Ratio Calculator
Simplify a ratio between two numbers to its lowest terms.
Try an example
2 : 3
About this calculator
What Is a Ratio?
A ratio compares two or more quantities by showing how many times one contains the other. It is usually written with a colon, like 2:3, or read as "2 to 3," or written as the fraction 2/3. If a recipe uses 1 cup of butter for every 2 cups of sugar, the butter-to-sugar ratio is 1:2. Ratios have no units of their own — they describe relative size — so they are a handy way to scale things up or down without changing proportions.
How to Solve a Ratio Problem
This calculator solves the proportion A : B = C : D when you know any three of the four values. The fourth is found by cross-multiplying: A × D = B × C, so D = (B × C) ÷ A. For example, if 3 : 5 = 12 : x, then x = (5 × 12) ÷ 3 = 20.
Scaling a Ratio
To scale a ratio, multiply or divide every term by the same number. If one cake needs butter, sugar and flour in the ratio 1 : 2 : 3, then five cakes need 5 : 10 : 15. Simplifying a ratio works the same way in reverse: divide every term by their greatest common factor (see the GCF Calculator), so 20 : 30 becomes 2 : 3.
Everyday Examples of Ratios
- Cooking and mixing: scaling recipes, mixing paint, or diluting concentrate.
- Maps and models: a scale of 1 : 50,000 means 1 cm on the map equals 50,000 cm on the ground.
- Screens and photos: aspect ratios such as 16 : 9 describe width to height.
- Finance and business: price-to-earnings, debt-to-income and many other ratios compare numbers that matter.
- Odds and probability: 1 : 4 odds relate to a 20% chance.
Ratios, Fractions and Percentages
These three describe the same relationship in different ways. A ratio of 1 : 4 compares one part with four parts; as a fraction of the whole (five parts in total) the first part is 1/5, or 20%. Always say whether you mean part-to-part (1 : 4) or part-to-whole (1 : 5). The Fraction Calculator and Percentage Calculator help you convert between them.
Worked example
8:12 shares a greatest common factor of 4 — divide both sides by 4 and the ratio simplifies to 2:3, equivalent to 8 ÷ 12 = 0.666667.
Frequently asked questions
How do you simplify a ratio?
Divide both numbers by their greatest common factor (GCF). For 8:12, the GCF is 4, so 8÷4 : 12÷4 gives 2:3.
What if the two numbers share no common factor?
Then the ratio is already in its simplest form — for example, 5:9 can't be reduced further since their GCF is 1.
What's the difference between a ratio and a fraction?
A ratio (2:3) compares two separate quantities, while a fraction (2/3) usually represents a part of a single whole — but the simplification math works the same way for both.
Can a ratio have more than two numbers?
Yes — ratios like 2:3:5 compare three or more quantities at once. This calculator handles two-number ratios; simplify a multi-part ratio by dividing every term by their shared GCF.
