# How to calculate 1 in _______ chance from a percentage?

I am wondering, how do I ago about calculating 1 in chances from a percentage?

Example:

• A 1 in 2 chance is 50% and 0.5 as a decimal.

What I want to do:

• I have the value 0.1431 (14.3%) and want to convert that into a 1 in chance - any help is much appreciated, thanks.
• $0.5 = 1/2$ is one chance over 2, so if the percentage is $x$ with $x=1/a$ .... Sep 25, 2020 at 9:15
• I think this is rather intuitive: For example $25~\%$ is "one in four", $5~\%$ is "one in 20" ... Can you guess how to calculate these numbers? It involves taking the inverse ... Sep 25, 2020 at 9:16
• Also, do you have requirements that the number should be an integer? Because, obviously, not all percentages (or fractions) can be written as "1 over an integer". For example $0.6667$ is $\frac{2}{3}$ ... Sep 25, 2020 at 9:22
• Thank you very much! So, from the first response, you divide 1 by the decimal if I am correct. For example: if I have 2%, I convert it into a decimal (0.02), then do 1/0.02, which equals 50 - giving the answer: 1 in 50 chance.
– user828171
Sep 25, 2020 at 9:22
• Not bad, but not intuitive enough. After you convert the percentage $(p)$ into a fraction (typically with a denominator = 100), you end up with an equation like $\frac{1}{n} = \frac{p}{100}.$ This is the intuition behind the math. Once you have stretched your intuition here, the math should fall into place. Sep 25, 2020 at 10:00

A $$1$$ in $$n$$ chance can be written as $$\frac{1}{n}$$. This can be set equal to the probability in decimal form, $$p$$.

$$p=\frac{p}{1}=\frac{1}{n}$$

You should notice that you are simply finding the reciprocal of $$p$$ to find $$n$$. This means that if $$p$$ is a fraction, you can simply swap the numerator and denominator to get $$n$$.

Simply divide $$1\div p$$ to get $$n$$.

In this example, that means: $$n=1\div0.1431\approx\boxed{6.988}$$

So, $$0.1431$$ ($$14.3\%$$) is approximately a $$1$$ in $$6.988$$ chance.

• percentages can be tricky :-) Jul 13, 2022 at 1:22