 1.0 means the exposed group had a lower risk, which is what you’d see when evaluating something protective like a vaccine or preventive treatment.
The further the value is from 1.0 in either direction, the stronger the association. A risk ratio of 3.0 means the exposed group had triple the risk. A risk ratio of 0.5 means the exposed group had half the risk.
Adding a Confidence Interval
A risk ratio on its own doesn’t tell you how precise your estimate is. A confidence interval gives you the range of values that plausibly contain the true risk ratio. The standard approach is a 95% confidence interval, meaning you can be 95% confident the true value falls within that range.
The calculation works on a logarithmic scale. You first convert your risk ratio to its natural log, calculate the standard error on that scale, then build the interval before converting back. For the 95% level, you add and subtract 1.96 times the standard error from the logged risk ratio, then take the antilog of both limits. For a 90% confidence interval, you use 1.645 instead of 1.96.
The key thing to check: if the confidence interval crosses 1.0 (for example, 0.85 to 2.10), the result is not statistically significant at that confidence level. The data is compatible with the exposure having no effect at all. If the entire interval stays above 1.0 or entirely below 1.0, you have a statistically significant finding.
When You Can and Cannot Use Risk Ratio
Risk ratio requires that you know the total number of people in each group who could have developed the outcome. This is possible in cohort studies (where you follow groups forward in time) and in randomized controlled trials. In both designs, you start with defined groups and measure how many develop the outcome.
You cannot calculate a risk ratio from a case-control study. In that design, you start by selecting people who already have the outcome and a comparison group who don’t. Because the researcher decides how many people go into each group, the data doesn’t reflect true population risks. The CDC notes that the odds ratio is the appropriate measure for case-control studies, since it doesn’t require knowing population-level risk.
Risk Ratio vs. Absolute Risk Difference
Risk ratio is a relative measure. It tells you how many times more (or less) likely the outcome is in one group compared to another, but it doesn’t tell you how common the outcome actually is. This distinction matters enormously for decision-making.
Consider two scenarios. In the first, a treatment reduces disease risk from 40% to 20%. In the second, it reduces risk from 0.002% to 0.001%. Both produce a risk ratio of 0.5, meaning the treatment cuts risk in half. But the first scenario means 20 fewer cases per 100 people, while the second means 1 fewer case per 100,000. The practical importance is vastly different.
The absolute risk difference captures this. It’s calculated by simply subtracting the risk in one group from the risk in the other: R1 minus R0. From the absolute risk difference, you can also calculate the number needed to treat (NNT), which is 1 divided by the absolute risk difference. The NNT tells you how many people need to receive a treatment for one additional person to benefit. In the first scenario above, the NNT is 5. In the second, it’s 100,000. Reporting both relative and absolute measures gives the fullest picture of what your data actually shows.
Reporting Your Results
International reporting standards for clinical trials (the CONSORT guidelines) require that you report both the effect size and its precision for every primary and secondary outcome. In practice, this means presenting the risk ratio alongside its 95% confidence interval. A complete result looks like: RR = 4.0 (95% CI: 1.55 to 16.05). This tells the reader the point estimate, the direction of the effect, and how much uncertainty surrounds it.
When the outcome you’re measuring isn’t rare, be careful about substituting prevalence ratios for risk ratios. The two are only equivalent when certain conditions hold: the disease duration is similar in both groups, the disease is rare, and the disease doesn’t influence the exposure. Outside those conditions, the numbers can diverge meaningfully.