# Relative Risk Reduction Formula Calculator

Determines the relative decrease in the risk of an adverse event in the treatment group compared to the control group.

Refer to the text below the tool for more information about RRR, how its calculated and its properties.

Relative Risk Reduction (RRR) is a term used in epidemiology to define the relative decrease in the risk of an adverse event (contracting a disease or other attributes) in the exposed or treatment group compared to an unexposed or control group.

In short, the RRR tells us by how much the treatment reduced the risk of the adverse outcomes in the treatment group compared to the incidence of the adverse outcomes in the group that didn’t receive the treatment.

`Relative Risk Reduction (RRR) = ((ARC - ART) / ARC) x 100`

Where:

• ARC = Number of events in control group / Number of people in control group
• ART = Number of events in treatment group / Number of people in treatment group

## Control Group

Absolute Risk in Control Group (ARC) Known?
ARC

## Treatment Group

Absolute Risk in Treatment Group (ART) Known?
ART
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Steps on how to print your input & results:

2. Then you can click on the Print button to open a PDF in a separate window with the inputs and results. You can further save the PDF or print it.

Please note that once you have closed the PDF you need to click on the Calculate button before you try opening it again, otherwise the input and/or results may not appear in the pdf.

## Determining Relative Risk Reduction

Relative Risk Reduction (RRR) is a term used in epidemiology to define the relative decrease in the risk of an adverse event (contracting a disease or other attributes) in the exposed or treatment group compared to an unexposed or control group.

The formula may be described as the difference between the incidence in the control and treatment group divided by the incidence in the control group. This is usually expressed as a percentage.

`Relative Risk Reduction (RRR) = ((ARC - ART) / ARC) x 100`

Where:

• ARC = Number of events in control group / Number of people in control group
• ART = Number of events in treatment group / Number of people in treatment group

The RRR is linked to the Relative Risk (RR) which is the ratio between ART and ARC. For example, a RR of 0.8 is synonym to a RRR of 20%, meaning a 20% reduction in the relative risk of the specified outcome in the treatment group compared with the control group.

It is also important to note that RRR is usually constant across a range of absolute risks.

## References

Irwig L, Irwig J, Trevena L, et al. Smart Health Choices: Making Sense of Health Advice. London: Hammersmith Press; 2008. Chapter 18, Relative risk, relative and absolute risk reduction, number needed to treat and confidence intervals.

Elbarbary M. Understanding and expressing "Risk". J Saudi Heart Assoc. 2010; 22(3):159-64.

Griffith JM, Lewis CL, Hawley S, Sheridan SL, Pignone MP. Randomized trial of presenting absolute v. relative risk reduction in the elicitation of patient values for heart disease prevention with conjoint analysis. Med Decis Making. 2009; 29(2):167-74.

Specialty: Epidemiology

Article By: Denise Nedea

Published On: October 27, 2020 · 12:00 AM

Last Checked: October 27, 2020

Next Review: October 27, 2025