Cross Multiplication Calculator

Name: Cross Multiplication Calculator
Author: Jitendra Kumar

Solve missing proportion values or check whether two ratios are equal with exact diagonal products.

Last Updated: May 2026

Missing term

A numerator

Top-left term in a / b = c / d.

B denominator

Bottom-left term. Denominators cannot be zero.

C numerator

Top-right term in a / b = c / d.

D denominator

Bottom-right term. Denominators cannot be zero.

C value

Decimal value

Left cross product

Right cross product

Item	Value	Meaning
Completed proportion	3 / 4 = 15 / 20	The final setup after solving or checking.
Cross products	3 x 20 and 4 x 15	Multiply diagonally across the equal sign.
Left cross product	60	a x d
Right cross product	60	b x c
Status	Cross products match	The proportion is true.
Formula used	c = (a x d) / b	Rearranged cross-product equation.

Cross products

Cross multiplication turns a / b = c / d into a x d = b x c.

Proportion check

The diagonal products match, so the two ratios are equal.

Inputs

Integers, finite decimals, fractions, and percentages are parsed exactly before solving.

Math Setup Notice

This calculator performs exact cross-product arithmetic for educational use. Denominators cannot be zero, and the result depends on placing each value in the correct numerator or denominator position for your problem.

Reviewed For Methodology, Labels, And Sources

Every CalculatorWallah calculator is published with visible update labeling, linked source references, and founder-led review of formula clarity on trust-sensitive topics. Use results as planning support, then verify institution-, policy-, or jurisdiction-specific rules where they apply.

Reviewed By

Jitendra Kumar, Founder & Editorial Standards Lead, oversees methodology standards and trust-sensitive publishing decisions.

Review editor profile

Topic Ownership

Sales tax and tax-sensitive estimate tools, Education and GPA planning calculators, Health, protein, and screening-formula pages, Platform-wide publishing standards and methodology

See ownership standards

Methodology & Updates

Page updated May 2026. Trust-critical pages are reviewed when official rates or rules change. Evergreen calculator guides are checked on a recurring quarterly or annual cycle depending on topic volatility.

Sources & methodology About the review process

How to Use the Cross Multiplication Calculator

Step 1: Choose what is missing
Select A, B, C, or D if one term is unknown, or choose no missing term to check a completed proportion.
Step 2: Enter the known values
Use the setup a / b = c / d. You can enter integers, decimals, fractions, or percentages.
Step 3: Review the cross products
The calculator multiplies a x d and b x c so you can see whether the proportion balances.
Step 4: Use the exact answer
Read the solved value as an exact fraction or integer, then use the decimal form when an approximation is easier.

How Cross Multiplication Works

A proportion states that two ratios are equal. In the standard equation a / b = c / d, the diagonal products must match, so a x d = b x c. This is the cross multiplication rule.

To solve a missing term, the calculator rearranges that cross-product equation. For example, 3 / 4 = x / 20 becomes 4x = 60, so x = 15.

When all four terms are known, the calculator simply compares the two cross products. If they are equal, the ratios are proportional. If they differ, the proportion is false.

Cross Multiplication Guide

Cross Multiplication Rules

Cross multiplication is a compact way to solve proportion equations. The key is to keep the ratio setup consistent: top-left over bottom-left equals top-right over bottom-right.

Task	Formula	Use
Proportion setup	a / b = c / d	Two ratios are written as equal fractions.
Cross products	a x d = b x c	Multiply diagonally to check whether the ratios match.
Solve a	a = (b x c) / d	Use when the left numerator is missing.
Solve b	b = (a x d) / c	Use when the left denominator is missing.
Solve c	c = (a x d) / b	Use when the right numerator is missing.
Solve d	d = (b x c) / a	Use when the right denominator is missing.

Worked Examples

These examples show the same diagonal-product rule for missing values, ratio checks, decimals, and percent-based setups.

Problem	Cross multiplication setup	Result
3 / 4 = x / 20	x = (3 x 20) / 4	x = 15
5 / 8 = 15 / 24	5 x 24 = 8 x 15	120 = 120, so the proportion is true.
4 / 9 = 12 / 28	4 x 28 and 9 x 12	112 != 108, so the ratios are not equal.
17.5 / 37.5 = 7 / d	d = (37.5 x 7) / 17.5	d = 15
15% / 100% = x / 240	x = (15% x 240) / 100%	x = 36

Choosing the Correct Setup

Most cross multiplication errors come from putting a value in the wrong numerator or denominator position. Convert units first, then write both ratios in the same order.

Situation	Setup tip
Missing numerator	Put x on top of one ratio, then solve with the opposite diagonal product.
Missing denominator	Keep the known numerator above it and solve for the bottom term.
Ratio comparison	Choose no missing term and compare the two diagonal products.
Percent setup	Use 100% as the whole when translating percent-of-whole problems.
Units	Convert units first if the two ratios use different measurement systems.

Related Ratio Tools

If you need to scale a ratio after solving the proportion, use the proportion calculator. For exact fraction cleanup, use the fraction calculator.

Keep the research moving with Proportion Calculator, Fraction Calculator, Decimal Calculator, and Division Calculator.

Frequently Asked Questions

Cross multiplication is the proportion rule that says if a / b = c / d, then a x d = b x c. It is used to solve missing values and test whether two ratios are equal.

Select C as the missing term, enter A = 3, B = 4, and D = 20. The calculator uses x = (3 x 20) / 4, so x = 15.

Yes. The calculator accepts integers, finite decimals, fractions such as 3/4, and percentages such as 15%. It converts them to exact rational values before calculating.

No. The denominator terms b and d cannot be zero because a ratio with a zero denominator is undefined.

Yes. Choose the no-missing-term option. If the two cross products are different, the ratios do not form a true proportion.

This calculator focuses specifically on the cross-product equation a x d = b x c. The proportion calculator also includes ratio scaling workflows.

Rounding before the final step can change the cross products. Keep exact fractions or full decimal values until the answer is complete.