Free Ratio of 2 Numbers Calculator

What is a Ratio?

A ratio expresses how many times one value contains another. For two numbers $A$ and $B$, the ratio is typically written as $A : B$ (read “A to B”) and is mathematically identical to the fraction $\dfrac{A}{B}$. For instance, mixing 150 g of yeast with 600 g of water gives a yeast‑to‑water ratio of $150 : 600$, which reduces to $1 : 4$ after dividing both terms by 150. This indicates that the water weighs four times as much as the yeast.

Capabilities of the Calculator

This two number ratio calculator covers the most common ratio operations. It acts as a simplify ratio calculator that reduces any pair to its lowest terms; as an equivalent ratio calculator that scales both numbers by a given factor; as an A:B ratio calculator that can force the ratio into the forms $1 : n$ or $n : 1$; and as a proportion solver that finds a missing term when you already know three of the four values in a proportion $A : B = C : D$. Whether you need a quick simplify ratio online tool for homework or a robust helper for everyday math, this calculator handles integers, decimals, and fractions without hassle.

How to Use the Ratio Calculator

1. Enter the two numbers (A and B) that make up your ratio.
2. Choose the operation you want:
   • Simplify – the tool computes the reduced ratio using the GCD.
   • Scale to 1 : n or n : 1 – one term becomes 1 while the proportion remains unchanged.
   • Generate an equivalent ratio – multiply both terms by a factor you specify.
   • Find a missing term – supply either C or D in $A : B = C : D$ and the calculator solves for the unknown.
3. If required, enter the factor or the known term (C or D).
4. The result is displayed instantly.

Manual Method to Simplify a Ratio

For Whole Numbers

1. List all factors of A and all factors of B.
2. Identify the greatest common divisor (GCD) of the two numbers.
3. Divide A and B by the GCD.
4. The resulting pair $A\div\text{GCD} : B\div\text{GCD}$ is the simplified ratio.

For Decimals, Fractions, or Mixed Numbers

Consider the ratio as the fraction $\dfrac{A}{B}$. Eliminate decimal points or fractions by multiplying both numerator and denominator by an appropriate number (e.g., 10, 100, or the least common denominator) to obtain two integers. Then apply the whole‑number steps above.

Equivalent Ratios and Proportion Solving

Multiplying (or dividing) both terms of a ratio by the same non‑zero number yields an equivalent ratio — for example, $2 : 5$ is equivalent to $4 : 10$ (multiplied by 2). If you have a proportion $A : B = C : D$, the cross‑product rule $A \times D = B \times C$ lets you solve for any missing value. The calculator automates this process, making it a versatile equivalent ratio calculator.

Practical Applications

Ratios appear everywhere: in recipes, model building, financial calculations, and comparing proportions. This tool saves time by providing immediate results, whether you are simplifying a ratio online or finding a missing component in a proportional relationship.