Relative Risk & Odds Ratio Calculator
Calculate relative risk (RR), odds ratio (OR), attributable risk, and group-specific risks from a 2×2 cohort study table. Essential for epidemiology and clinical research.
Relative Risk & Odds Ratio
intermediateCalculate relative risk, odds ratio, and attributable risk from cohort data
Formula
RR = (a/(a+b))/(c/(c+d)), OR = ad/bc
How It Works
From a cohort study comparing exposed vs. unexposed groups:
Exposed Risk = a/(a+b) — risk of outcome in exposed group
Unexposed Risk = c/(c+d) — risk of outcome in unexposed group
Relative Risk (RR) = Exposed Risk / Unexposed Risk
Odds Ratio (OR) = (a×d)/(b×c)
Attributable Risk (AR) = (Exposed Risk − Unexposed Risk) × 100%
Example
Study of smoking and lung cancer: 30 of 100 smokers developed cancer vs 10 of 100 non-smokers.
Smoker Risk = 30/100 = 0.30
Non-smoker Risk = 10/100 = 0.10
RR = 0.30/0.10 = 3.00
OR = (30×90)/(70×10) = 2700/700 = 3.86
AR = (0.30 − 0.10) × 100 = 20%
Smokers have 3× the risk of developing lung cancer compared to non-smokers.
Frequently Asked Questions
When should I use RR vs OR?
RR is preferred for cohort studies and randomized trials where we can directly measure risk. OR is used in case-control studies and when adjusting for confounders in logistic regression.
What does a RR of 1 mean?
RR = 1 means no difference in risk between groups. RR > 1 indicates increased risk (harmful exposure), RR < 1 indicates decreased risk (protective exposure).
What is attributable risk?
Attributable risk (or risk difference) tells you how much of the risk in the exposed group is due to the exposure itself. In the example above, 20% of smokers' lung cancer risk is attributable to smoking.