Risk Ratio Calculator
Calculate risk ratios from event counts in exposed and control populations. Determine the attributable risk, attributable fraction, and population attributable fraction — key measures for understanding how much disease burden an exposure explains in epidemiological research.
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What is a Risk Ratio?
The risk ratio (also called the relative risk) is the ratio of the event probability in the exposed group to the event probability in the unexposed group. It is the most direct measure of how much an exposure multiplies (or reduces) the risk of an outcome. An RR of 3.0 means exposed individuals have three times the risk of the outcome compared to unexposed individuals.
Beyond the basic risk ratio, epidemiologists use attributable risk (AR) — the absolute difference in event rates between groups — and the attributable fraction (AF) — the proportion of cases in the exposed group that can be attributed to the exposure. The population attributable fraction (PAF) extends this to the entire population, estimating how much disease would be prevented if the exposure were eliminated entirely.
使用される計算公式・方程式
この計算ツールは5つの主要な公式を使用しています：
1 Risk Ratio ▼
Exposed rate: 15 per 1000. Unexposed rate: 5 per 1000. RR = 15/5 = 3.0.
2 Attributable Risk ▼
AR = 15/1000 - 5/1000 = 10/1000. The exposure accounts for 10 extra cases per 1000.
3 Population Attributable Fraction ▼
If 30% of population exposed and RR = 3: PAF = 0.3×2 / (1+0.3×2) = 0.375 = 37.5%.
Explore all calculation options on the 比率計算ツール home page.
比率計算ツールの使い方
この比率計算ツールは、以下の3ステップで簡単にご利用いただけます：
数値を入力
入力欄に既知の比率の値を入力します。求めたい未知数の入力欄は空欄のままにしておきます。
モードを選択
比率モード（解く、簡素化、スケーリング）を選択します。各モードで異なる計算式が適用されます。
結果を確認
計算するボタンを押します。結果画面に答えと、視覚的な比率バー、円グラフ、詳細なステップバイステップの解決プロセスが表示されます。
実例問題と段階的な解説
本比率計算ツールを使って、以下の3つの例題をステップバイステップで解決するプロセスです：
入力 1 Disease rates: 20/1000 exposed vs 5/1000 unexposed
入力 2 Calculate PAF: 40% exposed, RR = 2.5
入力 3 Protective factor: vaccinated risk 3%, unvaccinated 12%
よくある質問 (FAQ)
What is the difference between risk ratio and rate ratio? ▼
Risk ratio compares cumulative incidence proportions (events ÷ population at risk). Rate ratio compares incidence rates (events ÷ person-time at risk). Risk ratios work for fixed-period studies; rate ratios handle variable follow-up. For short studies with little loss to follow-up, they are approximately equal.
What is attributable risk? ▼
Attributable risk (AR) = Risk in exposed − Risk in unexposed. It measures the absolute excess risk due to the exposure. If exposed risk is 15% and unexposed risk is 5%, AR = 10 percentage points. This means 10 extra cases per 100 exposed individuals are attributable to the exposure.
What is the attributable fraction? ▼
Attributable fraction (AF) = (Risk_exposed − Risk_unexposed) ÷ Risk_exposed = (RR − 1) ÷ RR. It represents the proportion of cases among the exposed that can be attributed to the exposure. AF of 0.75 means 75% of cases in the exposed group would not have occurred without the exposure.
What is population attributable fraction (PAF)? ▼
PAF estimates the proportion of all cases in the entire population attributable to the exposure: PAF = P_e × (RR − 1) ÷ [P_e × (RR − 1) + 1], where P_e is the prevalence of exposure. A PAF of 25% means eliminating the exposure would prevent 25% of all cases in the population.
Can risk ratio be negative? ▼
No. Risk ratio is a ratio of two non-negative probabilities and ranges from 0 to infinity. RR = 0 would mean zero events in the exposed group. RR < 1 indicates reduced risk (protective effect). The concept of 'negative risk' does not apply to ratios.
How do I calculate risk ratio from a 2×2 table? ▼
RR = (a/(a+b)) ÷ (c/(c+d)), where a = exposed events, b = exposed non-events, c = unexposed events, d = unexposed non-events. Example: a=30, b=470, c=10, d=490: RR = (30/500) ÷ (10/500) = 0.06/0.02 = 3.0.
Is a higher risk ratio always worse? ▼
It depends on the outcome. RR = 3.0 for disease risk means the exposure triples disease risk (bad). RR = 3.0 for treatment success means the treatment triples the chance of success (good). The interpretation depends on whether the outcome is desirable or undesirable.
How does confounding affect the risk ratio? ▼
Confounders can inflate or deflate the observed RR. For example, if smokers also drink more alcohol, the crude RR for smoking and liver disease will be confounded by alcohol use. Adjusted RR (from stratification or regression) removes confounding to estimate the independent effect of the exposure.
What is the prevented fraction? ▼
When an exposure is protective (RR < 1), the prevented fraction = 1 − RR. It represents the proportion of potential cases prevented by the exposure. For a vaccine with RR = 0.10, the prevented fraction is 90% — the vaccine prevents 90% of cases that would have otherwise occurred.
Can I calculate risk ratio for continuous outcomes? ▼
No. Risk ratio is defined for binary (yes/no) outcomes. For continuous outcomes (blood pressure, weight, test scores), use mean difference, standardized mean difference, or ratio of means. Risk ratio specifically compares the probability of a dichotomous event between groups.