risk ratio calculator

What is a risk ratio?

A risk ratio (also called relative risk) compares the probability of an event in one group versus another. It is commonly used in cohort studies, clinical trials, epidemiology, and public health reports.

In plain language, risk ratio answers: “How many times as likely is the event in the exposed group compared with the unexposed group?”

Formula

Let:

• a = events in exposed group
• b = non-events in exposed group
• c = events in unexposed group
• d = non-events in unexposed group

Then:

Risk in exposed = a / (a + b)
Risk in unexposed = c / (c + d)
Risk Ratio = [a / (a + b)] / [c / (c + d)]

How to use this calculator

1. Enter the number of events in the exposed group.
2. Enter the total number of people in the exposed group.
3. Enter the number of events in the unexposed group.
4. Enter the total number of people in the unexposed group.
5. Click Calculate to see risk, risk ratio, confidence interval (when available), and interpretation.

How to interpret risk ratio values

RR = 1

No relative difference in risk between groups.

RR > 1

The exposed group has a higher risk. Example: RR = 1.50 means 50% higher risk.

RR < 1

The exposed group has a lower risk. Example: RR = 0.70 means 30% lower risk.

Example

Suppose 30 out of 200 exposed individuals experience the outcome, while 15 out of 220 unexposed individuals experience it.

• Exposed risk = 30/200 = 0.15 (15%)
• Unexposed risk = 15/220 ≈ 0.0682 (6.82%)
• Risk ratio ≈ 0.15 / 0.0682 ≈ 2.20

Interpretation: the exposed group has about 2.2 times the risk of the outcome relative to the unexposed group.

Risk ratio vs odds ratio

Risk ratio and odds ratio are related but not interchangeable:

• Risk ratio compares probabilities directly.
• Odds ratio compares odds, and is often used in case-control studies or logistic regression.
• When outcomes are rare, odds ratio and risk ratio can be numerically similar.

Common mistakes to avoid

• Using percentages directly without converting to probabilities consistently.
• Entering totals smaller than event counts.
• Interpreting association as proof of causation.
• Ignoring confidence intervals and sample size.

Important notes

This tool is intended for educational and analytical use. Always interpret results in context: study design, confounders, bias, and clinical significance all matter.

If you are evaluating medical outcomes, policy interventions, or safety decisions, consult a qualified statistician, epidemiologist, or clinician before making high-stakes conclusions.