Ratio to Fraction Converter
The simplified fraction and decimal value behind a whole-number ratio.
Result
How it is calculated
The ratio a : b is written as the fraction a / b and reduced to lowest terms. The engine finds the greatest common divisor g of the two numbers with the Euclidean algorithm (repeatedly replacing the pair by the divisor and the remainder until the remainder is 0), then outputs (a ÷ g) / (b ÷ g). It also gives the decimal value a ÷ b to four decimals. Both entries must be whole numbers: a value such as 1.5 returns no result, so multiply both sides by 10 first (1.5 : 3 becomes 15 : 30). The second term cannot be 0 and neither can be negative. A ratio that reduces to a whole number appears with a denominator of 1, for example 3/1.
Worked example
Take the ratio 45 : 120. The Euclidean algorithm gives: 120 = 2 × 45 + 30, 45 = 1 × 30 + 15, 30 = 2 × 15 + 0, so the greatest common divisor is 15. Dividing both terms by 15 gives 45 ÷ 15 = 3 and 120 ÷ 15 = 8, so the simplified fraction is 3/8. The decimal check is 45 ÷ 120 = 0.3750. A part-to-part ratio is turned into a fraction of its second term, not of the total.
Common mistakes
- Reading the result as a share of the whole. The ratio 3 : 5 becomes 3/5, a part compared with the other part; the share of the total is 3/8. Add the terms first if you want the part-to-whole fraction.
- Entering decimals such as 2.5 : 4. The tool accepts only whole numbers, so scale both sides to whole numbers first (25 : 40, which reduces to 5/8).
- Reversing the order. 2 : 5 gives 2/5 but 5 : 2 gives 5/2, so check which quantity comes first in your wording.
- Entering a ratio with a zero in the second position. A denominator of 0 is undefined, so there is no result.
- Expecting a mixed number. An improper result like 9/4 is kept as it is; the tool does not write it as 2 1/4.
About this calculator
A ratio written as a:b and a fraction written as a/b express the same relationship between two quantities, just in different notations. This tool converts the ratio to a fraction and then simplifies it by dividing both terms by their greatest common divisor (GCD) — for example, a ratio of 12:18 becomes the fraction 12/18, which reduces to 2/3 once both numbers are divided by their GCD of 6.
Students and teachers use this conversion constantly when moving between ratio and fraction notation in math class, and it comes up in everyday practical contexts too: scaling a recipe, mixing concrete or paint in a fixed proportion, or reading a map scale all rely on the same ratio-to-fraction logic to get a clean, simplified working number.
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