What is relative risk?

Relative risk (RR), also called the risk ratio, is the probability of an event occurring in the exposed group divided by the probability in the unexposed group. RR = 1 means no difference; RR > 1 means increased risk; RR < 1 means reduced risk.

How is relative risk different from odds ratio?

Relative risk is based on probabilities (risk), while odds ratio (OR) is based on odds. They give similar results when the outcome is rare, but diverge as event rates increase. RR is more intuitive for cohort studies; OR is common in case-control studies and logistic regression.

What is absolute risk reduction (ARR)?

ARR is the arithmetic difference between the event rate in the control group and the event rate in the treated/exposed group. It represents the absolute benefit of an intervention. For example, ARR of 5% means the intervention prevents 5 events per 100 people.

What is number needed to treat (NNT)?

NNT = 1 / ARR. It is the number of patients who need to receive the treatment to prevent one additional adverse event. A lower NNT indicates a more effective intervention.

How are the confidence intervals calculated?

The 95% CI for RR uses the log-normal method (Wald interval on log scale). The 95% CI for OR uses the same log-normal approach with the standard error of log(OR). Both require all four cell counts to be greater than zero.

When is the result statistically significant?

If the 95% confidence interval for RR or OR does not include 1, the result is considered statistically significant at the p < 0.05 level. An interval crossing 1 means the observed difference could be due to chance.

Relative Risk Calculator

Name: Relative Risk Calculator
Availability: InStock
Author: Nham Vu

Enter a 2x2 contingency table to compute relative risk, odds ratio, absolute risk reduction, and number needed to treat with 95% confidence intervals.

2×2 Contingency Table

Enter the cell counts for your exposed and unexposed groups.

	Event	No Event	Total
Exposed			—
Unexposed			—

Exposed group label

Unexposed group label

Load example:

Enter cell counts and click Calculate

Results will appear here

Relative Risk (RR)

—

95% CI: —

Odds Ratio (OR)

—

95% CI: —

Absolute Risk Reduction (ARR)

—

95% CI: —

Number Needed to Treat (NNT)

—

95% CI: —

Event Rates

Group	Events	Total	Risk

Summary

Enter a 2x2 contingency table to compute relative risk, odds ratio, absolute risk reduction, and number needed to treat with 95% confidence intervals.

How it works

Enter the number of events and non-events for the exposed group.
Enter the number of events and non-events for the unexposed (control) group.
Click Calculate to compute all statistics instantly.
Review relative risk, odds ratio, ARR, and NNT with 95% confidence intervals.
Use the interpretation panel to understand whether your result is statistically significant.

Use cases

Evaluate clinical trial outcomes comparing treatment vs. placebo groups.
Analyze cohort study results for disease risk in exposed vs. unexposed populations.
Determine how many patients need treatment to prevent one event (NNT).
Compare vaccine efficacy by computing risk reduction between vaccinated and unvaccinated groups.
Support epidemiology research and public health decision-making.
Quickly check statistical significance of 2x2 table data.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu