Odds To Probability Calculator

Work out odds to probability instantly with clear inputs, formula shown and shareable results.

About Odds To Probability Calculator

Odds compare favourable to unfavourable outcomes, so odds of a to b mean probability a/(a + b). Decimal odds quote the total return per unit staked, which is the reciprocal of the probability.

Formulas

Odds to probability

p = favourable / (favourable + against)

Decimal odds

decimal = 1 / p

Worked example

With the default values below, Odds To Probability Calculator returns Probability of 0.30000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Odds for (favourable outcomes)minimum 0: 3
Odds against (unfavourable outcomes)minimum 0: 7

Results

Probability: 0.30000000
As a percentage: 30.0000 %
Odds as a single ratio: 0.42857143
Decimal (European) odds: 3.33333333

Step by step

1Values used
2Odds to probability
3Decimal odds
4Probability= 0.30000000
5As a percentage= 30.0000 %
6Odds as a single ratio= 0.42857143
7Decimal (European) odds= 3.33333333

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 8 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

What probability do odds of 3 to 7 give?

3/10 = 0.3, that is 30%, with decimal odds of 3.333.

Why are odds and probability confused?

Because '3 to 1' means a probability of 0.25, not 0.33. Odds use a ratio of two counts, probability a fraction of the total.