Fractional Odds Calculator

Created by Kenneth Alambra
Reviewed by Michael Darcy
Last updated: Oct 06, 2022

If you're wondering how fractional odds work, this fractional odds calculator is for you. This tool will help you determine the odds of a game or any statistical situation, given you know the number of chances of winning or losing or the probability of winning or losing. Keep on reading to learn:

  • What fractional odds are;
  • How to calculate fractional odds; and
  • How to use this fractional odds calculator.

What are fractional odds?

Fractional odds or fractional betting odds represent the chances of losing versus the chances of winning in terms of fractions. So, how do fractional odds work? Let's say you're trying to guess the fractional odds of a single roll of one regular six-sided dice. Since each side has a different number, you only have one chance to win against five chances of losing. In fractional odds form, we express that as 5/1, which we read as "five to one".

In general, we call chances of winning "chances of success" since sometimes we don't win anything at all and instead only want a particular preferable result.

How to calculate fractional odds

To calculate the fractional odds of a given situation, we first must determine the number of chances of success and failure. Here are the straightforward formulas for them:

odds=CasCs\text{odds} = \frac{C_{as}}{C_s}

Where:

  • odds\text{odds} is the fractional odds;
  • CsC_s is the number of chances for success or winning; and
  • CasC_{as} is the number of chances against success.

You can also use these formulas if you know either the numbers of chances for success or against success, and either the probability of winning, PsP_s, or the probability of losing, PasP_{as}:

When you know the number of chances for success and probability of winning:

odds=CsPsCsCs\text{odds} = \frac{\frac{C_s}{P_s}-C_s}{C_s}

When you know the number of chances for success and probability of losing:

odds=Cs1PasCsCs\text{odds} = \frac{\frac{C_s}{1-P_{as}}-C_s}{C_s}

When you know the number of chances against success and the probability of losing:

odds=CasCasPasCas\text{odds} = \frac{C_{as}}{\frac{C_{as}}{P_{as}}-C_{as}}

When you know the number of chances against success and the probability of winning:

odds=CasCas1PsCas\text{odds} = \frac{C_{as}}{\frac{C_{as}}{1-P_s}-C_{as}}

It's also worth simplifying the resulting fraction if possible.

Remember that you must know at least the number of chances of winning or the number of chances of losing to find the odds.

How to use this fractional odds calculator

To use this fractional odds calculator:

  1. Enter your estimated or known chances for success.
  2. Input the number of chances against success. Alternatively, instead of entering the number of chances of failing, you can enter either the probability of winning or the probability of losing.
  3. The result will show the fractional betting odds.

In case you don't know the number of chances for success, to use our calculator correctly, you should at least know the number of chances against success and either the probability of winning or losing.

At this point, our tool should already display the fractional odds of your entered information. Consequently, you'll also see a winning vs. losing pie chart.

If you want more details about your entered values, you can click on the Advanced mode button below our tool. In the advanced mode, you'll see other means of expressing odds, like decimal odds and Moneyline odds. You'll also be able to enter more details about the probability of winning and losing, which is perfect for specific scenarios.

Moreover, in the advanced mode, you can enter a betting stake to find your potential net profit.

🙋 However, note that these are all for informational purposes only. Omni Calculator does not support or recommend any form of betting.

If you find this tool interesting, perhaps you'll also enjoy some of our other related tools listed below:

FAQ

What are the odds of winning a toss coin?

The odds of winning a toss coin is one is to one, or 1/1 in fractional odds format. Coins usually have two sides (i.e., heads and tails), and every flip of a coin results in either a win or loss. Since there is one chance of winning and one chance of losing a coin toss, the odds of winning (or losing) a coin toss is, therefore: 1 ÷ 1 = 1/1, or one is to one.

How do I convert fractional odds to decimal odds?

To convert fractional odds to decimal odds, taking the losing odds to be 1/2:

  1. First, add the denominator of the fractional odds to its numerator. For our example, we get: 1 + 2 = 3.
  2. Then, divide the sum we get by the denominator to obtain: 3 ÷ 2 = 1.5.

That's it! The decimal odds equivalent of 1/2 fractional odds is 1.5.

Kenneth Alambra
Chances for success
Chances against success
Probability of winning
%
Probability of losing
%
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