Calculator
Enter your 2×2 study counts, choose formatting options, and calculate the risk ratio.
Example Data Table
This sample study compares event occurrence between an exposed group and an unexposed group.
| Group | Events | Non-events | Total | Risk |
|---|---|---|---|---|
| Exposed group | 42 | 158 | 200 | 21.00% |
| Unexposed group | 21 | 179 | 200 | 10.50% |
Example relative risk: 2.0000
Example 95% confidence interval: 1.2304 to 3.2509
Formula Used
Risk in exposed group = a / (a + b)
Risk in unexposed group = c / (c + d)
Relative risk = [a / (a + b)] / [c / (c + d)]
Risk difference = Risk in exposed − Risk in unexposed
Log standard error = √[(1/a) − (1/(a+b)) + (1/c) − (1/(c+d))]
Confidence interval = exp[ln(RR) ± z × standard error]
Here, a is exposed events, b is exposed non-events, c is unexposed events, and d is unexposed non-events.
If a zero cell appears and continuity correction is enabled, 0.5 is added to each cell before interval estimation.
How to Use This Calculator
- Enter labels for the study, groups, and outcome.
- Fill the four counts from your 2×2 table.
- Choose the confidence level and output precision.
- Add population exposure prevalence if you need population attributable fraction.
- Enable continuity correction when any study cell is zero.
- Press calculate to show results above the form, then export them as CSV or PDF.
Frequently Asked Questions
1. What does relative risk mean?
Relative risk compares event probability between two groups. A value above 1 suggests higher risk in the exposed group, while a value below 1 suggests lower risk.
2. How is relative risk different from odds ratio?
Relative risk compares probabilities directly. Odds ratio compares odds instead of probabilities. Relative risk is often easier to interpret in cohort studies and prospective designs.
3. What does an RR of 1.00 mean?
An RR of 1.00 means the event probability is the same in both groups. It suggests no measurable difference in risk between exposure groups.
4. Why are confidence intervals important?
Confidence intervals show the plausible range for the true relative risk. If the interval includes 1.0, the observed association may not be statistically distinct.
5. When should I use continuity correction?
Use continuity correction when one or more cells are zero. It stabilizes interval estimation by adding a small amount to each cell before calculation.
6. Is this calculator suitable for cohort studies?
Yes. Relative risk is especially useful for cohort studies and trials where event probabilities can be measured directly in exposed and unexposed groups.
7. What if one group has no events?
A zero event count can make interval estimation unstable. Turn on continuity correction to generate a more stable approximate interval and summary.
8. Does a large relative risk prove causation?
No. A large relative risk shows association, not proof of causation. Study design, bias, confounding, and evidence quality still matter.