Ratio Calculator

A ratio is a comparison between two or more quantities, showing how many times one value contains or is contained within the other. Ratios are typically expressed as a:b (read as 'a to b') or as a fraction a/b.

To simplify a ratio, divide both terms by their greatest common divisor (GCD). For example, the ratio 12:8 can be simplified by dividing both terms by 4, giving us 3:2.

A ratio compares two quantities (like 3:4), while a proportion states that two ratios are equal (like 3:4 = 6:8). Proportions are used to find missing values when you know three of the four terms.

To solve a proportion a:b = c:x, cross-multiply: a × x = b × c, then solve for x: x = (b × c) ÷ a. For example, in 2:3 = 4:x, we get x = (3 × 4) ÷ 2 = 6.

Yes, ratios can include decimal numbers. For example, 1.5:2.5 is a valid ratio. However, it's often more convenient to convert decimals to whole numbers by multiplying both terms by the same factor.

Scaling a ratio means multiplying both terms by the same factor to get an equivalent ratio. For example, scaling 2:3 by a factor of 4 gives us 8:12, which represents the same proportional relationship.

To compare ratios, convert them to decimal form by dividing the first term by the second term. The ratio with the larger decimal value is the larger ratio. You can also cross-multiply to compare ratios directly.

Ratios are used in cooking (recipe proportions), finance (financial ratios), architecture (scale drawings), photography (aspect ratios), medicine (dosage calculations), and many other fields where proportional relationships matter.

Yes, ratios can have multiple terms. For example, 2:3:5 represents a three-term ratio. This is common in mixing colors, combining ingredients, or distributing resources among multiple parties.

A ratio compares two quantities directly (like 3:4), while a percentage expresses one quantity as a fraction of 100. However, ratios can be converted to percentages: the ratio 3:4 equals 75% (3÷4 × 100).