Relative Risk Calculator
Calculate and interpret relative risk by comparing the probability of an outcome between an exposed group and an unexposed group.
The Relative Risk Calculator is designed to compare the risk of a specified outcome between two groups: an exposed group and an unexposed group. Relative risk, also called the risk ratio, is commonly used in epidemiological, biological, clinical, cohort, and population research.
Enter the number of individuals with and without the outcome in both groups. The calculator determines the total size of each group, calculates the risk in each group, and then calculates the relative risk.
The result also includes the mathematical formula, substituted calculation, and a research-focused interpretation to help explain what the calculated value represents.
Calculate Relative Risk
Relative Risk Calculator
Calculate the relative risk of an outcome between an exposed group and an unexposed group.
Study Data
| Outcome / Case | No Outcome | |
|---|---|---|
| Exposed Group | ||
| Unexposed Group |
Calculation Result
Relative Risk (RR) = Risk in Exposed Group ÷ Risk in Unexposed Group
Risk in Exposed Group = a ÷ (a + b)
Risk in Unexposed Group = c ÷ (c + d)
How the Relative Risk Calculator works
1. Exposed group
Enter the number of individuals in the exposed group who experienced the specified outcome and the number who did not experience the outcome.
2. Unexposed group
Enter the corresponding outcome and no-outcome counts for the unexposed or comparison group.
3. Calculate group risks
The risk in each group is calculated by dividing the number of individuals with the outcome by the total number of individuals in that group.
4. Calculate Relative Risk
The risk in the exposed group is divided by the risk in the unexposed group to obtain the Relative Risk.
Relative Risk Formula
Relative Risk (RR) = Risk in Exposed Group ÷ Risk in Unexposed Group
Risk in Exposed Group = a ÷ (a + b)
Risk in Unexposed Group = c ÷ (c + d)
Therefore:
RR = [a ÷ (a + b)] ÷ [c ÷ (c + d)]
Relative Risk worked example
Suppose a study contains the following observations:
- 30 exposed individuals experienced the outcome.
- 70 exposed individuals did not experience the outcome.
- 15 unexposed individuals experienced the outcome.
- 85 unexposed individuals did not experience the outcome.
The exposed-group risk is:
30 ÷ (30 + 70) = 0.30 = 30%
The unexposed-group risk is:
15 ÷ (15 + 85) = 0.15 = 15%
Therefore:
RR = 0.30 ÷ 0.15 = 2
The observed risk in the exposed group is therefore 2 times the observed risk in the unexposed group in this example.
How to interpret Relative Risk
RR = 1
A Relative Risk of approximately 1 indicates that the observed risk is the same in the exposed and unexposed groups in the analyzed dataset.
RR > 1
A Relative Risk greater than 1 indicates that the observed risk is higher in the exposed group than in the unexposed group.
RR < 1
A Relative Risk below 1 indicates that the observed risk is lower in the exposed group than in the unexposed group.
Relative Risk describes the relationship observed in the analyzed data. It should not automatically be interpreted as proof of causation. Interpretation should consider study design, sample size, exposure classification, outcome definition, follow-up period, potential confounding variables, selection effects, and statistical uncertainty.
Factors that can affect Relative Risk interpretation
Study design
Relative risk is particularly useful when the risks or incidences of an outcome can be estimated for defined groups over a specified observation period.
Sample size
Small datasets can produce unstable estimates. The magnitude of Relative Risk should therefore be considered together with appropriate statistical uncertainty.
Outcome definition
The outcome should be defined consistently between the exposed and unexposed groups.
Exposure classification
Misclassification of exposure status can influence the calculated relationship between exposure and outcome.
Confounding
Other variables associated with both exposure and outcome may influence an observed Relative Risk.
Follow-up
Differences in observation or follow-up periods between groups can affect interpretation of observed risks.
How to calculate Relative Risk
- Record the number of outcome events and non-events in the exposed group.
- Record the number of outcome events and non-events in the unexposed group.
- Calculate the total number of individuals in each group.
- Calculate the risk in the exposed group.
- Calculate the risk in the unexposed group.
- Divide the exposed-group risk by the unexposed-group risk.
- Interpret the resulting Relative Risk in the context of the research design and study population.
How to report Relative Risk in research
When reporting Relative Risk in a research paper, thesis, dissertation, epidemiological analysis, or biological study, provide enough information for readers to understand how the estimate was obtained.
- Define the exposed and unexposed groups.
- Clearly define the outcome.
- Report the number of outcome and non-outcome observations.
- State the observation or follow-up period when relevant.
- Report the calculated Relative Risk.
- Include an appropriate confidence interval or other measure of uncertainty when required by the study design.
- Describe relevant confounding variables and analytical methods when applicable.
Relative Risk and other epidemiological measures
Relative Risk vs Odds Ratio
Relative Risk compares risks between two groups, whereas Odds Ratio compares the odds of an outcome between groups. The two measures have different mathematical interpretations and should not automatically be treated as interchangeable.
Relative Risk vs Prevalence
Relative Risk compares outcome risks between groups, while prevalence describes the proportion of a population with an existing condition at a defined time or observation point.
Relative Risk vs Incidence
Incidence measures the occurrence of new cases or events over a specified population and time framework. Relative Risk compares the resulting risks between groups.
Relative Risk vs Mortality
Mortality measures describe deaths in a defined population, whereas Relative Risk can be used to compare the risk of a specified outcome between two groups.
Relative Risk Calculator FAQ
What is Relative Risk?
Relative Risk is the ratio of the risk of an outcome in an exposed group to the risk of the same outcome in an unexposed group.
What does a Relative Risk of 2 mean?
A Relative Risk of 2 means that the observed risk in the exposed group is twice the observed risk in the unexposed group in the analyzed dataset.
What does Relative Risk equal to 1 mean?
A Relative Risk of 1 indicates that the observed risk is the same in the exposed and unexposed groups.
What does Relative Risk below 1 mean?
A Relative Risk below 1 indicates that the observed risk is lower in the exposed group than in the unexposed group.
What does Relative Risk above 1 mean?
A Relative Risk above 1 indicates that the observed risk is higher in the exposed group than in the unexposed group.
Is Relative Risk the same as Odds Ratio?
No. Relative Risk compares risks, whereas Odds Ratio compares odds. They are different measures and can produce different numerical values, particularly when the outcome is not rare.
Does Relative Risk prove causation?
No. Relative Risk describes an observed association between exposure and outcome. Causal interpretation requires consideration of study design, confounding, bias, temporal relationships, and other evidence.
Continue your epidemiological analysis
Use Relative Risk in your research workflow
Calculate the risks in both study groups, obtain the Relative Risk, review the mathematical formula, and interpret the result in relation to your research design and defined outcome.
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