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Ratio & Proportion Calculator

Solve for X in ratios (A:B = C:D).

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Inputs

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Results

Missing Value

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Assumptions

  • The values in each ratio should describe the same kind of quantity, such as width-to-height or cups-to-eggs.
  • The relationship is treated as linear, so the same scale factor applies across both ratios.
  • A value used as a denominator cannot be zero; zero makes the proportion undefined.

Sensitivity preview

A -10%: Missing Value 13.33

A Current: Missing Value 12

A +10%: Missing Value 10.91

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About this Ratio Calculator

Ratios compare two quantities, while a proportion states that two ratios are equal (A is to B as C is to D). This calculator helps you solve for the unknown variable 'X' in any proportion, making it perfect for scaling dimensions or ingredients.

Who this calculator is for

  • People scaling recipes, drawings, or project measurements.
  • Students solving proportion and cross-multiplication problems.
  • Anyone who needs to keep two quantities in the same relationship.

When to use it

  • Use this calculator when one value in a proportion is missing.
  • Use it to scale a recipe, photo, or layout up or down.
  • Use it to compare quantities that should stay in the same ratio.

Key assumptions

  • The values in each ratio should describe the same kind of quantity, such as width-to-height or cups-to-eggs.
  • The relationship is treated as linear, so the same scale factor applies across both ratios.
  • A value used as a denominator cannot be zero; zero makes the proportion undefined.

Accuracy and testing

Review formula sources, default test cases, assumptions, unit handling, rounding rules, and changelog for this calculator.

View accuracy page

How this calculator works

The calculator uses the Cross-Multiplication rule: If $\frac{A}{B} = \frac{C}{D}$, then $A \times D = B \times C$. To solve for any missing variable (e.g., D), rearrange the formula: $D = \frac{B \times C}{A}$.

Inputs explained

A : B

The first known ratio (e.g., 16 : 9 for a widescreen video).

C : D

The second ratio. Enter the missing value as 0 only as a placeholder when solving for that position.

Understanding your results

The result is the value that makes the two ratios equivalent. For example, if 1:2 = 50:X, the result is 100.

Example scenarios

Image Resizing

Original is 4:3 (A:B). New width is 800 (C). Solve for Height (D). Formula: 4/3 = 800/D. Result: D = 600.

Recipe Scaling

Recipe calls for 2 cups flour (A) for 3 eggs (B). You have 5 eggs (D). How much flour (C)? Formula: 2/3 = C/5. Result: C = 3.33 cups.

Key Features

  • Instant Calculation
  • Private & Secure
  • Mobile Optimized

Tips & Best Practices

  • This is essentially the 'Rule of Three'.
  • Always ensure A and C are the same unit type (e.g., width), and B and D are the same unit type (e.g., height).

Glossary of Terms

Ratio
The quantitative relation between two amounts showing the number of times one value contains or is contained within the other.
Proportion
An equation stating that two ratios are equal.
Cross Product
The product of the numerator of one ratio and the denominator of the other.

Frequently Asked Questions

How do I simplify a ratio?
Divide both sides by their Greatest Common Divisor (GCD). For example, 10:20 simplifies to 1:2.
What is the Golden Ratio?
The Golden Ratio (phi) is approximately 1.618. It is a special ratio found often in nature, art, and architecture.
Can ratios have decimals?
Yes. 1.5 : 3 is a valid ratio, which is equivalent to 1 : 2.