Ratio to Fraction Calculator

What is a ratio to fraction calculator?

A ratio to fraction calculator turns a ratio written in the form $a:b$ into a fraction written as $\frac{a}{b}$, then reduces that fraction to its lowest terms. A ratio and a fraction express the same idea — a comparison between two quantities — so the ratio $3:4$ and the fraction $\frac{3}{4}$ describe the same relationship. The calculator takes the two terms of the ratio, treats the first as the numerator and the second as the denominator, and simplifies the result.

How does it work?

The two parts of a ratio have names: the antecedent is the first term ($a$) and the consequent is the second term ($b$). Writing the ratio as a fraction is direct:

To put that fraction in lowest terms, divide both the numerator and the denominator by their greatest common divisor (GCD):

The GCD is the largest whole number that divides both terms exactly, found with the Euclidean algorithm. Dividing both terms by it removes any shared factor without changing the value of the fraction.

Worked examples

Convert the ratio $3:4$. The GCD of 3 and 4 is 1, so the fraction is already in lowest terms:

Convert the ratio $6:8$. The GCD of 6 and 8 is 2, so both terms are divided by 2:

Convert the ratio $10:5$. The GCD of 10 and 5 is 5:

A result such as $\frac{2}{1}$ shows that the ratio represents a whole number — here, the first quantity is exactly twice the second.

Practical notes

The consequent must be a non-zero value, since a fraction with a denominator of zero is undefined. If you reverse the direction of the comparison you can go the other way and write a fraction as a ratio at the ratio side, for example with the fraction to ratio calculator. To express the same value as a single decimal number instead, use the ratio to decimal calculator.

FAQ

Is a ratio the same as a fraction? They carry the same numeric value when written as $a:b$ and $\frac{a}{b}$, but they are read differently. A ratio compares two parts to each other, while a fraction usually compares one part to a whole. The arithmetic of converting between them is identical.

Why does 6:8 become 3/4? Both 6 and 8 are divisible by 2. Dividing each term by their greatest common divisor, 2, gives the equivalent but simpler fraction $\frac{3}{4}$, which has no remaining common factor.

What happens with a ratio like 10:5? It reduces to $\frac{2}{1}$, which is simply the whole number 2. Whenever the second term divides the first exactly, the reduced fraction has a denominator of 1.