[Durgical](https://durgical.com/en/) › [DurgiPedia](https://durgical.com/en/durgipedia/) › [Epidemiology](https://durgical.com/en/epidemiology/) › [Measures of frequency and association](https://durgical.com/en/epidemiology/areas/measures/) › Relative risk

# Relative risk

- Measure

How many times more (or less) often the exposed become ill compared with the unexposed.

Updated Nov 5, 2026

## Key points

- RR = [a/(a+b)] / [c/(c+d)].
- RR = 1: no association; RR above 1: exposure raises risk; RR below 1: exposure lowers it (protective).
- It is calculated in cohorts and trials, not in case-control studies.
- If the 95% CI includes 1, the association is not statistically significant at the 5% level.
- RR says nothing about absolute size: an RR of 2 can mean 2 to 4 per million or 20% to 40%.

On this page

- The basics Key points
- What it is
- Formula and reading
- Worked example
- How to read the relative risk
- Markers
- How to read it
- Common pitfalls
- Memory aid

- Study Test yourself

- Connections Connections

## What it is

The relative risk (RR) divides the risk of the outcome in the exposed by the risk in the unexposed. It is calculated in cohort studies and clinical trials, where disease-free people are followed and new cases counted. It shows the strength of an association: an RR of 3 means the exposed have three times the risk. Its confidence interval shows whether the result is compatible with no effect.

## Formula and reading

- RR = risk in the exposed / risk in the unexposed = [a/(a+b)] / [c/(c+d)].
- RR 1.5 = 50% more risk; RR 0.7 = 30% less risk.
- The 95% CI of an RR is asymmetric because it is calculated on the log scale.
- Reading the CI: 2.1 to 4.2 excludes 1, which is compatible with a real increase in risk.

## Worked example

- Data: of 800 families drinking untreated well water, 96 have diarrhoea over the summer; of 1,200 with treated water, 48 do.
- Risk in the exposed = 96 / 800 = 0.12 (12%).
- Risk in the unexposed = 48 / 1,200 = 0.04 (4%).
- RR = 0.12 / 0.04 = 3.0.
- With the usual log method, the 95% CI is about 2.1 to 4.2: it does not include 1.
- Reading: drinking untreated water is linked to three times the risk of diarrhoea in this example.

## How to read the relative risk

| RR value | Reading | Example |
| --- | --- | --- |
| 1 | No association | Same risk in both groups |
| Above 1 | Risk factor | RR 3: three times the risk |
| Below 1 | Protective factor | RR 0.6: 40% less risk |
| 95% CI crossing 1 | Not significant at 5% | RR 1.4 (CI 0.9 to 2.2) |

## Markers

- RR
- 95% CI

## How to read it

- A trial reporting an RR of 0.80 for myocardial infarction shows 20% less relative risk with treatment; a decision also needs the absolute reduction.
- In outbreak investigations, risk is compared between people who ate a food and people who did not.

## Common pitfalls

- Calculating an RR in a case-control study.
- Reading a high RR as a high absolute risk.
- Forgetting that association is not causation: bias or confounding may explain it.

## Memory aid

Relative risk is relative to the unexposed: it is always a fraction with the unexposed underneath.

## Test yourself

Think of the answer, then tap the question to see it.

## In a cohort, 20 of 100 exposed and 5 of 100 unexposed people become ill. What is the RR?

RR = 0.20 / 0.05 = 4: the exposed have four times the risk.

## How is an RR of 0.75 with a 95% CI of 0.60 to 0.94 read?

Exposure is linked to 25% less risk and the interval excludes 1, so it is statistically significant at the 5% level.

## Why is RR not calculated in a case-control study?

Because the number of cases and controls is set by the investigator; incidence in the exposed and unexposed is never observed.

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## Connections

## Related 6

- [The 2×2 table](https://durgical.com/en/epidemiology/the-2-2-table/)
- [Odds ratio](https://durgical.com/en/epidemiology/odds-ratio/)
- [Absolute risk reduction](https://durgical.com/en/epidemiology/absolute-risk-reduction/)
- [Relative risk reduction](https://durgical.com/en/epidemiology/relative-risk-reduction/)
- [Cohort study](https://durgical.com/en/epidemiology/cohort-study/)
- [Confidence interval](https://durgical.com/en/epidemiology/confidence-interval/)

[← All of epidemiology](https://durgical.com/en/epidemiology/)

Educational content on epidemiological and statistical methods; the examples use made-up numbers to teach the calculation. Not a clinical or legal guide: current Colombian rules are in the official sources.

Sources: [Principles of Epidemiology | Lesson 3 - Section 5](https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson3/section5.html) (Centers for Disease Control and Prevention, 2012); [Chapter 6: Choosing effect measures and computing estimates of effect](https://www.cochrane.org/authors/handbooks-and-manuals/handbook/current/chapter-06) (Cochrane, 2024).

## **Spotted a mistake?** We are always improving for the community. Tell us what is wrong and our team will review it. Report a mistake

Representative model, for educational purposes only.

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