Mathematics, Statistics & Geometry

Ratio Calculator

Simplify, scale, and compare ratios instantly. Find equivalent ratios, missing values, and reduce any ratio to its simplest form.

Simplified Ratio
3 : 2
As a Fraction3/2
Decimal Equivalent1.5
Calculation StepsOriginal Ratio: 12 : 8 GCF of 12 and 8 = 4 Divide both by GCF: 3 : 2

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The Complete Guide to Ratios

A ratio calculator simplifies, compares, and converts ratios instantly. Whether you are scaling a recipe, analysing financial metrics, or solving a maths problem, this tool reduces any two-part ratio to its simplest form and provides the fraction and decimal equivalents.

a:b=a÷gcd⁡(a,b)b÷gcd⁡(a,b)\begin{aligned} a : b = \frac{a \div \gcd(a,b)}{b \div \gcd(a,b)} \end{aligned}

Where:
a=
The first quantity in the ratio
b=
The second quantity in the ratio
gcd⁡(a,b)\gcd(a,b)=
The largest number that divides both a and b evenly

What Is a Ratio?

A ratio is a way of comparing two quantities by showing how many times one value contains or relates to the other. It is written as a : b and read as "a to b". Unlike a fraction, which expresses a part of a whole, a ratio compares two separate quantities.

For example, if a classroom has 15 boys and 10 girls, the ratio of boys to girls is 15:10, which simplifies to 3:2. This tells you that for every 3 boys, there are 2 girls.

How to Simplify a Ratio Step by Step

  1. Write the ratio: Start with the two values, for example 12 : 8.
  2. Find the GCF: The greatest common factor of 12 and 8 is 4.
  3. Divide both sides: 12 / 4 = 3, 8 / 4 = 2.
  4. Result: 12 : 8 = 3 : 2

Worked Example: Decimal Ratios

Ratios do not always start as whole numbers. Suppose a recipe calls for 1.5 cups of flour to 2.5 cups of sugar.

  • Step 1: Multiply both by 10 to eliminate decimals: 15 : 25
  • Step 2: GCF(15, 25) = 5
  • Step 3: 15 / 5 = 3, 25 / 5 = 5
  • Result: 1.5 : 2.5 = 3 : 5

Ratios vs. Fractions vs. Proportions

  • A ratio compares two quantities side by side (3:2).
  • A fraction represents a part of a whole (3/5 of the group are boys).
  • A proportion states that two ratios are equal (3:2 = 6:4).

Understanding the distinction is critical for solving word problems correctly.

The Golden Ratio

One of the most famous ratios in mathematics is the golden ratio (approximately 1 : 1.618). It appears in art, architecture, nature (sunflower spirals, nautilus shells), and design. Our dedicated Golden Ratio Calculator explores this concept in depth.

Real-World Applications

  • Cooking: Scaling recipes up or down while preserving proportions.
  • Finance: Debt-to-equity ratio, price-to-earnings ratio, and current ratio are all fundamental financial metrics.
  • Maps and Models: Scale ratios (e.g. 1:50,000) relate distances on a map to real-world distances.
  • Screens: Aspect ratios (16:9, 4:3, 21:9) define the shape of displays and video formats.
  • Medicine: Drug concentration ratios, dilution ratios, and mixing instructions.

Frequently Asked Questions

A ratio is a mathematical comparison of two or more quantities, showing how many times one value contains or is contained within the other. It is written with a colon (e.g. 3:2) or as a fraction (3/2). Ratios express relative size, not absolute amounts.

Divide both numbers by their greatest common factor (GCF). For example, 12:8 has a GCF of 4, so it simplifies to 3:2. If the ratio involves decimals, first multiply both sides by a power of 10 to eliminate the decimal, then simplify.

A ratio compares two separate quantities (e.g. 3 boys to 2 girls, written as 3:2). A fraction represents a part of a single whole (e.g. 3/5 of the class are boys). While ratios can be expressed as fractions, their conceptual meanings differ.

Yes. Ratios can compare three or more quantities, such as a recipe requiring flour, sugar, and butter in a 4:2:1 ratio. Our calculator handles two-part ratios, which are the most common form.

Yes. Our calculator automatically converts decimal ratios to whole numbers before simplifying. For example, 1.5:2.5 is first multiplied by 10 to get 15:25, then simplified to 3:5.

A 1:1 ratio means the two quantities are equal. For every unit of one quantity, there is exactly one unit of the other. This is sometimes called parity or an even split.

Ratios appear in cooking (ingredient proportions), finance (debt-to-equity ratios), maps (scale ratios like 1:50,000), screen displays (aspect ratios like 16:9), and medicine (drug concentration ratios). They are one of the most universally applicable mathematical concepts.

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