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Relative Risk Calculator

The Relative Risk Calculator computes the ratio of event probabilities between exposed and unexposed groups in cohort studies. Determine relative risk (RR), absolute risk reduction (ARR), and number needed to treat (NNT) from your study data.

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Relative Risk
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        What is Relative Risk?

        Relative risk (RR) compares the probability of an event in the exposed group to the probability in the unexposed group. An RR of 2.0 means exposed individuals are twice as likely to experience the outcome. An RR of 0.5 means exposure halves the risk (50% risk reduction).

        Relative risk is the standard measure of association in cohort studies and randomized controlled trials. It's more intuitive than odds ratio because it directly represents probability ratios. RR = 1.0 means no difference between groups.

        Formulas & Equations Used

        This Relative Risk Calculator uses the following core equations:

        1 Relative Risk ▼
        RR = (a / (a + b)) / (c / (c + d))

        Risk in exposed = a/(a+b). Risk in unexposed = c/(c+d). RR is their ratio.

        2 Absolute Risk Reduction ▼
        ARR = Risk_unexposed - Risk_exposed

        If control risk = 20% and treatment risk = 12%: ARR = 20% - 12% = 8 percentage points.

        3 Number Needed to Treat ▼
        NNT = 1 / ARR

        ARR of 8%: NNT = 1/0.08 = 12.5. You need to treat 13 patients to prevent 1 event.

        How to Use This Relative Risk Calculator

        Follow these 3 simple steps:

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        Enter Your Values

        Type the known values into the input fields above. The Relative Risk Calculator accepts any positive numbers.

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        Choose Calculation Mode

        Select Solve, Simplify, or Scale mode in the calculator. Each applies different equations to your inputs.

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        View Results

        Click Calculate to see your answer with a visual ratio bar, pie chart, and step-by-step solution breakdown.

        Example Problems & Step-by-Step Solutions

        Here are 3 worked examples using this Relative Risk Calculator:

        Example 1 Drug trial: treated group vs placebo
        1 Treated: 30 events in 500 (risk = 6%)
        2 Placebo: 75 events in 500 (risk = 15%)
        3 RR = 0.06 / 0.15 = 0.40
        ✓ RR = 0.40 — drug reduces risk by 60%
        Example 2 Smoking and heart disease (cohort study)
        1 Smokers: 150 cases in 2000 (risk = 7.5%)
        2 Non-smokers: 50 cases in 3000 (risk = 1.67%)
        3 RR = 7.5% / 1.67% = 4.5
        ✓ RR = 4.5 — smokers have 4.5× the risk
        Example 3 Calculate NNT for a vaccine
        1 Unvaccinated risk: 12%
        2 Vaccinated risk: 2%
        3 ARR = 12% - 2% = 10%
        4 NNT = 1/0.10 = 10
        ✓ NNT = 10 — vaccinate 10 to prevent 1 infection

        Frequently Asked Questions

        What does a relative risk of 1.0 mean? ▼

        RR = 1.0 means the event is equally likely in both groups — no association between exposure and outcome. RR > 1 indicates increased risk; RR < 1 indicates decreased risk (protection).

        How is relative risk different from odds ratio? ▼

        RR uses probabilities (events/total), while OR uses odds (events/non-events). For rare outcomes (<10%), they're nearly equal. For common outcomes, OR overstates the association compared to RR.

        What is a clinically significant relative risk? ▼

        This depends on context. In cancer screening, RR = 0.80 (20% risk reduction) may be significant. In vaccine trials, RR = 0.05 (95% efficacy) is transformative. Always consider both RR and ARR.

        Can relative risk be used in case-control studies? ▼

        No. Case-control studies sample by outcome, not exposure, so you can't calculate true incidence rates. Use odds ratio instead. RR is only valid in cohort studies and RCTs where you follow groups over time.

        What is the number needed to treat (NNT)? ▼

        NNT is the inverse of absolute risk reduction. It tells you how many patients must receive treatment to prevent one adverse event. Lower NNT = more effective treatment. NNT of 10 means treat 10 patients to prevent 1 event.

        Learn About Ratios

        What is a ratio?

        A ratio is a comparison between two or more quantities showing the relative size of one to another. Written as A : B, it means 'for every A units of the first quantity, there are B units of the second.' For example, a ratio of 3 : 4 means for every 3 parts of A, there are 4 parts of B. Ratios are used in cooking, construction, finance, science, and everyday life.

        How do I solve a proportion?

        A proportion is an equation that says two ratios are equal: A : B = C : D. To solve for a missing value, use cross-multiplication. If D is unknown: D = (B × C) / A. This works because in equal ratios, the cross products are always equal: A × D = B × C. Our Proportion Solver does this automatically — just enter any 3 values and it finds the 4th.

        How do I simplify a ratio?

        To simplify a ratio, find the Greatest Common Divisor (GCD) of both numbers and divide each by it. For example, 24 : 36 — the GCD of 24 and 36 is 12. So 24 ÷ 12 = 2 and 36 ÷ 12 = 3, giving the simplified ratio 2 : 3. Our Simplifier automatically finds the GCD and reduces your ratio to its lowest terms.

        What is ratio scaling and when is it useful?

        Scaling a ratio means multiplying both parts by the same factor to create an equivalent, larger (or smaller) ratio. For instance, scaling 2 : 5 by a factor of 3 gives 6 : 15. This is extremely useful for recipes (tripling a recipe), construction (scaling blueprints), mixing solutions, or any scenario where you need to maintain the same proportion at a different magnitude.

        What's the difference between a ratio and a fraction?

        A ratio A : B compares two quantities to each other (part-to-part), while a fraction A/B typically represents a part-to-whole relationship. However, any ratio can be expressed as a fraction: 3 : 4 is equivalent to 3/4 = 0.75. The key difference is context — ratios compare quantities side-by-side, while fractions represent a portion of a total.