Relative Risk Calculator

What Relative Risk Means

Relative risk, also called the risk ratio, compares the probability of an event in an exposed group with the probability of the same event in a control group. It is widely used in epidemiology, clinical studies, and public-health reporting. Related tools: Post-Test Probability Calculator and P Hat Calculator.

Relative Risk Formula

From a 2×2 table, $a$ is exposed with the event, $b$ is exposed without the event, $c$ is control with the event, and $d$ is control without the event:

$$RR = \frac{a/(a+b)}{c/(c+d)}$$

$RR = 1$ means no difference. $RR > 1$ means higher risk in the exposed group. $RR < 1$ means lower risk in the exposed group.

Confidence Interval

The log method interval is

$$\exp\left(\ln(RR) \pm z \sqrt{\frac{1}{a}+\frac{1}{c}-\frac{1}{a+b}-\frac{1}{c+d}}\right)$$

If the interval includes 1, the observed difference is not statistically significant at that confidence level. Larger samples shrink the interval. For sample planning, see the Sample Size Calculator.

Example

If 24 of 200 exposed people have the event and 9 of 200 controls have it, then $RR = 0.12 / 0.045 = 2.67$. The exposed group has about 2.67 times the event risk of the control group.