Calculator

Odds Converter

About this calculator

By Alex Thornton · author of the MIT-licensed teachersbettextbook library · Last reviewed 24 July 2026

One price, five ways of writing it. Same number every time, with the arithmetic next to each one.

The probability side of the conversion, in depth →

An odds converter rewrites one price in every notation the market uses: American, decimal, fractional, implied probability, and a contract price in cents. Same price, five spellings.

They are all the same thing

American, decimal, fractional, implied probability, and a prediction-market contract price in cents. Five costumes on one quantity: the win rate the price needs just to break even.

Converting between them is exact. Nothing is lost and nothing is assumed. −150, 1.667, 2/3 and 60% are the same statement said four ways.

What a converted price is not is a forecast. 60% implied does not mean it happens 60% of the time. It means the price behaves as though it does, cut included.

Want more math?the Nerd Corner

Every conversion runs through the probability. American odds reach it in two cases, by sign:

q = \dfrac{100}{100 + m}\ \ (m > 0), \qquad q = \dfrac{|m|}{|m| + 100}\ \ (m < 0)

and the rest follow:

d = \dfrac{1}{q}, \qquad b = d - 1, \qquad \text{cents} = 100\,q

and it converts back to American, same two cases reversed:

m = -\dfrac{100\,q}{1 - q}\ \ (q \ge 0.5), \qquad m = \dfrac{100\,(1 - q)}{q}\ \ (q < 0.5)

where:

$m$ : the American moneyline, unitless. Negative is the stake needed to profit $100; positive is the profit on a $100 stake.
$q$ : the implied, vig-inclusive probability the price demands, 0 to 1. Every other format converts through it.
$d$ : decimal odds (total return per $1 staked, stake included). Always above 1.
$b$ : net profit per $1 staked, stake excluded. Fractional odds are this number as a ratio: $b = 10/11$ is written 10/11.
$\text{cents}$ : the price of a $1 event contract on a prediction market such as Kalshi, in cents. Before fees, that price is the probability.

Worked example: the price in the form below

The standard American football price, −110:

q = \dfrac{110}{110 + 100} = \dfrac{110}{210} = 52.38\%

d = \dfrac{1}{0.5238} = 1.909, \qquad b = 0.909 = \tfrac{10}{11}, \qquad \text{cents} = 52.4

Five ways of saying the same thing: −110 = 1.909 = 10/11 = 52.38% = 52.4¢. A $100 stake returns $190.91, of which $90.91 is profit.

The five formats

American (moneyline): two directions from a $100 unit. −150 risks $150 to profit $100, +150 risks $100 to profit $150. The US standard; the formula changes sign at even money, so most math converts out of it first.
Decimal (European): total return per $1, stake included (2.50 returns $2.50 on a $1 bet). The format the math prefers, since probability is $1/d$ and parlay legs multiply rather than add.
Fractional (UK): net profit per unit risked (10/11 pays $10 for every $11). Net, not gross, so 10/11 is decimal 1.909 and not 0.909. UK books round to a fixed ladder, so a posted fraction can be approximate.
Implied probability: the break-even win rate the price demands. The only format comparable across venues, and the one carrying the venue’s margin inside it.
Contract price in cents: a contract settling at $1 or $0 makes 52¢ a 52% market. Most converters skip the format, which is awkward now that exchanges quote the same games sportsbooks do.

Conversion table

Common prices, all five formats. Fractions exact, probabilities rounded.

American	Decimal	Fractional	Implied	Contract	$100 returns
−1000	1.100	1/10	90.91%	90.9¢	$110.00
−300	1.333	1/3	75.00%	75.0¢	$133.33
−200	1.500	1/2	66.67%	66.7¢	$150.00
−150	1.667	2/3	60.00%	60.0¢	$166.67
−110	1.909	10/11	52.38%	52.4¢	$190.91
+100	2.000	1/1	50.00%	50.0¢	$200.00
+110	2.100	11/10	47.62%	47.6¢	$210.00
+150	2.500	3/2	40.00%	40.0¢	$250.00
+200	3.000	2/1	33.33%	33.3¢	$300.00
+300	4.000	3/1	25.00%	25.0¢	$400.00
+1000	11.000	10/1	9.09%	9.1¢	$1,100.00

Converting a prediction-market price

An event contract settles at $1 if the event happens and $0 if it does not, so its price in cents is a probability in percent. The conversion is trivial; fees then sit on top of it:

52¢, converted and then fee-adjusted

\$0.52 \text{ per contract} \Rightarrow q = 52.00\%, \quad d = 1.923, \quad m = -108.33

p_{\text{break-even}} = 0.52 + 0.07 \times 0.52 \times 0.48 = 53.75\%

The converted price is 52.00%; the fee-adjusted break-even is 53.75%. Fair and executable are two different numbers, and the second is the one a position has to clear. See the full fee schedule.

What a converted price is not

Conversion is lossless and inert: it moves a number between notations without learning anything about the event.

Not a probability estimate. The 52.38% behind −110 is what the price demands, not what the venue believes. Both sides of a −110/−110 market convert to 52.38%, and 104.76% of probability cannot exist: the excess is margin, measured here, removed here.
Not a fair price. Fair is what is left once margin comes out: on −110/−110, even money both sides, which no book posts.
Not an edge. Which of two converted prices is larger is arithmetic; whether either beats a fair estimate is expected value, which needs a reference line this page never asks for.

Check this number yourself

The same two functions the site runs on, in the MIT-licensed teachersbettextbook package:

pip install teachersbettextbook

>>> from teachersbettextbook import moneyline_to_prob, moneyline_to_odds
>>> moneyline_to_prob(-110)
0.5238095238095238
>>> moneyline_to_odds(-110)      # net profit per $1: the fractional value
0.9090909090909091
>>> 1 + moneyline_to_odds(-110)  # decimal odds
1.9090909090909092

Same inputs, same digits. More: open source.

Converting is step zero. The converted probability still contains the venue’s margin: measure it, remove it, then price the remainder as expected value.

Frequently asked questions

How do you convert American odds to decimal odds?

For a positive American price, divide by 100 and add 1: +150 becomes 2.50. For a negative price, divide 100 by the absolute value and add 1: −150 becomes 1.667. Both are shortcuts for the same rule: decimal odds are 1 divided by the implied probability.

What does −110 convert to in every format?

−110 is 1.909 in decimal, 10/11 fractional, 52.38% implied probability and a 52.4-cent contract price. A $100 stake returns $190.91, which is $90.91 of profit. Every one of those numbers is the same fact written five ways.

How do prediction-market cents convert to American odds?

A contract price in cents is already a probability: 52 cents is 52%, which converts to −108.33 in American odds and 1.923 in decimal. The caveat is fees. On Kalshi’s standard taker schedule a 52-cent contract needs better than 53.75% to break even, so the price and the break-even are not the same number.

Why is there no American price between −100 and +100?

American odds measure a $100 unit in two directions: a positive number is the profit on a $100 stake, a negative number is the stake required to profit $100. Both meet at even money, where +100 and −100 describe the identical payout, so the range between them is empty rather than merely unused. Decimal odds have no such gap: even money is simply 2.00.

Are decimal 1.91 and −110 the same price?

Not quite. −110 is 1.9090909… in decimal, so a book posting 1.91 is offering −109.89, a fraction better. The implied probabilities are 52.381% and 52.356%, a gap of 0.025 probability points, which is small but real when the same price is compared across venues that quote in different formats.