Relative Risk Calculator
Calculate relative risk, risk difference and 95% confidence interval from a cohort 2×2 table. Compare event risk across two groups.
Relative risk
3
Risk in exposed ÷ risk in unexposed
95% confidence interval
1.6484 – 5.4597
Taylor series
Risk difference
0.4
Exposed 0.6 vs unexposed 0.2
RR = 1 means no difference; RR > 1 means the exposure raises risk. Relative risk needs a defined unexposed group.
Relative Risk Calculator on True Calculator gives you an instant, accurate answer with no sign-up and no app install. Calculate relative risk, risk difference and 95% confidence interval from a cohort 2×2 table. Compare event risk across two groups. Every result shows the formula and a worked example so you can verify the calculation yourself, and all values are computed in your own browser — your numbers never leave your device.
Popular uses: relative risk calculator · risk ratio calculator · relative risk confidence interval
Reviewed by the True Calculator team · Last updated: August 2026
How We Calculate
This calculator uses standard statistical formulas as defined in textbooks and statistical software. All calculations are performed instantly in your browser using JavaScript — no data is sent to any server.
Formulas follow the conventions used in academic statistics, including population and sample variants where they differ.
When to Use This Calculator
Use the relative risk calculator whenever you compare event rates between two defined groups followed over time — the standard design in cohort studies, vaccine trials, clinical research and workplace safety studies across India. Researchers compute the risk in the exposed group and the unexposed group, then divide to get the relative risk and subtract to get the risk difference, both of which this calculator produces alongside the 95% confidence interval. Insurance underwriters apply the same logic to policyholder claims data, and HR teams compare injury rates between departments. Because the output separates the two group risks from the ratio, it also serves as a quick risk comparison tool for any 2×2 outcome table, with the interval signalling whether the observed difference is statistically meaningful or plausibly due to chance.
How to Use This Calculator
- Step 1: Enter the number of exposed people who had the event in cell a.
- Step 2: Enter the number of exposed people without the event in cell b.
- Step 3: Enter the unexposed counts with and without the event in cells c and d.
- Step 4: Read the relative risk, 95% interval, group risks and risk difference.
Worked Example
A cohort study in Punjab follows 100 farmers: 30 of 50 using a new pesticide developed a skin condition (a = 30, b = 20), while 10 of 50 not using it did (c = 10, d = 40). The exposed risk is 30/50 = 0.6 and the unexposed risk is 10/50 = 0.2, so the relative risk is 0.6 ÷ 0.2 = 3 — the condition is three times as likely with the pesticide. The 95% interval spans about 1.65 to 5.46, excluding 1, and the risk difference of 0.4 means 40 more cases per 100 exposed people.
Tips and Common Mistakes
- •Tip 1: Use the risk difference for public messaging — '40 extra cases per 100 exposed' is more concrete than a ratio.
- •Tip 2: Relative risk requires cohort-style data; for case-control studies switch to the odds ratio calculator.
- •Tip 3: A relative risk below 1 indicates a protective exposure — for example, a vaccine reducing risk to 0.3.
- ✗Mistake 1: Reporting relative risk when the unexposed group had zero events — the ratio is undefined, so the calculator refuses.
- ✗Mistake 2: Quoting only the ratio without the interval; a large RR from a tiny study can still be statistically weak.
Frequently Asked Questions
What is relative risk?
Relative risk (RR) is the ratio of the event rate in an exposed group to the event rate in an unexposed group: RR = (a/(a+b)) ÷ (c/(c+d)). An RR of 3 means the event is three times as likely in the exposed group. RR = 1 means no difference, and values below 1 mean the exposure is protective.
How is relative risk different from an odds ratio?
Relative risk compares probabilities directly and is intuitive, but it requires a cohort study where both groups are followed over time. The odds ratio compares odds and is used for case-control studies. When an event is rare, the two numbers are close; when it is common, the odds ratio exaggerates the risk. For a = 30, b = 20, c = 10, d = 40, RR = 3 while OR = 6.
What is the risk difference?
The risk difference is simply the exposed event rate minus the unexposed event rate: 0.6 − 0.2 = 0.4 in the example above. It states in absolute terms how many more (or fewer) events occur per person in the exposed group, which is often more meaningful for public policy than the ratio.
How is the 95% confidence interval computed?
The calculator uses the Taylor series method: it takes the natural log of RR, adds and subtracts 1.96 times the standard error, then converts back. For RR = 3 the 95% interval is about 1.65 to 5.46. Since it excludes 1, the elevated risk is statistically significant.
When is relative risk used in Indian healthcare?
Cohort studies on lifestyle and disease report relative risk constantly — for example, the elevated risk of heart disease among smokers compared with non-smokers, or the protective effect of a vaccine. The calculator is also used in epidemiological tables, clinical trial reports and insurance underwriting risk models.
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