Convert an odds ratio to a percentage change in odds, or to an event probability when you add a baseline risk. Also finds the odds ratio from two risks.

Baseline risk (for a probability)
Risk in the reference group. Leave blank to get the percent change in odds only.

Varies baseline risk by this amount; endpoints are bounded to 0%–100%.

Related Calculators

Odds Ratio to Event Percentage

An odds ratio compares two groups’ event odds. It does not determine an event percentage without a baseline risk. Raw event odds instead compare events with non-events in one group.

Formulas

Use decimal probabilities p0 (baseline) and p1 (comparison).

p1 = OR * p0 / (1 - p0 + OR * p0)

OR = (p1 / (1 - p1)) / (p0 / (1 - p0))

Raw-odds probability = odds / (1 + odds)

How to Use the Calculator

  1. Select odds ratio to percentage, two probabilities to odds ratio, or raw event odds.
  2. Enter the visible values. Risk units can be percent or decimal probability; changing units preserves the quantity.
  3. Leave the optional baseline risk blank to get the percent change in odds, (OR − 1) × 100. For baseline conversion, the expandable sensitivity setting defaults to ±5 percentage points and can be changed from 0 to 49.
  4. Select Calculate. Review risk measures and expand calculation details for assumptions. Inputs changed afterward mark the result as out of date.

Worked Example

At a 20% baseline risk and an odds ratio of 2, the comparison probability is 0.4 / 1.2 = 33.333333%. The risk difference is 13.333333 percentage points and the risk ratio is 1.666667. The odds ratio is therefore not the same as doubling the baseline probability.

With a ±5 percentage-point sensitivity setting, baselines of 15% and 25% give converted risks of approximately 26.086957% and 40%. This holds the odds ratio fixed and is a scenario range, not a confidence interval. Endpoints are bounded to 0%–100%.

Risk Measures and Limits

Risk difference is p1 minus p0; risk ratio is p1 divided by p0 and is undefined at zero baseline. The reciprocal absolute risk difference is the mathematical NNT/NNH magnitude. Clinical benefit or harm requires an appropriate causal comparison, outcome and follow-up period; the calculation alone does not establish it.

Baseline conversion accepts 0% to below 100% with a positive odds ratio. A finite positive odds ratio solved from two probabilities requires both above 0% and below 100%. Raw event odds may be zero. Extreme inputs that exceed reliable finite numerical measures are rejected. Displayed values are rounded to six decimal places.

Use comparable populations, outcomes and observation periods. An adjusted odds ratio does not automatically determine an individual risk. These are statistical scenario estimates, not personal medical advice.

Saving and Resetting

A successful calculation is stored in this browser and restored on a later visit. Other scripts on this site may access saved values. Reset clears this calculator’s inputs, result and saved scenario; the sensitivity setting returns to its disclosed default.

Sources

CDC Field Epidemiology Manual: measures of association; Cochrane Handbook: interpreting relative and absolute effects.