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Relative Risk Calculator

Exposed group

Control group


Table of Content


The relative risk calculator helps you to calculate the risk ratio between two groups with different exposure levels. This tool makes it easier for researchers and healthcare professionals to understand how different exposures affect health outcomes by showing the difference in risk between the two groups.

What is relative risk?

The relative risk (RR), also known as the risk ratio, is a statistical measure used to compare the risk of an event occurring in an exposed group to the risk of that event occurring in an unexposed group.

Relative risk formula:

The formula for calculating relative risk is:

Relative risk = [a / (a + b)] / [c / (c + d)]


  • a – The number of individuals in the exposed group who experienced the outcome (e.g., developed the disease).
  • b – Individuals in the exposed group who did not experience the outcome.
  • c – Number of individuals who experienced the outcome in the unexposed group.
  • d – Unexposed individuals who didn’t experience the outcome.

How to calculate the relative risk rate?

To calculate the relative risk, we've included a helpful example below. It demonstrates the application of the formula we mentioned earlier. 


Let’s say, we are conducting a study to analyze the relationship between smoking and lung cancer. Here’s the data:

  • a = 10: 10 smokers in our study developed lung cancer.
  • b = 90: 90 smokers in our study did not develop lung cancer.
  • c = 2: 2 non-smokers in our study developed lung cancer.
  • d = 98: 98 non-smokers in our study did not develop lung cancer.

Now use the RR formula to calculate the relative risk:

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

Now add up the values into this equation:

  • RR = [10 / (10 + 90)] / [(2 / (2 + 98)]
  • RR = [10 / 100)] / [(2 / 100)]
  • RR = 0.1 / 0.02
  • RR = 5

In this scenario, the relative risk is 5. This implies that the risk of developing lung cancer is 5 times higher in the group of smokers compared to the group of non-smokers. 

You can get rid of these manual calculations by using our relative risk calculator, this tool makes the entire process much easier for you.

What is the difference between relative risk, odds ratio, and hazard Ratio?

Relative Risk (RR), Odds Ratio (OR), and Hazard Ratio (HR) are all measures of association used in epidemiology and statistical analysis, but they are applied in different contexts and have different interpretations:

Relative Risk (RR):

  • Formula: RR = [a / (a + b)] / [c / (c + d)]
  • Interpretation: Represents the probability of an event occurring in the exposed group compared to the unexposed group. An RR of 1 implies no difference, greater than 1 suggests increased risk and less than 1 suggests decreased risk.

Odds Ratio (OR):

  • Formula: OR = (a/b) / (c/d) (same variables as RR)
  • Interpretation: Captures the odds of the event occurring in the exposed group versus the unexposed group. It is used when the outcome is rare. An OR of 1 implies no association, greater than 1 suggests a positive association and less than 1 suggests a negative association. You can easily calculate it by calculatored relative risk calculator.
  • Example: An OR of 4 for developing a disease after taking a drug means the odds of getting sick are 4 times higher in the exposed group.

Hazard Ratio (HR):

  • Formula: HR = Probability of event in exposed group / Probability of event in unexposed group within a specific time period.
  • Interpretation: Compares the rates of events occurring in the exposed and unexposed groups over time. Often used in survival analysis. An HR of 1 implies no difference in hazards, greater than 1 suggests an increased hazard in the exposed group, and less than 1 suggests a decreased hazard.
  • Example: An HR of 1.5 for developing cancer after radiation exposure means individuals exposed are 1.5 times more likely to develop cancer within a certain time frame compared to unexposed individuals.

Choosing the right measure:

  • When studying risk directly: Use RR if appropriate (common events, large sample size).
  • When dealing with rare events: Consider OR for better interpretation.
  • For time-dependent outcomes: Use HR for survival analysis.

What are confidence intervals and confidence levels?

Risk Ratio Confidence Interval:

A risk ratio confidence interval is like a range of possibilities that helps us understand how certain or uncertain we are about the risk ratio calculated in a study. Instead of giving a single number, it provides a range within which we think the real risk ratio could fall.

Confidence Level:

The confidence level is a measure of how sure we are about our range of possibilities. It's like saying, I'm confident the true value lies somewhere in this range. Common confidence levels are often expressed as percentages, like 95%, meaning we are 95% sure the true value is in our range.

Alan Walker

Studies mathematics sciences, and Technology. Tech geek and a content writer. Wikipedia addict who wants to know everything. Loves traveling, nature, reading. Math and Technology have done their part, and now it's the time for us to get benefits.

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