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Ratio Calculator – Simplify & Solve Ratios Instantly

Ratio Calculator

This ratio calculator covers three types of ratio problems: solving for a missing value in a proportion (A:B = C:D), simplifying a ratio to its lowest terms, and scaling a ratio up or down by a given factor. Enter your values, click Calculate, and full step-by-step working will be displayed.

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Ratio Calculator

Enter any three values in the proportion A : B = C : D and leave the unknown field empty. The calculator will solve for the missing value using cross-multiplication.
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Simplify Ratio Calculator

Enter a ratio to reduce it to its simplest form by dividing both values by their Greatest Common Divisor (GCD).
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Ratio Scaling Calculator

Enter a ratio and a scaling factor to enlarge or shrink it. Each part of the ratio will be multiplied or divided by the factor.
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What is a Ratio?

A ratio is a quantitative relationship between two or more numbers that expresses how many times one value contains or is contained within another. Ratios describe relative size rather than absolute size, making them applicable across cooking, construction, finance, medicine, and engineering.

Ratios can be expressed in several equivalent ways. The ratio of 3 to 4 can be written as 3:4, as the fraction 3/4, or in words as 3 to 4. The colon notation (3:4) is the most commonly used form in everyday contexts, while the fraction form is more natural in algebraic manipulation.

Proportions and the A:B = C:D Relationship

A proportion is a statement that two ratios are equal. When we write A:B = C:D, the product of the outer terms (A and D) always equals the product of the inner terms (B and C). This gives us A × D = B × C, which can be rearranged to solve for any one of the four values.

A : B = C : D   ⇒   A × D = B × C
Example: 2 : 3 = 4 : ?  ⇒  2 × ? = 3 × 4  ⇒  ? = 12 ÷ 2 = 6

Simplifying a Ratio

A ratio is in its simplest form when both values share no common factor other than 1. Simplifying means dividing both parts by their Greatest Common Divisor (GCD) — the largest number that divides both values without a remainder.

Simplified ratio = A ÷ GCD(A, B) : B ÷ GCD(A, B)
Example: 12 : 8  ⇒  GCD = 4  ⇒  12÷4 : 8÷4 = 3 : 2

Scaling a Ratio

Scaling a ratio means multiplying or dividing each part by the same factor, producing a new ratio that describes a larger or smaller version of the same proportional relationship.

Enlarged: A : B × k = (A × k) : (B × k)
Shrunk:   A : B ÷ k = (A ÷ k) : (B ÷ k)
Example: 2:3 enlarged by 4 = 8:12 = 2:3 (simplified)

Practical Applications

Ratios appear in virtually every area of life — recipe scaling, concrete mixes, financial metrics (price-to-earnings, debt-to-equity), drug concentrations, map scales, and screen aspect ratios. Understanding ratios allows you to compare, convert, and scale quantities confidently across any domain.