Ratio and Proportion Calculator

Find the unknown value in A : B = C : D, or simplify any ratio to its lowest terms.

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Proportion — leave the unknown field empty:

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=
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Leave exactly one field (A, B, C or D) empty to find the unknown. Fill all four to check whether the proportion holds.

Simplify a ratio:

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Examples

ProblemSolution
3 : 4 = ? : 8? = 6
5 : ? = 10 : 6? = 3
? : 7 = 3 : 21? = 1
2 : 3 = 6 : ?? = 9

Formula

A / B = C / D
A × D = B × C

A : B = C : D means A/B = C/D, so A × D = B × C (cross-multiplication). To find D: D = B × C / A.

How to use?

  1. 1
    Enter three valuesFill in any three of the four fields A, B, C, D. Leave the unknown blank.
  2. 2
    Click CalculateThe missing value is found via cross-multiplication: A × D = B × C.
  3. 3
    Simplify a ratioEnter X and Y in the lower section to reduce the ratio X : Y to its lowest terms.

FAQ

What is a proportion?
A proportion states that two ratios are equal: A/B = C/D. Cross-multiplying gives A × D = B × C, which is used to find any missing value.
How do I simplify a ratio?
Divide both numbers by their Greatest Common Divisor (GCD). For example 12:8 — GCD is 4, so 12/4 : 8/4 = 3 : 2.
What is the difference between a ratio and a proportion?
A ratio compares two quantities (e.g. 3:4). A proportion states that two ratios are equal (e.g. 3:4 = 6:8). This calculator handles both.

Ratios and Proportions Explained

A ratio compares two numbers: 3:4 means for every 3 units of A there are 4 units of B. A proportion says two ratios are equal: 3:4 = 6:8. Cross-multiplication (A × D = B × C) lets you find any missing term.

Real-World Uses

Ratios appear in cooking (scale recipes), maps (1:50 000), construction (mix ratios), finance (price-to-earnings), and school exams worldwide.

Ratio calculation is useful whenever two or more values need to stay in the same relationship. Recipes, map scales, screen sizes, mixtures, financial splits, classroom comparisons and proportional math problems all use the same idea. If one side of a ratio changes, the matching side must change by the same factor to preserve the proportion.

A ratio is not always the same as a percentage. Percentages compare a value with 100, while ratios compare values directly, such as 3:2 or 16:9. Before calculating, make sure the values describe compatible things and use the same unit where needed. This prevents common mistakes when resizing images, scaling ingredients, converting plans or comparing performance figures.

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