Simplify ratios, find missing values in proportions, scale ratios, and compare two ratios — all in one tool.
Enter two values to simplify to the lowest terms.
Enter three values in a proportion A:B = C:D and solve for the missing one (leave one blank).
Enter a ratio and a scale factor to multiply or divide it.
Enter two ratios to compare them and find which is larger.
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A ratio is a comparison of two quantities that shows how many times one value contains another. Ratios are written as A:B, A/B, or "A to B." For example, if a class has 12 boys and 8 girls, the ratio of boys to girls is 12:8, which simplifies to 3:2 — meaning for every 3 boys there are 2 girls. Ratios are used in cooking, maps, finance, science, and everyday problem solving.
To simplify a ratio, divide both values by their greatest common divisor (GCD). For example, to simplify 18:12, find the GCD of 18 and 12, which is 6. Divide both: 18÷6 = 3, 12÷6 = 2. So 18:12 simplifies to 3:2. A simplified ratio shows the relationship in the smallest possible whole numbers.
A proportion states that two ratios are equal: A:B = C:D. If three of the four values are known, the missing one can be found using cross-multiplication: A × D = B × C. For example, if 3:4 = 9:?, then 3 × ? = 4 × 9 = 36, so ? = 12.
A ratio compares two quantities (A:B), while a fraction represents a part of a whole (A/B where B is the total). For example, a ratio of 3:2 can be expressed as the fraction 3/5 (3 out of 5 total parts). They're related but used in different contexts.
A proportion is an equation that states two ratios are equal: A:B = C:D. Proportions are used to scale quantities up or down while maintaining the same relationship. For example, if a recipe calls for 2 cups of flour for every 3 cups of water, you can scale it up proportionally.
Multiply both sides by a power of 10 to eliminate decimals, then simplify. For example, 1.5:2.5 → multiply by 2 → 3:5. This is already in simplest form since GCD(3,5) = 1.
Equivalent ratios are different ratios that represent the same relationship. For example, 1:2, 2:4, 3:6, and 10:20 are all equivalent ratios. You can create equivalent ratios by multiplying or dividing both parts by the same number.
Ratios appear everywhere: map scales (1:50,000 means 1cm = 50,000cm in real life), cooking (1:2 rice to water), finance (price-to-earnings ratio), photography (aspect ratios like 16:9), medicine (drug dosages), and construction (slope and grade measurements).
A unit ratio is a ratio where one of the values is 1. For example, 3:2 as a unit ratio is 1.5:1 or 1:0.667. Unit ratios make it easy to compare different ratios on a common scale.