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Risk Ratio Calculator

The Risk Ratio Calculator computes the risk ratio (incidence rate ratio) between exposed and unexposed populations. Calculate attributable risk and population attributable fraction to quantify the public health impact of risk factors.

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        What is a Risk Ratio?

        A risk ratio (also called incidence rate ratio) compares the incidence of an outcome in an exposed group to that in an unexposed group. It is mathematically identical to relative risk when calculated from cumulative incidence data. RR = 3.0 means the exposed group has 3 times the incidence rate of the outcome.

        Risk ratios are preferred in public health because they directly communicate the fold-increase in disease risk. Combined with attributable risk (AR = risk_exposed - risk_unexposed), they quantify both relative and absolute disease burden from an exposure.

        Formulas & Equations Used

        This Risk Ratio Calculator uses the following core equations:

        1 Risk Ratio
        RR = Incidence_exposed / Incidence_unexposed

        Exposed rate: 15 per 1000. Unexposed rate: 5 per 1000. RR = 15/5 = 3.0.

        2 Attributable Risk
        AR = Incidence_exposed - Incidence_unexposed

        AR = 15/1000 - 5/1000 = 10/1000. The exposure accounts for 10 extra cases per 1000.

        3 Population Attributable Fraction
        PAF = P_exposed × (RR - 1) / (1 + P_exposed × (RR - 1))

        If 30% of population exposed and RR = 3: PAF = 0.3×2 / (1+0.3×2) = 0.375 = 37.5%.

        How to Use This Risk Ratio Calculator

        Follow these 3 simple steps:

        1

        Enter Your Values

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

        2

        Choose Calculation Mode

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

        3

        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 Risk Ratio Calculator:

        Example 1 Disease rates: 20/1000 exposed vs 5/1000 unexposed
        1 RR = 20/5 = 4.0
        2 AR = 20 - 5 = 15 per 1000
        3 Risk difference: 15 extra cases per 1000 exposed
        RR = 4.0, Attributable Risk = 15/1000
        Example 2 Calculate PAF: 40% exposed, RR = 2.5
        1 PAF = 0.40 × (2.5-1) / (1 + 0.40 × (2.5-1))
        2 PAF = 0.40 × 1.5 / (1 + 0.60)
        3 PAF = 0.60 / 1.60 = 0.375 = 37.5%
        37.5% of cases attributable to the exposure
        Example 3 Protective factor: vaccinated risk 3%, unvaccinated 12%
        1 RR = 3% / 12% = 0.25
        2 Risk Reduction = 1 - 0.25 = 0.75 = 75%
        3 NNT = 1 / (0.12 - 0.03) = 11.1
        RR = 0.25 (75% risk reduction), NNT = 11

        Frequently Asked Questions

        How is risk ratio different from odds ratio?

        Risk ratio uses incidence proportions: events/total. Odds ratio uses odds: events/non-events. For rare outcomes (< 10%), OR ≈ RR. For common outcomes (> 10%), OR overestimates the strength of association compared to RR.

        What does attributable risk tell us?

        Attributable risk (AR) is the absolute difference in risk between exposed and unexposed groups. It tells you how many additional cases per unit of population are caused by the exposure, which is useful for public health resource planning.

        What is population attributable fraction?

        PAF estimates the proportion of disease in the total population that would be prevented if the exposure were eliminated. A PAF of 37.5% means eliminating the exposure would prevent 37.5% of all cases.

        Can risk ratio be calculated from case-control studies?

        No. Case-control studies sample by outcome status, making the denominator (total exposed/unexposed) unknown. Use odds ratio instead. Risk ratio requires cohort data where you follow groups forward in time.

        What is a clinically meaningful risk ratio?

        Context matters. In oncology, RR = 0.80 (20% reduction) may be significant for a deadly cancer. In preventive medicine, RR = 0.50 (50% reduction) is typically considered clinically meaningful. Always report alongside AR and NNT.

        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.