Epidemiology & Public Health
Intermediate

Relative Risk

How many times more likely the exposed group is to develop the disease compared to the unexposed group.

Formula

RR=Risk in ExposedRisk in UnexposedRR = \frac{\text{Risk in Exposed}}{\text{Risk in Unexposed}}

Variables

RRRelative risk
\text{Risk in Exposed}Incidence in the exposed group
\text{Risk in Unexposed}Incidence in the control group

Example

30 % incidence in exposed vs 10 % in unexposed → RR = 3

How it works

Relative risk compares the probability of an outcome in a group that was exposed to a factor with the probability in a group that was not exposed. It works by taking two risks on the same scale and forming a ratio, so a value above 1 means the exposure is associated with a higher risk, a value below 1 means a lower risk, and a value of 1 means no difference. This is useful in studies that follow people over time, because it tells you how much more or less likely disease is in the exposed group.

When to use it

Use relative risk in cohort studies, clinical trials, and other situations where you can directly measure incidence in exposed and unexposed groups. It is especially helpful when you want a simple comparison of disease risk between two groups.

Worked example, step by step

Suppose 12 out of 80 people exposed to a new workplace chemical develop asthma. Risk in exposed = 12/80 = 0.15 Suppose 6 out of 120 people not exposed to the chemical develop asthma. Risk in unexposed = 6/120 = 0.05 RR = Risk in Exposed / Risk in Unexposed RR = 0.15 / 0.05 = 3 Interpretation: the exposed group has 3 times the risk of developing asthma compared with the unexposed group.

Common mistakes to avoid

  • Using the number of cases instead of the incidence proportion in each group
  • Dividing exposed risk by the total sample risk instead of the unexposed risk
  • Interpreting relative risk as the same thing as absolute risk increase

Did You Know?

RR = 1 means no extra risk from the exposure; RR > 1 suggests a harmful factor; RR < 1 suggests a protective one.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026