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Ratio Calculator

Simplify a ratio to its lowest terms, or solve a missing value in a proportion like a:b = c:d.

Quick Presets:

Simplify Ratio (A : B)

Ratio Analysis

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Definition: A ratio compares two quantities
Simplification: Divide by the GCF
Proportion: a : b = c : d solves cross products
Use case: Recipes, maps, mixes, finance

What is a ratio?

A ratio compares two quantities of the same kind, written as a:b. The ratio 12:18 tells you that for every 12 units of the first quantity there are 18 of the second. Ratios keep the relationship even when the actual sizes change.

Simplifying a ratio means dividing both parts by their greatest common factor. Since the GCF of 12 and 18 is 6, the ratio 12:18 simplifies to 2:3 — the same relationship in its smallest whole-number form.

Solving proportions

A proportion states that two ratios are equal: a:b = c:d. Because the cross products are equal (a × d = b × c), you can solve any missing term: d = b × c / a.

Ratios appear everywhere: doubling a recipe (2 cups flour : 1 cup sugar), scale maps (1 cm : 10 km), mixing ratios and financial analysis. Percentages are just ratios scaled to 100.

How to use this calculator

  1. To simplify, enter the two parts of the ratio and press Simplify.
  2. To solve a proportion, enter a, b and c of a:b = c:d.
  3. Press the solve button to find the missing d.
  4. Read the simplified ratio and percentage shares together.

Pro tips

  • A ratio like 0.5:2 is valid; the calculator simplifies using exact math.
  • Percentages are ratios where the whole is 100.
  • Cross-multiply to check any proportion by hand.

Advantages & considerations

✅ Advantages

  • Simplifies any ratio to lowest terms
  • Solves missing terms in proportions
  • Shows each part as a percentage of the whole

⚠️ Considerations

  • Both ratio parts must be non-zero
  • Proportion tool solves for the fourth term only

Frequently asked questions

How do I simplify a ratio?▶
Divide both parts by their greatest common factor. For 12:18 the GCF is 6, so the simplified ratio is 2:3.
How do I solve a:b = c:d?▶
Use cross multiplication: d = b × c / a. For 2:3 = 8:d, that gives d = 3 × 8 / 2 = 12.
What is the difference between a ratio and a fraction?▶
A ratio a:b compares two separate quantities, while a fraction a/b expresses one quantity as a part of a whole. They often convert into each other.
Can ratios have decimals?▶
Yes. Decimal ratios are common in engineering and recipes. The calculator handles them and simplifies to clean values when possible.
How do I turn a ratio into a percentage?▶
Each part as a percentage of the total: a/(a+b) × 100 and b/(a+b) × 100. For 2:3, that is 40% and 60%.