Proportion Calculator — Solve a/b = c/d for Missing Value

The Formula

A proportion is an equation that states two ratios are equal (a/b = c/d). Cross-multiplication (a × d = b × c) transforms the proportion into a simple algebraic equation. Given any three values, the fourth can be found by dividing the cross product by the remaining known value. Proportions are fundamental in scaling, unit conversion, recipe adjustments, map reading, and financial analysis.

Variable Definitions

How to Use This Calculator

1. 1

   Enter any three of the four values a, b, c, d. Leave the missing value empty or enter "?". The calculator solves for the missing value automatically.

2. 2

   All provided values must be positive numbers. The calculator validates that the proportion holds by cross-multiplying.

3. 3

   Review the fraction form (a/b = c/d) and the percentage equivalent to understand the proportion in different formats.

4. 4

   Check the verification result — it confirms whether a/b = c/d holds within a small tolerance (0.01%).

5. 5

   Use the solution steps panel to see the cross-multiplication formula and how the missing value was computed.

Quick Reference

Common Applications

• Scaling recipes: if 2 cups of flour serves 4 people, how many cups serve 6? Set 2/4 = x/6.
• Map reading: on a 1:100,000 scale map, 1 cm = 1 km. Use a proportion to find real distances.
• Unit conversion: convert miles to kilometers (1 mi ≈ 1.609 km) or currencies using exchange rates.
• Percentages: "what is 15% of 80" becomes 15/100 = x/80, giving x = 12.
• Financial analysis: compare price-to-earnings ratios, debt-to-income ratios, or profit margins.

A proportion states two ratios are equal. Cross-multiplication transforms a/b = c/d into a×d = b×c, allowing you to solve for any missing value.

Understanding the Concept

A proportion is a mathematical statement that two ratios are equal, written as a/b = c/d. This simple equation is one of the most powerful tools in mathematics because it allows you to solve for an unknown quantity when you know the relationship between three known quantities. The fundamental principle behind solving proportions is cross-multiplication: multiply the numerator of each ratio by the denominator of the other ratio. This gives a × d = b × c, which is a simple linear equation. If you know any three of the four values, you can solve for the fourth by dividing the cross product by the remaining known value. For example, to solve for d: d = (b × c) / a. Proportions appear everywhere in daily life and professional work. In cooking, recipes use proportions to scale ingredients: if a recipe calls for 2 cups of flour for 4 servings (2/4), you can find the flour needed for 6 servings by solving 2/4 = x/6, giving x = 3 cups. In cartography, map scales are proportions: a 1:100,000 scale means 1 unit on the map equals 100,000 units in reality. In finance, ratios like price-to-earnings (P/E) and debt-to-income (DTI) are compared using proportions. The percentage sign itself (%) is a proportion per hundred: 15% means 15/100. Understanding proportions unlocks the ability to work with percentages, fractions, scaling, and rates seamlessly.

Frequently Asked Questions

Sources & References