# Relative Risk Calculator

Free relative risk calculator. Calculate the risk ratio, absolute risk difference, and NNT from a 2x2 contingency table with 95% confidence interval.

## What this calculates

Calculate the relative risk (risk ratio) comparing event rates between exposed and unexposed groups. Also computes absolute risk difference, NNT, and 95% confidence interval.

## Inputs

- **a: Exposed + Event** — min 0 — Number in exposed group who experienced the event.
- **b: Exposed + No Event** — min 0 — Number in exposed group who did NOT experience the event.
- **c: Unexposed + Event** — min 0 — Number in unexposed group who experienced the event.
- **d: Unexposed + No Event** — min 0 — Number in unexposed group who did NOT experience the event.

## Outputs

- **Relative Risk (RR)** — The risk ratio comparing exposed to unexposed.
- **Risk in Exposed Group** — formatted as percentage — Event rate in the exposed group: a / (a + b).
- **Risk in Unexposed Group** — formatted as percentage — Event rate in the unexposed group: c / (c + d).
- **Absolute Risk Difference** — formatted as percentage — Difference in risk between groups.
- **95% CI Lower** — Lower bound of the 95% confidence interval.
- **95% CI Upper** — Upper bound of the 95% confidence interval.
- **NNT (Number Needed to Treat)** — Number needed to treat/harm (1 / absolute risk difference).
- **Interpretation** — formatted as text — Plain language interpretation.

## Details

Relative risk compares the probability of an event between two groups.

Formula:
RR = [a/(a+b)] / [c/(c+d)]

Interpretation

- RR = 1: Equal risk in both groups

- RR > 1: Higher risk in exposed group

- RR < 1: Lower risk in exposed group

Absolute Risk Difference (ARD):
ARD = risk_exposed - risk_unexposed

Number Needed to Treat (NNT):
NNT = 1 / |ARD|

NNT tells you how many people need to be treated for one additional person to benefit (or be harmed).

## Frequently Asked Questions

**Q: When can I use relative risk vs. odds ratio?**

A: Relative risk can be directly calculated from cohort studies, randomized controlled trials, and cross-sectional studies. In case-control studies, only the odds ratio can be calculated because the sampling design does not preserve the incidence rate. When the outcome is rare (< 10%), OR and RR are approximately equal.

**Q: What is the Number Needed to Treat (NNT)?**

A: NNT is the reciprocal of the absolute risk difference. It tells you how many patients need to receive the treatment for one additional patient to benefit. For example, NNT = 20 means you need to treat 20 people for 1 person to benefit. Lower NNT = more effective treatment.

**Q: Why is absolute risk difference important alongside relative risk?**

A: A large relative risk can be misleading if the baseline risk is tiny. A treatment reducing risk from 0.002% to 0.001% has RR = 2 (impressive sounding) but only reduces absolute risk by 0.001% (NNT = 100,000). Always consider both relative and absolute measures.

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Source: https://vastcalc.com/calculators/statistics/relative-risk
Category: Statistics
Last updated: 2026-04-21