Relative Risk Calculator

Calculate the relative risk (risk ratio) from a 2x2 contingency table. Relative risk compares the probability of an outcome in an exposed group versus an unexposed group.

2x2 Contingency Table

Event (+)No Event (-)
Exposed
Unexposed

a = exposed with event, b = exposed without event
c = unexposed with event, d = unexposed without event

RELATIVE RISK (RR)
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Risk in Exposed
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Risk in Unexposed
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95% CI (Lower)
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95% CI (Upper)
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What Is Relative Risk?

Relative risk (RR), also called the risk ratio, is a measure of association used in epidemiology and clinical research. It compares the probability of an outcome (e.g., disease) in an exposed group to the probability in an unexposed (control) group. RR is calculated from prospective (cohort) studies where subjects are followed over time.

An RR of 1.0 means no difference in risk between groups. An RR greater than 1.0 indicates increased risk in the exposed group, while an RR less than 1.0 indicates decreased risk (a protective effect). The further the RR is from 1.0, the stronger the association.

Formula

RR = [a / (a + b)] / [c / (c + d)]
95% CI = eln(RR) ± 1.96 × SE
SE = √(1/a - 1/(a+b) + 1/c - 1/(c+d))

Where a = exposed with outcome, b = exposed without outcome, c = unexposed with outcome, and d = unexposed without outcome. The 95% confidence interval uses the log-transformed RR and its standard error.

Interpreting Relative Risk

RR ValueInterpretationExample
RR = 1.0No associationExposure has no effect on outcome
RR > 1.0Positive association (risk factor)Smoking and lung cancer (RR ≈ 15-30)
RR < 1.0Negative association (protective)Vaccination and disease (RR ≈ 0.1)
RR = 2.0Double the riskExposed group has 2x the risk
RR = 0.5Half the riskExposed group has 50% lower risk

Frequently Asked Questions

What is the difference between relative risk and odds ratio?

Relative risk compares probabilities (risks) directly: P(event|exposed) / P(event|unexposed). The odds ratio compares odds: [a/b] / [c/d] = (a*d) / (b*c). The odds ratio is used in case-control studies where true risk cannot be calculated. When the outcome is rare (less than 10%), the odds ratio approximates the relative risk.

When is the 95% confidence interval important?

The 95% CI tells you the range of plausible values for the true relative risk. If the interval includes 1.0, the result is not statistically significant at the 5% level -- meaning you cannot conclude that the exposure is associated with the outcome. A narrow CI indicates a precise estimate, while a wide CI suggests more uncertainty.