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Probability Ratio Calculator

Compare two probabilities as a ratio and as an odds ratio.

About Probability Ratio Calculator

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.

Formula

Probability Ratio

Probability ratio = p₁ ÷ p₂; odds ratio = (p₁/(1−p₁)) ÷ (p₂/(1−p₂))

odds
Probability divided by its complement

Worked example

With the default values below, Probability Ratio Calculator returns Probability Ratio of 2.50000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Probability 1accepts 0–100 %
30 %
Probability 2accepts 0–100 %
12 %

Results

Probability Ratio
2.50000
Odds Ratio
3.14286
Odds for Probability 1
0.42857
Odds for Probability 2
0.13636
Absolute Difference
18.000%

Step by step

  1. 1Values used
  2. 2Probability Ratio
  3. 3Probability Ratio= 2.50000
  4. 4Odds Ratio= 3.14286
  5. 5Odds for Probability 1= 0.42857
  6. 6Odds for Probability 2= 0.13636
  7. 7Absolute Difference= 18.000

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Probability Ratio calculated?

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.

Why does Probability Ratio matter?

Absolute difference matters more than either ratio for decision-making, since a tripling of a tiny risk is still a tiny risk.

What values do I need to enter?

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.

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