# Proportion Calculator

Solve any proportion a/b = c/d by finding the missing value. Enter three values to calculate the fourth. Free online proportion solver with cross.

## What this calculates

Solve any proportion by entering three known values to find the missing fourth value. This calculator uses cross multiplication to solve proportions of the form a/b = c/d instantly.

## Inputs

- **Value A (numerator left)** — Top-left value in the proportion a/b = c/d.
- **Value B (denominator left)** — Bottom-left value in the proportion a/b = c/d.
- **Value C (numerator right)** — Top-right value in the proportion a/b = c/d.
- **Value D (denominator right)** — Bottom-right value in the proportion a/b = c/d.

## Outputs

- **Missing Value** — The solved value that completes the proportion.
- **Complete Proportion** — formatted as text — The full proportion with all four values.
- **Cross Products** — formatted as text — Verification that a x d = b x c.
- **Ratio (decimal)** — The common ratio as a decimal value.

## Details

A proportion is an equation stating that two ratios are equal: a/b = c/d. Solving proportions is essential in scaling recipes, converting units, working with maps and blueprints, and solving percentage problems.

Cross Multiplication

The fundamental method for solving proportions is cross multiplication: a x d = b x c. If any one value is unknown, you can solve for it algebraically.

For example, if 3/4 = x/20, cross multiply: 3 x 20 = 4 x x, so 60 = 4x, giving x = 15.

Verification

To verify a proportion is correct, check that the cross products are equal. If a x d equals b x c, the proportion is valid. This calculator automatically verifies every solution.

## Frequently Asked Questions

**Q: What is a proportion?**

A: A proportion is a statement that two ratios are equal, written as a/b = c/d. For example, 2/3 = 4/6 is a proportion because both ratios simplify to the same value. Proportions are used to solve for unknown quantities when a constant ratio is maintained.

**Q: How does cross multiplication work?**

A: Cross multiplication converts a proportion into a simple equation. For a/b = c/d, multiply the diagonals: a x d = b x c. This eliminates the fractions and lets you solve for any unknown. For example, 5/8 = x/24 becomes 5 x 24 = 8 x x, so 120 = 8x, and x = 15.

**Q: When are proportions used in real life?**

A: Proportions are used everywhere: scaling recipes up or down, reading maps (scale factors), converting currencies, calculating medicine dosages based on body weight, determining paint coverage for larger areas, and resizing images while maintaining aspect ratios.

**Q: What is the difference between a ratio and a proportion?**

A: A ratio is a comparison of two quantities (like 3:4), while a proportion is an equation stating that two ratios are equal (like 3/4 = 6/8). A ratio is a single comparison; a proportion is a relationship between two comparisons that asserts they are the same.

**Q: Can a proportion have zero in the denominator?**

A: No, denominators in a proportion cannot be zero because division by zero is undefined. If b = 0 or d = 0, the proportion a/b = c/d is invalid. The calculator will alert you if a zero denominator would cause an undefined result.

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Source: https://vastcalc.com/calculators/math/proportion
Category: Math
Last updated: 2026-04-21