A relative risk tells you how the chance of an outcome in one group compares with the chance in another group. To calculate it, divide the risk in the group of interest by the risk in the comparison group: if 10 of 100 people in one group have an outcome and 20 of 100 in the comparison group do, the relative risk is 10% ÷ 20% = 0.5.
That 0.5 does not tell you the whole practical story by itself. You also need the actual event numbers, the time period, who was studied, and the comparison group. Disclosure: This educational page contains no product recommendations or purchase links.
What is relative risk?
Relative risk, also called a risk ratio, compares the probability of an outcome between two groups. In health research, the “outcome” may be a symptom, diagnosis, side effect, recovery, or another event the researchers counted.
The CDC epidemiology lesson defines a risk ratio as the risk in one group divided by the risk in a comparison group. The group in the top part of the calculation is often an exposed group or a treatment group, but check the study table rather than assuming.
How do you calculate relative risk?
Start with a two-by-two table. “Exposed” can mean people who received a treatment, had a particular characteristic, or encountered a possible risk factor. “Not exposed” is the comparison group.
| Group | Had the outcome | Did not have the outcome | Total | Risk |
|---|---|---|---|---|
| Group of interest | a | b | a + b | a ÷ (a + b) |
| Comparison group | c | d | c + d | c ÷ (c + d) |
Relative risk formula:
RR = [a ÷ (a + b)] ÷ [c ÷ (c + d)]
The same formula appears in the Alabama College of Osteopathic Medicine guide. Risk means the number with the outcome divided by everyone in that group. It is not the number with the outcome divided by the number without it; that second calculation is odds.
A relative risk calculation example
The CDC gives a useful real-world outbreak example. In a 1999 tuberculosis outbreak investigation among 294 prison inmates, 28 of 157 people in one dormitory wing developed tuberculosis, compared with 4 of 137 in the other wing. This is an outbreak comparison, not a timed follow-up trial.
| Step | Calculation | Result |
|---|---|---|
| Risk in East wing | 28 ÷ 157 | 0.178, or 17.8% |
| Risk in West wing | 4 ÷ 137 | 0.029, or 2.9% |
| Relative risk | 17.8% ÷ 2.9% | 6.1 |
In that comparison, the East-wing group had 6.1 times the risk of tuberculosis seen in the West-wing group. The number describes an association between the groups. It does not, by itself, settle why the difference occurred.
What do common relative risk numbers mean?
| Relative risk | Plain-language meaning |
|---|---|
| 0.5 | The group of interest had half the risk of the comparison group, a 50% relative reduction. |
| 0.75 | The group of interest had 75% of the comparison group’s risk, a 25% relative reduction. |
| 1.0 | The two groups had the same measured risk. |
| 1.2 | The group of interest had 1.2 times the risk, or a 20% relative increase. |
| 2.1 | The group of interest had 2.1 times the risk, or a 110% relative increase. |
| 2.5 | The group of interest had 2.5 times the risk, or a 150% relative increase. |
There is no single “good” relative risk score. A value below 1 may be welcome when the outcome is harmful, but not when the outcome is beneficial. A value above 1 may matter a great deal or very little depending on what happened, how common it was, and over what period.
Why absolute risk changes the meaning
Absolute risk is the actual chance of the outcome in a group: number with the outcome ÷ total number in that group. Relative risk compares two absolute risks. The distinction protects you from headlines that sound larger than the underlying change.
For example, a relative risk of 1.2 can mean a rise from 30% to 36%: 30% × 1.2 = 36%. It can also mean a rise from 1% to 1.2%. Both are a 20% relative increase, but the absolute changes are 6 percentage points and 0.2 percentage points. A peer-reviewed tutorial in the International Journal of Environmental Research and Public Health explains why relative measures should be read with absolute measures such as risk difference.
For a closer look at this issue in health headlines, see Relative Risk and Absolute Risk.
What does relative risk reduction mean?
When relative risk is less than 1, relative risk reduction is calculated as:
Relative risk reduction = (1 − relative risk) × 100
For an RR of 0.75, the calculation is (1 − 0.75) × 100 = 25%. That means a 25% relative reduction compared with the reference group. It does not tell you how many people had the outcome until you look at the two original risks.
A 2021 tutorial describes a four-year randomized, placebo-controlled trial of 6,729 men aged 50 to 75. The outcome occurred in 659 of 3,305 people in the treatment group and 858 of 3,424 people in the placebo group: 20% versus 25%, for a relative risk of 0.80. The relative reduction was 20%, while the absolute difference was 5 percentage points. The study type, sample size, four-year follow-up, and placebo comparison all matter when reading that number.
Relative risk versus odds ratio: are they the same?
No. Risk is the number with an outcome divided by everyone in the group. Odds are the number with an outcome divided by the number without it. A relative risk compares risks; an odds ratio compares odds.
Odds ratios are commonly used in case-control studies, where researchers begin with people who already have an outcome and compare their earlier exposures with a control group. The CDC notes that this design usually cannot provide the population risk needed to calculate a risk ratio. When an outcome is rare, an odds ratio and a relative risk can be close; when it is common, they can differ substantially.
What does a 1.5 hazard ratio mean?
A hazard ratio is a different, time-based measure. A hazard ratio of 1.5 means the study estimated a 50% higher event rate over the period analyzed for one group versus the comparison group. Read it with the follow-up length, the number of events, and the absolute risks; it is not calculated with the simple two-by-two relative-risk formula above.
What should you check before trusting a relative risk claim?
- Which group is on top? Reversing the groups changes the ratio.
- What were the actual risks? Ask for both percentages and the number of people in each group.
- How long were people followed? A result over weeks can mean something different from a result over years.
- What kind of study was it? A randomized trial assigns groups by chance; a cohort study follows groups based on an exposure; a case-control study generally reports odds ratios instead.
- What is the confidence interval? A confidence interval is a range showing how precise an estimate is. If an RR confidence interval includes 1, the range includes no difference between groups.
- Who was studied? Age, health status, and setting affect how well a result applies to you or the person you care for. Who Was Studied Matters can help you ask that question.
Questions to take to a clinician
- What are the absolute risks for someone like me over the stated time period?
- What was the comparison group, and does it fit my situation?
- Was this a randomized trial, a cohort study, or a case-control study?
- What does the confidence interval say about how certain the estimate is?
- Which benefits and harms matter most for my decision?
Bring the headline or study with you and write down your questions beforehand. MedlinePlus visit preparation guidance recommends bringing a list of questions and your medicines, vitamins, and supplements to an appointment. You can also use this site’s Open-Questions List to keep the numbers and questions together.
By Health Evidence Literacy Guide Editorial Team
This article is for general information purposes only and does not constitute medical advice. Consult your doctor or qualified healthcare provider before making changes to your health routine.
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