Compare two probabilities as a ratio and as an odds ratio.
The probability ratio and odds ratio agree only when both probabilities are small. As probabilities rise, the odds ratio becomes progressively larger than the probability ratio. Absolute difference matters more than either ratio for decision-making, since a tripling of a tiny risk is still a tiny risk.
Probability Ratio
Probability ratio = p₁ ÷ p₂; odds ratio = (p₁/(1−p₁)) ÷ (p₂/(1−p₂))
Probability ratio = p₁ ÷ p₂; odds ratio = (p₁/(1−p₁)) ÷ (p₂/(1−p₂)) The probability ratio and odds ratio agree only when both probabilities are small. As probabilities rise, the odds ratio becomes progressively larger than the probability ratio.
Absolute difference matters more than either ratio for decision-making, since a tripling of a tiny risk is still a tiny risk.
This calculator takes 2 inputs: Probability 1, Probability 2. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.