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Ratio Calculator

Use this free online ratio calculator to simplify ratios, find equivalent ratios, and solve missing ratio values. Enter two numbers to get the simplest form instantly.

Enter Values

First Value (A)

Second Value (B)

Result

Enter values above and click Calculate to see your result.

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Formula

Simplified Ratio = A/GCD(A,B) : B/GCD(A,B)

Divide both parts of the ratio by their greatest common divisor (GCD) to get the simplest form.

Worked Example

Simplify the ratio 12:8 Step 1: Find GCD(12, 8) = 4 Step 2: Divide both → 12/4 : 8/4 = 3 : 2 Result: 3:2

What Is a Ratio?

A ratio is a way to compare two quantities by showing how many times one value contains or is contained within another. Ratios are written as A:B and can be simplified just like fractions by dividing both sides by their greatest common divisor.

The ratio 6:4 simplifies to 3:2, meaning for every 3 of the first there are 2 of the second
Ratios can compare parts to parts (boys to girls) or parts to whole (boys to total students)
Equivalent ratios maintain the same relationship: 1:2, 2:4, and 3:6 are all equivalent
Unlike fractions, ratios compare two separate quantities rather than expressing part of a whole

Ratios are used extensively in cooking (ingredient proportions), maps (scale), finance (debt-to-income), mixing (paint colors), and architecture (golden ratio).

You can also calculate changes using our Proportion Calculator, GCD Calculator or Fraction Calculator.

Frequently Asked Questions

What is a ratio?

A ratio is a comparison of two quantities showing how many times one value contains or is contained within another. For example, a ratio of 3:1 means the first quantity is three times the second.

How do I simplify a ratio?

Divide both parts by their greatest common divisor (GCD). For example, 12:8 simplifies to 3:2 because GCD(12,8) = 4.

What is a proportion?

A proportion states that two ratios are equal, e.g. 1:2 = 3:6. Proportions are used to scale recipes, convert units, and solve many real-world problems.

How are ratios different from fractions?

A ratio compares two separate quantities (e.g., 3 boys to 2 girls). A fraction represents a part of a whole (e.g., 3/5 of the class are boys). Ratios can be converted to fractions and vice versa.

What is the golden ratio?

The golden ratio is approximately 1:1.618 (or 1.618:1). It appears in nature, art, and architecture and is considered aesthetically pleasing. It is an irrational number often denoted by the Greek letter phi.

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