Odds Converter

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

One price, five notations. American, decimal, fractional, implied probability, and the cents price of a prediction-market contract — converted instantly, with the arithmetic beside each answer.

An odds converter rewrites one betting price in every notation the market uses: American moneyline, decimal, fractional, implied probability, and the cents price of a prediction-market contract. All five encode the same quantity — the break-even probability the price demands — so converting between them is arithmetic, not estimation.

Every conversion runs through the probability. American odds convert to it in two cases, depending on the sign:

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

and from that probability the other four formats follow directly:

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

and the probability converts back to an American price with the same two-case rule, in reverse:

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 (e.g. −110 or +150), 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, between 0 and 1. This is the pivot every other format converts through.
$d$ — decimal odds: total return per $1 staked, stake included. Always greater than 1.
$b$ — net profit per $1 staked, stake excluded. Fractional odds are exactly this number written as a fraction: $b = 10/11$ 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 probability side of the conversion, in depth →

The five formats, and who quotes which

American (moneyline)

Two directions from a $100 unit. −150 means $150 risked to profit $100; +150 means $100 risked to profit $150. Standard at US sportsbooks. It is the least convenient format for arithmetic, because the formula changes sign halfway through, which is why almost everything downstream converts out of it first.

Decimal (European)

Total return per $1 staked, stake included. 2.50 returns $2.50 on a $1 bet: $1.50 profit plus the dollar back. Decimal is the format the math prefers — probability is just $1/d$ , and parlay legs multiply.

Fractional (UK)

Net profit as a fraction of the stake. 10/11 pays $10 profit for every $11 risked; 5/2 pays $5 for every $2. It is decimal odds minus one, written as a ratio. Traditional UK books round to conventional fractions, so a posted fraction is sometimes a rounded version of the real price.

Implied probability

The price as a percentage: the break-even win rate it demands. This is the only format that is directly comparable across venues, and the one every calculation on this site runs on. It is also the format that hides a trap — it includes the venue’s margin. More on that on the implied probability page.

Contract price in cents

Prediction markets (Kalshi, Polymarket) quote a contract that settles at $1 if the event happens and $0 if it does not. The price in cents is the market’s probability in percent, near enough: a contract at 52¢ is a 52% market. Competing odds converters skip this format entirely, which is increasingly awkward now that event-contract exchanges quote the same games sportsbooks do.

Conversion table

Common prices in all five formats. Fractions are exact; probabilities are rounded to two decimals.

American	Decimal	Fractional	Implied	Contract	$100 returns
−1000	1.100	1/10	90.91%	90.9¢	$110.00
−500	1.200	1/5	83.33%	83.3¢	$120.00
−300	1.333	1/3	75.00%	75.0¢	$133.33
−250	1.400	2/5	71.43%	71.4¢	$140.00
−200	1.500	1/2	66.67%	66.7¢	$150.00
−150	1.667	2/3	60.00%	60.0¢	$166.67
−125	1.800	4/5	55.56%	55.6¢	$180.00
−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
+125	2.250	5/4	44.44%	44.4¢	$225.00
+150	2.500	3/2	40.00%	40.0¢	$250.00
+200	3.000	2/1	33.33%	33.3¢	$300.00
+250	3.500	5/2	28.57%	28.6¢	$350.00
+300	4.000	3/1	25.00%	25.0¢	$400.00
+500	6.000	5/1	16.67%	16.7¢	$600.00
+1000	11.000	10/1	9.09%	9.1¢	$1,100.00

Why American odds skip the middle

There is no American price between −100 and +100, and the gap is structural rather than a convention. The format measures a $100 unit in two directions: positive numbers count profit on a $100 stake, negative numbers count the stake required to profit $100. At even money both readings collide — risk $100 to win $100 — so +100 and −100 name the identical payout and everything between them would have to describe a price that pays less than the stake back.

Decimal has no gap: even money is 2.00, and the numbers run continuously from just above 1.00 upward. Books that quote American odds print EVEN, PK or +100 at that point. This converter shows both signs at exactly 50%, because both are correct.

Decimal 1.91 is not −110

Precision differences between formats are small and real. −110 is 1.9090909… in decimal, so a book quoting 1.91 is quoting a slightly better price:

The same bet at two venues, quoting in two formats

-110 \Rightarrow d = 1.9091,\quad q = 52.381\%

1.91 \Rightarrow m = -109.89,\quad q = 52.356\%

A gap of 0.025 probability points. That is far too small to matter on one bet and far too big to ignore when the same price is being compared across ten venues, because those comparisons are exactly what the third decimal place is for.

The converter reports the exact converted value alongside the rounded one whenever rounding to a whole American number would move the price. Any tool that silently rounds −109.89 to −110 is throwing away the difference it was asked to measure.

Converting a prediction-market price

An event contract on Kalshi settles at $1 if the event happens and $0 if it does not, so the price in cents is a probability in percent. That makes the conversion trivial and the interpretation subtle.

52¢ in every format

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

\text{taker fee} = \lceil\,0.07 \times C \times 0.52 \times 0.48\,\rceil_{\text{cent}}

The round-up applies to the order, not to each contract. One contract is $0.017472 raw, charged as $0.02; 100 contracts are $1.7472 raw, charged as $1.75. The break-even below uses the un-rounded rate:

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

The converted price says 52.00%. The fee-adjusted break-even is 53.75%. Those are two different numbers and the second is the one a position has to clear — see the Kalshi fee calculator for the full schedule.

The reverse direction has the same catch. A sportsbook price converted to cents is comparable to a contract price only after both sides have been put on the same footing: the book’s price carries vig, the contract’s price carries fees, and neither is visible in the converted number. The prediction-market odds calculator handles that comparison directly.

What a converted price still is not

Conversion is lossless and it is also inert: it moves a number between notations without learning anything about the event. Three things the output does not tell you.

It is 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 — the vig calculator measures it and the no-vig calculator removes it.
It is not a fair price. The fair price is the one left after the margin comes out. On a −110/−110 market that is even money on both sides, which no book posts.
It is not an edge. Comparing two converted prices tells you which is larger; whether the larger one beats a fair estimate is the expected value calculation, and it needs a reference line this page never asks for.

Common mistakes

Treating implied probability as the market’s forecast. It is the break-even rate for that price, margin included. On a two-way market the two implied probabilities always sum above 100%.
Adding decimal odds across parlay legs. Decimal odds multiply: three legs at 1.9091 combine to 6.958, not 5.727. The parlay calculator does the multiplication and shows what the margin does when it compounds.
Converting fractional odds as if they included the stake. 10/11 is $10 profit per $11 risked — a decimal of 1.909, not 0.909. Fractional odds are net; decimal odds are gross.
Reading a contract price as a break-even. On a fee-charging exchange the break-even sits above the purchase price, by $0.07\,P(1-P)$ per contract on Kalshi’s standard taker schedule.
Rounding mid-chain. Converting −110 to 52% and back returns −108.33, which is a different price. The converter keeps full precision internally and rounds once, at the end.
Assuming a posted fraction is exact. UK fractional odds are traditionally quoted from a fixed ladder, so a price of 0.913 profit per unit may be posted as 10/11 (0.909). The converter marks approximations with “≈” rather than presenting them as exact.

Check this number yourself

The conversions on this page are the same two functions the rest of the site runs on, published in the MIT-licensed teachersbettextbook package. No account, no sign-up, four lines:

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 on what is open and what is not: open source.

Converting is step zero. What the converted probability leaves out is the venue’s margin — measured by the vig calculator, removed by the no-vig calculator, and turned into an edge estimate by expected value. The beginner lesson starts from the same place and assumes nothing.

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.