How do you convert probability to odds?

Divide the probability by one minus the probability. 0.2 ÷ 0.8 = 0.25, so a 20% chance is odds of 1 : 4 in favour, or 4 : 1 against. For a percentage, use the decimal: 60% is 0.6 ÷ 0.4 = 1.5 : 1.

How do you convert odds to probability?

Odds in favour ÷ (1 + odds). Odds of 2 : 1 in favour are 2 ÷ 3 = 66.7%. If the odds are quoted against, flip them first: 5 : 1 against is 1 : 5 in favour, so 1 ÷ 6 = 16.7%.

What is the difference between odds and probability?

Probability counts successes out of all trials; odds count successes against failures. A coin flip is probability ½ and odds 1 : 1 (even). They agree in ranking — higher probability, higher odds — but not in size.

What do 3/1 or 5/2 odds mean?

Fractional betting odds are odds against: 3/1 means three failures for each success, an implied 25% chance; 5/2 means 2.5 : 1 against, about 28.6%. Enter the odds against as a decimal (2.5) in the odds → probability mode, or flip them to odds in favour first.

Probability to Odds Converter (Odds For, Odds Against, 1 in N)

Probability to odds and back — odds in favour, odds against, fractional and decimal forms, and '1 in N'.

Inputs

Convert

Probability (0–1)

Decimal odds

01,000,000,000

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Odds in favour

0.3333 : 1

Working: p ÷ (1 − p) = 0.25 ÷ 0.75 = 0.3333
Probability: 25.00% — 1 in 4
Odds against: 3 : 1
Bookmaker-style (fractional, against): 3/1 — decimal 4

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What each Probability to Odds input means

Convert: Probability → odds, or odds → probability.
Probability (0–1): A probability between 0 and 1, exclusive: 0.25 for 25%, 0.6 for 60%. Divide a percentage by 100 first.
Decimal odds: Odds in favour as a single number — successes per failure. 3 : 1 in favour is 3; odds of 5 : 1 against are 1 : 5 in favour, so enter 0.2.

Probability to Odds conversion formula

odds in favour = p ÷ (1 − p) · odds against = (1 − p) ÷ p · p = odds ÷ (1 + odds) · '1 in N' means p = 1 ÷ N

\text{odds} = \frac{p}{1 - p} \qquad p = \frac{\text{odds}}{1 + \text{odds}}

Probability and odds say the same thing in different units. A probability is the share of trials that succeed: 0.25 means one success in four trials. Odds compare successes with failures: one success against three failures, 1 : 3 in favour or 3 : 1 against. So odds in favour are p ÷ (1 − p), and to go back, p = odds ÷ (1 + odds). The two are close for rare events — a 1% chance is odds of 0.0101 — and far apart for likely ones: an 80% chance is odds of 4 : 1 in favour. Bookmakers quote odds against, so '3/1' means a 25% implied chance; the page shows that form too, plus the plain '1 in N' that news reports use.

Probability to Odds conversion worked example

A 25% chance: p ÷ (1 − p) = 0.25 ÷ 0.75 = 0.3333, so the odds in favour are 1 : 3 and the odds against are 3 : 1 — one success for every three failures, or 1 in 4. Going the other way, odds of 3 : 1 in favour are p = 3 ÷ (1 + 3) = 0.75, a 75% chance.

More Probability to Odds examples

A 60% chance of rain: 0.6 ÷ 0.4 = 1.5, so the odds in favour are 1.5 : 1 — three wet days for every two dry ones — and the odds against are 0.6667 : 1.

A horse at 5/1 against is 1 : 5 in favour, odds of 0.2: the implied probability is 0.2 ÷ 1.2 = 16.6667%, or 1 in 6 — before the bookmaker's margin is taken out.

Where the Probability to Odds converter can give the wrong answer

Probabilities of exactly 0 or 1 have no finite odds (0 ÷ 1 = 0 and 1 ÷ 0 is undefined), so the page takes values strictly between them.
'Odds' in everyday speech usually means odds against — 'the odds are 3 to 1' means a 25% chance — while statistics texts define odds in favour. The page labels both so there is no guessing.
Bookmakers' odds include a margin, so the implied probabilities across all outcomes add to more than 100%. Converting a quoted price gives the bookmaker's implied chance, not a true one.
Odds ratios in medical papers compare two sets of odds; they are not the odds of one event and cannot be turned into a probability with this page alone.
Decimal odds in betting (e.g. 4.00) are payout per unit staked including the stake, so decimal odds = 1 ÷ p, which is one more than the odds against. The page shows that figure on the bookmaker line.

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Probability to Odds conversion reference table

Common probabilities as odds
Probability	Odds in favour	Odds against	Decimal (betting) odds
1%	1 : 99	99 : 1	100
5%	1 : 19	19 : 1	20
10%	1 : 9	9 : 1	10
20%	1 : 4	4 : 1	5
25%	1 : 3	3 : 1	4
33.3%	1 : 2	2 : 1	3
50%	1 : 1 (evens)	1 : 1	2
60%	3 : 2	2 : 3	1.67
75%	3 : 1	1 : 3	1.33
80%	4 : 1	1 : 4	1.25
90%	9 : 1	1 : 9	1.11

Source: Arithmetic: odds in favour = p ÷ (1 − p); decimal odds = 1 ÷ p, with no bookmaker's margin

Probability to Odds conversion FAQ

: Divide the probability by one minus the probability. 0.2 ÷ 0.8 = 0.25, so a 20% chance is odds of 1 : 4 in favour, or 4 : 1 against. For a percentage, use the decimal: 60% is 0.6 ÷ 0.4 = 1.5 : 1.
: Odds in favour ÷ (1 + odds). Odds of 2 : 1 in favour are 2 ÷ 3 = 66.7%. If the odds are quoted against, flip them first: 5 : 1 against is 1 : 5 in favour, so 1 ÷ 6 = 16.7%.
: Probability counts successes out of all trials; odds count successes against failures. A coin flip is probability ½ and odds 1 : 1 (even). They agree in ranking — higher probability, higher odds — but not in size.
: Fractional betting odds are odds against: 3/1 means three failures for each success, an implied 25% chance; 5/2 means 2.5 : 1 against, about 28.6%. Enter the odds against as a decimal (2.5) in the odds → probability mode, or flip them to odds in favour first.