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Cross Multiplication Calculator

Solve proportions using cross multiplication. Given a/b = c/d, find the unknown value when three of the four values are known.

Reviewed by Christopher FloiedPublished Updated

This free online cross multiplication calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

Results

Unknown Value (or product if verifying)

60

Complete Proportion

3/5 ≡ 12/20 (valid)

Cross Products

a×d = 60, b×c = 60 ✓

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Cross Multiplication Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

The Cross Multiplication Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

When to Use This Calculator

  • •Use the Cross Multiplication Calculator when you need a quick mathematical result without writing out all the steps manually, saving time on repetitive calculations.
  • •Use it to verify hand calculations on tests or assignments and catch arithmetic mistakes.
  • •Use it when teaching or explaining mathematical concepts to others, demonstrating how changing inputs affects the result.
  • •Use it to explore the behavior of mathematical functions across a range of inputs.

About Cross Multiplication Calculator

Cross multiplication is a technique for solving proportions — equations stating that two ratios are equal. Given a/b = c/d, cross multiplication gives a × d = b × c. This technique is derived from multiplying both sides of the proportion by b × d. It is one of the most widely used methods in algebra, appearing in similar triangles, unit conversions, recipe scaling, map distances, scale drawings, and percentage problems. If you know three of the four values in a proportion, cross multiplication lets you find the fourth. For example, if 3/5 = x/20, cross multiplying gives 3 × 20 = 5 × x, so 60 = 5x, and x = 12. Cross multiplication works because equal ratios form a valid proportion, and the cross products of a valid proportion are always equal. This method extends to more complex ratio problems and is the foundation for solving similar triangle problems in geometry.

The Math Behind It

Cross multiplication is justified algebraically: starting from a/b = c/d, multiply both sides by bd to get ad = bc. This works because multiplication preserves equality, and bd/(bd) = 1. The converse also holds: if ad = bc (with b, d ≠ 0), then a/b = c/d. This equivalence is used extensively in proportion testing. Cross multiplication connects to the concept of ratios and proportional reasoning. Two quantities are proportional if their ratio is constant: y/x = k (or y = kx). The graph of a proportional relationship passes through the origin and is a straight line. Cross multiplication also relates to the determinant of a 2×2 matrix: the proportion a/b = c/d is equivalent to the matrix [a c; b d] having determinant ad − bc = 0. In geometry, similar triangles have proportional corresponding sides, and cross multiplication is used to find unknown lengths.

Formula Reference

Cross Multiplication

If a/b = c/d, then a × d = b × c

Variables: a, b, c, d — one may be unknown

Worked Examples

Example 1: Solving a Proportion

Solve: x/5 = 12/20

Step 1:Cross multiply: x × 20 = 5 × 12
Step 2:20x = 60
Step 3:x = 60/20 = 3

x = 3, so 3/5 = 12/20 ✓

Example 2: Recipe Scaling

A recipe uses 3 cups of flour for 4 servings. How much flour for 10 servings?

Step 1:Set up proportion: 3/4 = x/10
Step 2:Cross multiply: 3 × 10 = 4 × x
Step 3:30 = 4x, so x = 7.5

You need 7.5 cups of flour for 10 servings

Common Mistakes & Tips

  • !Setting up the proportion incorrectly — the corresponding quantities must be in the same positions.
  • !Cross multiplying when the equation is not a proportion (e.g., a/b + c/d).
  • !Forgetting that cross multiplication only applies when two ratios are equal, not for addition or subtraction of fractions.
  • !Not checking the answer by substituting back into the original proportion.

Related Concepts

Reciprocal

Proportions can be inverted: if a/b = c/d, then b/a = d/c.

GCF

Simplifying ratios to lowest terms uses the GCF.

Used in These Calculators

Calculators that build on or apply the concepts from this page:

Distributive Property Calculator

Reciprocal Calculator

Frequently Asked Questions

When can I use cross multiplication?

Cross multiplication applies when two fractions or ratios are set equal to each other (a/b = c/d). It does NOT apply when adding, subtracting, or comparing fractions without equality.

Can cross multiplication be used with units?

Yes! Unit conversions are proportions. For example, if 1 inch = 2.54 cm, then x inches / 10 cm = 1 inch / 2.54 cm, giving x = 10/2.54 ≈ 3.937 inches.