Relative Risk Calculator
The risk ratio between two groups, with its confidence interval — plus the absolute risk difference, which is what actually tells you whether the effect matters.
Relative risk is the probability of the outcome in the exposed group divided by the probability in the unexposed.
How the relative risk calculator works
Relative risk is the probability of the outcome in the exposed group divided by the probability in the unexposed. Its confidence interval is built on the log scale with standard error √(1/a − 1/(a+b) + 1/c − 1/(c+d)).
The relative figure is the headline; the absolute risk difference is the one that decides anything. A doubling of a 1-in-100,000 risk is still a 1-in-100,000 risk.
Formula: RR = [a/(a+b)] / [c/(c+d)]
Worked examples
| Inputs | Relative risk | Note |
|---|---|---|
| 30/100 against 15/100 | 2 | RR = 2.0, but only 15 points in absolute terms |
| No difference | 1 | RR = 1 |
| A rare outcome doubled | 2 | RR = 2, absolute difference 0.001 points |
FAQFrequently asked questions
What is relative risk?
The probability of an outcome in one group divided by the probability in another. RR = 2 means twice as likely.
Why does the absolute difference matter more?
Because it tells you how many people are actually affected. Doubling a 0.001% risk sounds alarming and changes almost nothing.
When can I use RR?
In cohort studies and trials, where you know who was exposed and follow them forward. Case-control studies can only give odds ratios.
What is the number needed to treat?
The reciprocal of the absolute risk difference — how many people you must treat for one to benefit. It is the single most useful number in clinical reporting.
Why do headlines always use relative figures?
Because they are larger. "50% higher risk" is a better headline than "0.3 percentage points", even when they describe the same finding.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Australian Curriculum (ACARA) — Mathematics — the terms and methods taught in Australian schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.