# Relative Risk Calculator

The relative risk calculator can be used to estimate the relative risk (or risk ratio) and its confidence interval for two different exposure groups.

Enter the data into the table below, select the required confidence level from the dropdown menu, click "Calculate" and the results will be displayed below.

Relative Risk (Risk Ratio) Calculator
Disease No Disease Total
Exposed Group A = B = ? = A + B
Not Exposed Group C = D = ? = C + D

Related

## What is Relative Risk Calculator

The relative risk is a statistical measure used in epidemiology and medical research to assess the association between an exposure (such as a risk factor or treatment) and an outcome (such as a disease or health condition). It quantifies the likelihood of an outcome occurring in one group compared to another.

To calculate relative risk, you need information about the number of individuals in two different groups (exposed and unexposed) and the number of individuals who experienced the outcome in each group.

The formula for calculating relative risk is as follows:

Relative Risk (RR) = (a / (a + b)) / (c / (c + d))

Where:

• "a" represents the number of individuals who are exposed and experience the outcome.
• "b" represents the number of individuals who are exposed but do not experience the outcome.
• "c" represents the number of individuals who are unexposed and experience the outcome.
• "d" represents the number of individuals who are unexposed and do not experience the outcome.

To use a relative risk calculator, you typically input the values for each category (a, b, c, and d), and the calculator provides you with the calculated relative risk.

Keep in mind that relative risk values above 1 indicate an increased risk associated with the exposure, values equal to 1 indicate no association, and values below 1 indicate a decreased risk associated with the exposure.

It's important to note that interpreting relative risk requires careful consideration of the study design, sample size, and other factors. Additionally, it's recommended to consult with experts or professionals when analyzing epidemiological data.

If you provide me with the specific values for a, b, c, and d, I can assist you further by calculating the relative risk.

## The relative risk calculator uses the following formulas:

Relative Risk (RR) = [A/(A+B)] / [C/(C+D)] = Probability of Disease in Exposed / Probability of Disease in Unexposed

Interpretation:

• If Relative Risk = 1, there is no association
• If Relative Risk < 1, the association is negative
• If Relative Risk > 1, the association is positive

Lower Bound of Confidence Interval (LB) = exp( ln(RR) − z * (1/A + 1/C − 1/(A + B) − 1/(C + D)) 1/2 )

Upper Bound of Confidence Interval (UB) = exp( ln(RR) + z * (1/A + 1/C − 1/(A + B) − 1/(C + D)) 1/2 )

Where z is the z-score corresponding to the desired confidence level (e.g., for a 95% confidence level, z = 1.96)

## Relative Risk Calculator Example

Sure! Let's say we have the following example data for a study on the association between smoking and lung cancer:

• Number of smokers who developed lung cancer (a): 200
• Number of smokers who did not develop lung cancer (b): 800
• Number of non-smokers who developed lung cancer (c): 50
• Number of non-smokers who did not develop lung cancer (d): 950

Using these values, we can calculate the relative risk as follows:

Relative Risk (RR) = (a / (a + b)) / (c / (c + d))

Relative Risk (RR) = (200 / (200 + 800)) / (50 / (50 + 950))

Relative Risk (RR) = (0.2) / (0.05)

Relative Risk (RR) = 4

In this case, the calculated relative risk is 4. This means that the risk of developing lung cancer for smokers is four times higher compared to non-smokers in the study.

Please note that this example is for illustrative purposes only. In real-world scenarios, it is crucial to consider additional factors such as study design, sample size, and statistical significance when interpreting the results.