Ratio Calculator

A ratio $A : B$ expresses the quantitative relationship between two quantities. To simplify a ratio to its lowest terms, divide both values by their Greatest Common Divisor (GCD): $$\text{Simplified Ratio} = \left(\frac{A}{\text{GCD}(A, B)}\right) : \left(\frac{B}{\text{GCD}(A, B)}\right)$$. For example, the ratio $24 : 36$ shares a maximum common factor of $12$, simplifying down to $2 : 3$ with a decimal value of $$0.667$$ ($$24 \div 36$$).

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The Ratio Simplification Formula

Simplifying a ratio reduces its components to the smallest possible integers while preserving the original relative scale:

Ratio Simplification & Decimal Conversion

$$\text{Simplified Form} = \frac{A}{\text{GCD}(A,B)} : \frac{B}{\text{GCD}(A,B)}$$

$$\text{Decimal Value} = \frac{A}{B}$$

Example ($$24 : 36$$):
$$\text{GCD}(24, 36) = 12$$
$$\text{Simplified} = \left(\frac{24}{12}\right) : \left(\frac{36}{12}\right) = \mathbf{2 : 3}$$
$$\text{Decimal} = \frac{24}{36} = \mathbf{0.667}$$

Common Ratio Reduction Reference Table

The matrix below demonstrates standard integer reductions alongside equivalent decimal quotients and percentage fractions:

Original Ratio ($$A : B$$) GCD Simplified Form Decimal Quotient Percentage ($$\frac{A}{B} \times 100\%$$)
$$24 : 36$$ $$12$$ $$2 : 3$$ $$0.667$$ $$66.67\%$$
$$50 : 200$$ $$50$$ $$1 : 4$$ $$0.250$$ $$25.00\%$$
$$15 : 45$$ $$15$$ $$1 : 3$$ $$0.333$$ $$33.33\%$$
$$100 : 25$$ $$25$$ $$4 : 1$$ $$4.000$$ $$400.00\%$$

Why the Greatest Common Divisor Matters

A ratio is fully reduced when its terms share no common factors greater than 1. Dividing both sides by their Greatest Common Divisor (GCD) yields the irreducible minimum form in a single mathematical step, eliminating the need to divide iteratively by smaller factors like 2 or 3.

How to Use This Calculator

  1. Enter two non-zero whole numbers into input fields A and B.
  2. The simplified ratio and decimal equivalent update instantly upon typing.
  3. To compare multiple proportions, observe the decimal quotient readout.

Frequently Asked Questions

How do I simplify a ratio?

Find the Greatest Common Divisor (GCD) of both numbers, then divide both terms by that common divisor.

What does a simplified ratio like 2:3 mean?

It expresses the exact same proportional relationship as the original values, represented using the smallest possible whole integers.

Can I use decimals in the ratio?

For decimal ratios, multiply both terms by 10, 100, or 1000 to convert them into whole integers before finding the Greatest Common Divisor.

What's the decimal equivalent of a ratio?

The decimal equivalent is calculated by dividing the first antecedent value by the second consequent value (A ÷ B).

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