How Much More Likely Is the Outcome?
Medical studies rarely say “this treatment works.” Instead they report that patients on the drug were twice as likely to recover — or that smokers face 15–30 times the lung-cancer risk of non-smokers. That “times as likely” number is the relative risk (RR): the ratio of two probabilities.
This free calculator takes a simple 2×2 table — exposed vs unexposed, outcome vs no outcome — and returns the risk ratio with a 95% confidence interval, both absolute risks, the absolute and relative differences, and a plain-English interpretation. Every step of the math is shown.
Risk ratio · 2×2 table · confidence interval
Exposed group
Unexposed (control) group
? How do I read a relative risk?
RR = 1 means the outcome is equally likely in both groups — no association. RR > 1 means higher risk in the exposed group (RR = 2 is double the risk). RR < 1 means the exposure is protective (RR = 0.5 is half the risk).
The confidence interval shows the plausible range of the true RR. If the interval includes 1 (e.g., 0.8–1.5), the result is not statistically significant at that confidence level — the data are compatible with no effect.
Please enter non-negative whole numbers. Each group needs at least one person.
Educational tool, not clinical advice. Relative risk describes association, not causation. Small samples produce wide confidence intervals; a non-significant result means “compatible with no effect,” not “proven safe.”
How to Use This Calculator
- Fill the 2×2 table. In the exposed group: how many had the outcome (a) and how many did not (b). Same for the unexposed group (c and d).
- Click Calculate Relative Risk. The calculator shows both absolute risks, the risk ratio, the 95% confidence interval and a written interpretation.
- Check the confidence interval. If it excludes 1.0, the association is statistically significant at the 5% level.
The Formulas
95% CI via the log method: SE(log RR) = √(1/a − 1/(a+b) + 1/c − 1/(c+d))
Worked example: in a trial, 20 of 100 treated patients recover (a=20, b=80) while 10 of 100 controls recover (c=10, d=90). Risk in treated = 0.20, risk in controls = 0.10, so RR = 0.20 ÷ 0.10 = 2.0 — treated patients are twice as likely to recover.
Reading the Result
| RR value | Meaning |
|---|---|
| > 1 | Exposure raises risk (e.g. 2.0 = twice the risk) |
| = 1 | No association between exposure and outcome |
| < 1 | Exposure is protective (e.g. 0.5 = half the risk) |
The 95% confidence interval is the real verdict: if it excludes 1.0 (e.g. 1.2–3.4), the association is statistically significant; if it includes 1.0 (e.g. 0.8–2.5), the data are consistent with no effect.
Don’t confuse with odds ratio
The odds ratio (OR) compares odds, not risks, and exaggerates the effect when outcomes are common — an OR of 3 with a 30% baseline risk is far less dramatic than it sounds. Relative risk is the number to quote whenever you have the raw 2×2 counts.
From Relative to Absolute: ARR and Number Needed to Treat
Relative risk tells you the multiple; two companion numbers tell you the size. The absolute risk reduction (ARR) is the simple difference between the two risks. In the worked example: 0.20 − 0.10 = 0.10 — ten percentage points. When the outcome is a benefit, like recovery, rather than a harm, the same difference is read as the absolute benefit increase; the arithmetic is identical.
Its reciprocal is the number needed to treat (NNT): 1 ÷ 0.10 = 10. Treat ten patients with the new approach instead of the control and, on average, one extra patient recovers. Clinicians lean on NNT because it is concrete in a way a ratio never is. An RR of 2.0 built on a baseline risk of 0.0001 would need 10,000 treated patients for one extra outcome; this RR of 2.0 needs only 10. Same relative risk, utterly different practical meaning — which is why reporting both numbers matters.
Frequently Asked Questions
What is relative risk in simple terms?
How many times more likely an outcome is in one group versus another. An RR of 2 means twice the risk; an RR of 0.5 means half the risk.
How is relative risk different from absolute risk?
Absolute risk is the raw probability (e.g. 2 in 100 people). Relative risk compares two absolute risks as a ratio. Always report both — a “doubled risk” from 1-in-10,000 to 2-in-10,000 is a very different story than from 10% to 20%.
What does a 95% confidence interval tell me?
The range of true risk ratios compatible with your data. If the interval excludes 1.0, the effect is statistically significant; if it includes 1.0, the data don’t rule out no effect.
Can relative risk be zero or negative?
It can be zero (no outcomes in the exposed group) but never negative — it’s a ratio of probabilities, and probabilities can’t be negative.
When should I use odds ratio instead?
In case-control studies, where you sample by outcome rather than exposure, you can’t compute risks directly — the odds ratio is the valid measure there. In cohort and trial data, prefer relative risk.
Why does my confidence interval look asymmetric?
It’s computed on the log scale (where the sampling distribution is symmetric) and then exponentiated back — so the interval is naturally asymmetric around the point estimate.
What is number needed to treat (NNT)?
The reciprocal of the absolute risk difference: NNT = 1 ÷ ARR. It is the number of people who must receive the treatment or exposure for one additional outcome to occur. An ARR of 0.10 gives an NNT of 10; smaller NNTs mean a stronger practical effect.
Final Thoughts
Relative risk turns a table of counts into a story you can actually quote: “twice as likely,” “half the risk.” Pair it with the confidence interval and the absolute risks, and you have the full, honest picture — which is exactly what this calculator gives you.
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