Math

Proportion Calculator

Solve A/B = C/D for any unknown value. Select the unknown, enter the other three values, and cross multiplication gives you the answer instantly.

Solve A / B = C / D for any missing value. Select which value is unknown, then enter the other three.

Unknown value

Select the unknown value and enter the other three to solve.

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Cross Multiplication Formula

For a proportion A/B = C/D, cross multiplication gives A × D = B × C. Rearrange to solve for any unknown.

A × D = B × C

D = (B × C) ÷ A

C = (A × D) ÷ B

B = (A × D) ÷ C

A = (B × C) ÷ D

Direct and Inverse Proportions

A direct proportion means that as one quantity increases, the other increases at a constant rate. The ratio between the two quantities remains constant. If y is directly proportional to x, then y = kx. Doubling x doubles y. This is the type of proportion A/B = C/D handles.

An inverse proportion means that as one quantity increases, the other decreases at a rate that keeps their product constant. If y is inversely proportional to x, then x × y = k, or equivalently A × B = C × D. Speed and travel time at a fixed distance are inversely proportional: double the speed and the journey takes half the time.

In practical problem-solving, always check whether a situation calls for direct or inverse proportionality before applying the proportion formula. The most common error is applying direct proportion arithmetic to an inverse proportion problem, which produces incorrect answers.

Frequently asked questions

What is a proportion?
A proportion is a mathematical statement that two ratios are equal. Written as A/B = C/D, it states that the ratio of A to B is the same as the ratio of C to D. Proportions are a fundamental concept in mathematics and are used whenever quantities need to be scaled while keeping their relative relationship constant. If a recipe requires 2 cups of flour for every 3 cups of water, the proportion 2/3 = 4/6 = 8/12 captures all valid scalings of that recipe.
How does cross multiplication work?
Cross multiplication is the standard technique for solving proportions. Given A/B = C/D, multiply each side by both denominators to obtain A × D = B × C (cross products). To solve for any unknown, isolate it using basic algebra. For D: D = (B × C) / A. For A: A = (B × C) / D. For B: B = (A × D) / C. For C: C = (A × D) / B. Cross multiplication works because multiplying both sides of a valid equation by the same value preserves equality.
What is the difference between a proportion and an equation?
A proportion is a specific type of equation that equates two ratios. All proportions are equations, but not all equations are proportions. An equation can relate any two expressions, while a proportion specifically states A/B = C/D. The cross-multiplication method is unique to proportions and exploits this special structure. In contrast, a general equation requires other algebraic manipulation techniques depending on its form.
What are some real-world uses of proportions?
Proportions are used in virtually every field. In cooking, they allow you to scale recipes up or down precisely. In medicine, drug dosing often uses proportional scaling by patient body weight: if 5 mg is required per 10 kg, then 150 mg is needed for a 300 kg dose calculation. In architecture, scale drawings use proportions to represent large structures accurately. In photography, maintaining aspect ratios when resizing images uses proportional reasoning. In finance, unit rate calculations and exchange rate conversions are proportional problems.
Can a proportion involve decimals or fractions?
Yes, proportions can involve any real numbers including decimals and fractions. The cross-multiplication approach works regardless of whether the numbers are integers, decimals, or fractions. When working with fractions, the arithmetic is more complex but the principle is identical. This calculator handles decimal inputs directly, so you can enter values like 2.5 and 7.75 without any conversion.
What is the constant of proportionality?
In a direct proportion A/B = C/D, the constant of proportionality is the common ratio k = A/B = C/D. It describes the multiplicative relationship between the two quantities. If y is directly proportional to x, then y = kx for some constant k. The constant k is the unit rate — for example, if a car travels at 60 miles per hour, k = 60 miles per hour is the constant of proportionality relating miles to hours. Knowing k allows you to solve for any unknown given the other variable.

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