MathsFree

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

Core Formula

\text{Ratio} = \frac{A}{\gcd(A,B)} : \frac{B}{\gcd(A,B)}

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

Review and Methodology

Updated Mar 17, 2026

This calculator runs locally in your browser. Inputs are converted into the units required by the formula, and the result is paired with supporting references so you can verify the method before using it for planning or estimates.

Worked Example

Simplify the ratio 12:8

1Step 1: Find GCD(12, 8) = 4

2Step 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.

How can I put this Ratio Calculator on my blog or website?

Yes, the Ratio Calculator is fully embeddable. Tap "Embed" above to configure appearance and copy the code. It is free to use, works on any platform (HTML, WordPress, CMS), and adjusts to any screen size automatically. Visit calculory.com/services/embed-calculators for the complete guide.

AI Assistant

Ask about this calculator

I can help you understand the ratio calculator formula, interpret your results, and answer follow-up questions.

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