How this instrument works
Relative risk (RR), also called the risk ratio, compares how often an event happens in two groups: one exposed to some factor and one not. Build a 2×2 table with four counts — a: exposed with the event, b: exposed without it, c: unexposed with the event, d: unexposed without it — and relative risk is simply the exposed group's event risk, a/(a+b), divided by the unexposed group's event risk, c/(c+d).
The result reads directly as a multiplier. RR = 2.0 means the event happened twice as often in the exposed group. RR = 1.0 means the exposure showed no measured association with the event — both groups had identical risk. RR = 0.25 means the exposed group's risk was only a quarter of the unexposed group's, the signature of a protective exposure such as a vaccine or a protective behaviour.
Relative risk is the standard summary statistic in cohort studies and clinical trials, where researchers follow two groups forward in time from exposure to outcome. It differs from the odds ratio, a related but distinct measure computed from the same four counts using odds instead of risk — the two converge for rare events but diverge noticeably when the event is common, which is a frequent source of confusion when reading published research.
- Enter the number of exposed subjects who experienced the event into Exposed with event (a).
- Enter the number of exposed subjects who did not experience the event into Exposed without event (b).
- Enter the number of unexposed subjects who experienced the event into Unexposed with event (c).
- Enter the number of unexposed subjects who did not experience the event into Unexposed without event (d).
- Read Relative risk (RR) — the exposed group's event risk divided by the unexposed group's event risk.
- The unexposed-group event count (c) must be greater than zero — with zero events in the unexposed group, the unexposed risk is zero and relative risk is undefined (a division by zero).
Worked example — a 200-subject exposure study
Enter a = 20, b = 80, c = 10, d = 90. The exposed group's risk is a/(a+b) = 20/100 = 0.2, and the unexposed group's risk is c/(c+d) = 10/100 = 0.1. Relative risk reads 2.0 — the exposed group experienced the event exactly twice as often as the unexposed group.
With 100 subjects in each group here, the two group sizes happen to match, which keeps the arithmetic simple, but relative risk works identically with unequal group sizes too — it only ever compares the within-group risk of each group, never the raw event counts across groups directly.
Questions
What's the difference between relative risk and odds ratio?
Relative risk compares risk — the probability of the event within each group, a/(a+b) versus c/(c+d). Odds ratio compares odds — the ratio of event to non-event within each group, (a/b) versus (c/d), then divides those two odds. The two measures give similar numbers when the event is rare in both groups, but diverge as the event becomes more common; odds ratios tend to overstate the effect size relative to relative risk for common events, which is why study design (cohort versus case-control) usually dictates which measure gets reported.
Why is relative risk undefined when the unexposed-group event count is zero?
Relative risk divides the exposed group's risk by the unexposed group's risk. If nobody in the unexposed group experienced the event, that group's risk is 0/(0+d) = 0, and dividing by zero has no defined result — mathematically, the exposed group would be 'infinitely' riskier by comparison, which isn't a meaningful number to report. In that situation, an odds ratio or a different comparison method is typically used instead.
What does a relative risk of exactly 1.0 mean?
RR = 1.0 means the two groups had identical event risk, so the exposure measured showed no association with the outcome in this data — neither harmful nor protective. Whether that result is statistically meaningful, as opposed to just close to 1.0 by chance, depends on the sample size and would normally be checked with a confidence interval or significance test alongside the point estimate this instrument returns.
Can relative risk be used outside of medical studies?
Yes — the same 2×2 structure applies anywhere you're comparing an event rate between an 'exposed' and an 'unexposed' group: a marketing campaign's conversion rate for two customer segments, a safety incident rate between two work shifts, or a defect rate between two manufacturing batches. Relative risk is a general epidemiological tool, not one confined to disease research, even though that's where the terminology originates.
How is relative risk different from absolute risk reduction?
Relative risk is a ratio (exposed event probability divided by unexposed event probability), while absolute risk reduction is a difference (unexposed probability minus exposed probability, when the exposure is protective). A treatment that lowers the event probability from 2% to 1% has the same RR of 0.5 as one that lowers it from 20% to 10%, but the absolute reduction is very different — 1 percentage point versus 10 — which is why both figures are usually reported together to avoid an overstated impression of a treatment's real-world effect.