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Definition — what does that mean?
How many times as likely the outcome is in the exposed group as in the unexposed group.
In Swedish: Relativ risk
RR
How many times as likely the outcome is in the exposed group as in the unexposed group: the exposed group’s risk divided by the unexposed group’s risk, each risk being cases over everyone in the group.
RR=3
RR equals (30 divided by (30 plus 70)) divided by (10 divided by (10 plus 90)), equals (30 divided by 100) divided by (10 divided by 100), equals 0.3 divided by 0.1, equals 3
You are given
a and b are the exposed with and without the outcome, c and d the unexposed with and without it. The risk in a group is the share with the outcome, cases over everyone in the group, and the relative risk is the exposed risk divided by the unexposed risk.
| Outcome | No outcome | |
|---|---|---|
| Exposed | a = 30 | b = 70 |
| Unexposed | c = 10 | d = 90 |
Exposed risk 30 / 100 = 0.30, unexposed risk 10 / 100 = 0.10: RR = 0.30 / 0.10 = 3. The outcome is three times as likely with the exposure.
A relative risk of 3 can be 30% against 10%, as here, or 0.3% against 0.1%. The absolute risk difference, 20 points in the first case and 0.2 in the second, is what the exposure means for a person, and a headline that gives the relative risk alone leaves it out. Its inverse, 1 / 0.20 = 5, is the number of exposed people per extra case.
The odds ratio compares odds instead of risks: (30 / 70) / (10 / 90) = 3.86 for the same table. The odds ratio is further from 1 whenever the outcome is common, and the two agree when it is rare. Risk is the measure a reader understands; the odds ratio is the one a case–control study can compute.
The groups were followed forward from the exposure, as in a cohort study or a trial, so that the share with the outcome in each group is a real risk. In a case–control study the researcher sets those shares, and the relative risk is not meaningful; the odds ratio is used instead.
What is a relative risk of 1?
No difference between the groups.
What is the relative risk reduction?
1 − RR when the exposure is protective: an RR of 0.75 is a 25% reduction in relative terms, however
small the absolute risk was.
Where is it calculated with an interval?
In the sensitivity and specificity calculator, which takes a 2×2 table of any kind.
| Solve for | Rearranged | With the numbers | Comes to |
|---|---|---|---|
| RR | aa | 3030 | 3 |
| a | RR·cc | 3·1010 | 30 |
| b | a(1 | 30(1 | 70 |
| c | a(a | 30(30 | 10 |
| d | c(1 | 10(1 | 90 |
Last reviewed October 20, 2026 ·How pages are reviewed
Statistics and probabilityAll formulas
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