Ratio Calculator

Divide both terms of the ratio by their greatest common divisor (GCD) - the largest number that evenly divides both. For example, 8:12 has a GCD of 4, so dividing both terms by 4 simplifies it to 2:3. A ratio is already in its simplest form when its two terms share no common divisor other than 1.

Cross-multiply, then divide: for a proportion A:B = C:X, the missing value X equals (B x C) / A. For example, if 3:7 = 9:X, then X = (7 x 9) / 3 = 21, so 3:7 and 9:21 are equivalent ratios. This method works because a true proportion means both ratios reduce to the same value, and cross-multiplication is a shortcut for confirming or solving that equality directly. This is the same calculation some people search for as a "cross multiplication calculator" or a general "ratio solver" - the Solve a Proportion mode above is exactly that.

A ratio (like 3:7) compares two quantities to each other, while a proportion is a statement that two ratios are equal to each other (like 3:7 = 9:21). A ratio is a single comparison; a proportion is an equation built from two ratios, which is why solving a proportion means finding a missing number rather than simplifying an existing one.

To convert a ratio A:B to a decimal, divide A by B - for example, 16:9 becomes 16 / 9 = 1.7778. To express it as a percentage of the combined total instead, divide A by (A + B) and multiply by 100 - a 3:2 ratio means the first part is (3 / 5) x 100 = 60% of the total. These are two different questions: a decimal compares the two parts directly, while a percentage-of-total describes each part's share of the whole.

A ratio and a fraction use the same underlying arithmetic - simplifying a ratio is identical to reducing a fraction to lowest terms - but they are conventionally used differently. A fraction like 3/4 usually represents a part of a single whole, while a ratio like 3:4 usually compares two separate quantities to each other, and is written with a colon rather than as a division. Mathematically, though, 3:4 and 3/4 simplify using the exact same greatest-common-divisor method.

Yes - ratios can compare three or more quantities at once, such as a 2:3:5 mixing ratio, and this calculator supports that directly. Check "Include a Third Term?" in Simplify mode to enter a three-term ratio, which is reduced the same way as a two-term one - by dividing every term by the greatest common divisor shared across all of them, not just a pair at a time. A 2:3:5 mixing ratio, for example, already shares no common divisor across all three terms, so it stays 2:3:5.

A ratio with one term equal to zero, like 0:5, is still a valid, well-defined ratio and simplifies to 0:1 - it means the first quantity is entirely absent relative to the second. A ratio of 0:0, however, is undefined, since there is no meaningful comparison to make between two absent quantities, and this calculator rejects that specific case rather than returning a misleading answer.

This calculator focuses on the relationship between two ratio terms - simplifying them, solving a proportion between two ratios, comparing two ratios, or converting between ratio, decimal, percentage, and fraction notation. The Percentage Calculator instead answers direct percentage questions such as what a specific percentage of a number is, or what percentage one number is of another that you already know, without treating the two numbers as a ratio's two parts.

A part-to-part ratio compares two parts of a group to each other, like 3 boys to 5 girls in a class of 8 (3:5), while a part-to-whole ratio compares one part to the entire group, like 3 boys out of 8 total students (3:8, or 3/8 as a fraction). Converting between them is straightforward: add the parts of a part-to-part ratio together to get the whole, then use that same total as the second term of a part-to-whole comparison - a 3:5 part-to-part ratio becomes a 3:8 part-to-whole one, since 3 + 5 = 8.

Write the percentage as a ratio of that number to 100 minus that number, then simplify using their greatest common divisor - for example, 60% becomes 60:40, which reduces to 3:2. This is the reverse of converting a ratio to a percentage: instead of finding a part's share of a total, you are starting from a share and rebuilding the two original parts it came from. The Percentage to Ratio mode above does this automatically for any whole-number percentage from 0 to 100.

The underlying math is identical - both divide every term by the greatest common divisor - but the two modes answer different questions and display the result differently. Simplify keeps the colon notation, so 16:9 stays a ratio ("16:9"), while Ratio to Fraction writes the same reduced numbers with a division line instead ("16/9"), which reads more naturally when you want to use the value in a calculation rather than as a comparison label.