Ratio Calculator

Simplify ratios, solve for missing values in proportions, or compare ratios to check equivalence.

Simplify: A:B only | Solve: 3 values | Compare: all 4

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help_outlineHow to Useexpand_more

Three Types of Ratio Calculations

This ratio calculator performs three operations: simplify ratios, solve for missing values in proportions, and compare ratios to determine if they're equivalent. Accepts integers, decimals, and scientific notation.

Simplify Ratios:

Enter A and B to find the simplified ratio. The calculator divides both terms by their greatest common factor (GCD), or creates an equivalent ratio if already simplified.

Solve for Missing Value:

Enter A, B, and C to find D: D = C × (B/A)
Enter A, B, and D to find C: C = D × (A/B)

Compare Ratios:

Enter all four values (A, B, C, D) to check if A:B = C:D. The calculator computes A/B and C/D to determine if the ratios are equivalent (true or false).

infoWhat is Ratio Calculator?expand_more

A ratio compares two quantities by division, showing how many times one value contains another. Written as A:B (read "A to B"), ratios express the relationship between two numbers. For example, a 1:2 ratio means for every 1 part of the first quantity, there are 2 parts of the second.

Proportions are equations stating that two ratios are equal: A:B = C:D. If you know three values, you can solve for the fourth using cross-multiplication. This is useful for scaling recipes, converting units, and solving real-world problems.

Converting ratio to fractions: A part-to-part ratio like 1:2 can be converted to fractions of the whole. Add the parts (1+2=3), then each term becomes a fraction: 1/3 and 2/3.

functionsFormulaexpand_more

Simplifying Ratios:

1. Find the GCD (Greatest Common Divisor) of A and B

2. Divide both A and B by the GCD

Example: 12:8 → GCD is 4 → 12÷4 : 8÷4 = 3:2

Solving Proportions:

A : B = C : D

D = C × (B / A)

C = D × (A / B)

Cross-multiply: A × D = B × C

Converting Ratio to Fractions:

1. Add ratio terms to get the whole: 1 + 2 = 3

2. Each term becomes a numerator: 1/3 and 2/3

So in ratio 1:2, first part is 1/3 of whole, second is 2/3

lightbulbExamplesexpand_more

Example 1: Simplify 12:8

Find GCD of 12 and 8: GCD = 4

Divide both by 4: 12÷4 = 3, 8÷4 = 2

12:8 simplified = 3:2

Example 2: Solve 3:4 = 6:?

Formula: D = C × (B/A)

D = 6 × (4/3) = 6 × 1.333... = 8

3:4 = 6:8

Example 3: Solve 2:5 = ?:15

Formula: C = D × (A/B)

C = 15 × (2/5) = 15 × 0.4 = 6

2:5 = 6:15

Example 4: Compare 1:2 and 2:4

Calculate: 1/2 = 0.5

Calculate: 2/4 = 0.5

0.5 = 0.5

True - Ratios are equivalent

quizFAQexpand_more

What's the difference between a ratio and a fraction?expand_more

A ratio (A:B) compares two separate quantities, while a fraction (A/B) represents a part of a whole. However, they're mathematically related: the ratio 3:4 can be written as the fraction 3/4. Ratios can also compare more than two quantities (A:B:C), which fractions cannot directly represent.

How do I find equivalent ratios?expand_more

Multiply or divide both parts of the ratio by the same non-zero number. For example, 2:3 is equivalent to 4:6, 6:9, 8:12, etc. (multiplying both by 2, 3, 4). Equivalent ratios represent the same proportion.

How do I convert a part-to-part ratio to fractions?expand_more

Add all ratio parts to get the whole. Each part then becomes a fraction of that whole. For ratio 1:2:3, the whole is 6 (1+2+3). The fractions are 1/6, 2/6 (or 1/3), and 3/6 (or 1/2).

What is a proportion?expand_more

A proportion is an equation stating that two ratios are equal: A:B = C:D. This means A/B = C/D, or equivalently, A×D = B×C (cross-multiplication). Proportions are used to solve for unknown values when comparing equivalent ratios.

When are ratios used in real life?expand_more

Ratios are everywhere: recipes (2 cups flour to 1 cup sugar), maps (1:100,000 scale), mixing (3:1 water to concentrate), finance (price-to-earnings ratio), and construction (cement to sand ratio). They help maintain consistent proportions when scaling up or down.