Relative Risk Calculator
Calculate relative risk (risk ratio), absolute risk reduction (ARR), relative risk reduction (RRR), and number needed to treat (NNT) from exposed and unexposed group data. Compare event rates between groups to quantify treatment effects and exposure risks — essential for clinical trials and epidemiological research.
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What is Relative Risk?
Relative risk (RR), also called the risk ratio, compares the probability of an event occurring in an exposed group to the probability in an unexposed group. An RR of 2.0 means the exposed group is twice as likely to experience the event. An RR of 0.5 means the exposed group has half the risk — indicating a protective effect. RR = 1.0 means no difference between groups.
Relative risk is the standard effect measure for prospective cohort studies and randomized controlled trials, where participants are followed forward in time from exposure to outcome. Unlike the odds ratio (used in case-control studies), RR directly compares probabilities and is more intuitive: RR 2.0 genuinely means 'twice the risk.' This calculator also computes the absolute risk reduction and number needed to treat for clinical decision-making.
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 Relative Risk ▼
Risk in exposed = a/(a+b). Risk in unexposed = c/(c+d). RR is their ratio.
2 Absolute Risk Reduction ▼
If control risk = 20% and treatment risk = 12%: ARR = 20% - 12% = 8 percentage points.
3 Number Needed to Treat ▼
ARR of 8%: NNT = 1/0.08 = 12.5. You need to treat 13 patients to prevent 1 event.
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 Drug trial: treated group vs placebo
入力 2 Smoking and heart disease (cohort study)
入力 3 Calculate NNT for a vaccine
よくある質問 (FAQ)
What does a relative risk of 1.0 mean? ▼
RR = 1.0 means the event rate is identical in both groups — no association between the exposure and the outcome. The exposure neither increases nor decreases risk. Values above 1.0 indicate increased risk; values below 1.0 indicate decreased risk (protection).
How is relative risk different from odds ratio? ▼
RR compares probabilities (events ÷ total), while OR compares odds (events ÷ non-events). For rare outcomes (< 10% incidence), they produce similar values. For common outcomes, OR systematically overstates the association compared to RR. RR is more intuitive ('twice the risk') and preferred when calculable.
What is a clinically significant relative risk? ▼
This depends entirely on context. For cancer screening, RR = 0.80 (20% risk reduction) may be highly significant. For a vaccine against a lethal disease, RR = 0.05 (95% efficacy) is transformative. Always consider absolute risk reduction and NNT alongside RR for clinical significance assessment.
Can relative risk be used in case-control studies? ▼
No. Case-control studies select participants based on outcome (cases vs. controls), not exposure. This design does not allow calculation of incidence rates, so RR cannot be computed. Use the odds ratio instead, which is the appropriate effect measure for case-control designs.
What is the number needed to treat (NNT)? ▼
NNT = 1 ÷ Absolute Risk Reduction. It represents how many patients must receive the treatment to prevent one additional adverse event. Lower NNT = more effective treatment. NNT of 10 means treating 10 patients prevents 1 event; NNT of 100 means treating 100 patients prevents 1 event.
How do I calculate vaccine efficacy from relative risk? ▼
Vaccine Efficacy = (1 - RR) × 100%. If vaccinated group has 5 infections per 1,000 and unvaccinated has 50 per 1,000: RR = 5/50 = 0.10. Efficacy = (1 - 0.10) × 100% = 90%. The vaccine reduces infection risk by 90%.
What is the difference between relative risk reduction and absolute risk reduction? ▼
RRR = (1 - RR) × 100%. ARR = Risk(control) - Risk(treatment). If control risk is 20% and treatment risk is 12%: RR = 0.60, RRR = 40%, ARR = 8 percentage points, NNT = 13. RRR sounds more impressive but ARR and NNT are more clinically informative.
How do I interpret a relative risk less than 1? ▼
RR < 1 indicates the exposure or treatment is protective — it reduces the risk of the outcome. RR 0.70 means a 30% lower risk in the exposed/treated group. RR 0.50 means half the risk. The closer to 0, the stronger the protective effect.
When should I use relative risk vs. hazard ratio? ▼
Use RR for fixed-time comparisons (what percentage had the event by time X). Use HR for time-to-event analysis where follow-up varies and you need to account for censoring. HR from Cox regression is preferred for survival analysis; RR from simple proportion comparison is used for fixed-duration studies.
How does sample size affect relative risk precision? ▼
Larger samples produce narrower confidence intervals around the RR estimate. A small study might produce RR = 0.60 with CI 0.20-1.80 (non-significant), while a larger study with the same effect produces RR = 0.60 with CI 0.45-0.80 (significant). Sample size does not change the point estimate but affects the precision.