What Is the Simplify Ratio Calculator?
A ratio compares two quantities, written as a:b. Just like a fraction, a ratio can usually be reduced to a simpler, equivalent form. This calculator takes any two numbers and reduces the ratio to its lowest terms by dividing both sides by their greatest common divisor (GCD). The result is the same proportion expressed with the smallest whole numbers possible.
How to Use It
Enter the first term (A) and the second term (B), then read off the simplified ratio. The tool also shows the GCD used to reduce the values and the decimal equivalent (A ÷ B), which is handy when you want a single scaling factor. Decimal inputs such as 1.5:3 are automatically scaled to whole numbers before being reduced.
The Formula Explained
To simplify a ratio you find \(g = \gcd(a, b)\), the largest number that divides both terms exactly. Dividing each term by g gives the reduced ratio \((a/g):(b/g)\). Because both terms are scaled by the same factor, the relationship between them never changes — only the size of the numbers does. The GCD is computed using the Euclidean algorithm, which repeatedly replaces the larger number with the remainder of dividing the two until one becomes zero.
$$\frac{\text{Term A}}{\text{Term B}} = \frac{\text{Term A} \div g}{\text{Term B} \div g} \qquad g = \gcd\!\left(\text{Term A},\, \text{Term B}\right)$$
Worked Example
Simplify 18:24. The divisors of 18 are 1, 2, 3, 6, 9, 18; for 24 they are 1, 2, 3, 4, 6, 8, 12, 24. The greatest shared divisor is 6. Dividing both terms gives \(18 \div 6 = 3\) and \(24 \div 6 = 4\), so 18:24 simplifies to 3:4, with a decimal equivalent of 0.75.
FAQ
Can I use decimals? Yes. Values like 2.5:5 are multiplied by a power of ten to make them whole before reducing, so the answer comes back as 1:2.
What if the ratio is already simplified? If the two terms share no common factor besides 1, the GCD is 1 and the ratio is returned unchanged.
Does order matter? Yes — 3:4 and 4:3 are different ratios. Keep your terms in the order that matches your problem.
