InfyCalculator

Relative Risk Calculator

Calculate relative risk (the risk ratio) from a 2×2 table of exposed and unexposed groups, with the underlying risks and a plain reading.

Exposed — cases
Exposed — total
Unexposed — cases
Unexposed — total
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How it works

RR = (a ÷ exposed total) ÷ (c ÷ unexposed total)

Relative risk compares the rate of an outcome between an exposed group and an unexposed group. Compute each group’s risk as its cases divided by its total, then divide the exposed risk by the unexposed risk. An RR of 1 means no difference, above 1 means the exposure is associated with more of the outcome, and below 1 means it is associated with less (a protective effect).

Worked example

If 30 of 100 exposed people develop the outcome (30%) and 10 of 100 unexposed do (10%), then RR = 0.30 ÷ 0.10 = 3.0. The exposed group has three times the risk — 200% higher — with an absolute risk difference of 20 percentage points.

Frequently asked questions

What is the difference between relative risk and odds ratio?

Relative risk compares probabilities directly and is intuitive for cohort studies, where you follow groups forward. The odds ratio compares odds and is used in case-control studies; for rare outcomes the two are close, but for common outcomes they diverge.

Why does absolute risk matter alongside relative risk?

A large relative risk can hide a tiny absolute change. Tripling a risk from 1 in a million to 3 in a million is an RR of 3 but almost no real-world impact — always read the relative and absolute figures together.

Does a relative risk above 1 prove the exposure is harmful?

No. It shows an association in this data, not causation. Confounding variables, study design and chance all matter, and a confidence interval around the RR is needed to judge whether the result is statistically meaningful.

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For education — check assumptions (sample size, distribution) before using statistics in real decisions.