Proportion Calculator – Find the Missing Value

Solve proportions A/B = C/D and find the unknown missing variable using cross-multiplication with step-by-step workings.

Need to simplify a ratio or split an amount? Check our companion calculators:

Ratio Calculator Divide Amount in Ratio

Solve Proportion (A / B = C / D)

Cross-Multiplication Formula

Select which variable to solve for (or leave its box empty), enter your known values, and click Calculate.

Select Variable to Solve For:

D (Unknown)

Quick Examples:

Solved Value:

D = 6

Equivalent Ratio: 2 / 3 = 4 / 6

Decimal Quotient: 0.6667 = 0.6667

Proportional Equality Verified

Step-by-Step Mathematical Explanation:

Understanding Proportions and Cross-Multiplication

A proportion is a statement that two ratios or fractions are equal. It is written as:

A / B = C / D (or A : B = C : D)

In this equation, A and D are called the extremes, while B and C are called the means. By the Fundamental Rule of Proportions, the product of the extremes equals the product of the means:

A × D = B × C

Formulas to Find Any Missing Term

Missing A:

A = (B × C) / D

Divide the product of B and C by D.

Missing B:

B = (A × D) / C

Divide the product of A and D by C.

Missing C:

C = (A × D) / B

Divide the product of A and D by B.

Missing D:

D = (B × C) / A

Divide the product of B and C by A.

Detailed Worked Examples

Example 1: Solve for x in 2 / 3 = x / 12

1. Identify the terms: A = 2, B = 3, C = x (unknown), D = 12.

2. Apply cross-multiplication: A × D = B × C → 2 × 12 = 3 × x → 24 = 3x.

3. Solve for x: x = 24 ÷ 3 = 8.

✓ Check: 2 / 3 = 0.6667 and 8 / 12 = 0.6667. Both ratios are identical.

Example 2: Solve for x in 5 / 8 = 25 / x

1. Identify the terms: A = 5, B = 8, C = 25, D = x (unknown).

2. Apply cross-multiplication: 5 × x = 8 × 25 → 5x = 200.

3. Solve for x: x = 200 ÷ 5 = 40.

✓ Check: 5 / 8 = 0.625 and 25 / 40 = 0.625. Equation holds true.

Ratio Calculator & Simplifier

Simplify any ratio (2 parts or multiple terms) to its irreducible form using GCD reduction.

Divide Amount in a Ratio

Split a total amount into proportional shares across 2 or more parties with exact percentage breakdowns.

How to Use Proportion Calculator – Find the Missing Value

Choose which variable you want to solve for (A, B, C, or D), or leave one input field empty.
Enter the three known numeric values into the proportion equation (A/B = C/D).
Click 'Solve Proportion' to calculate the missing term via cross-multiplication.
Examine the step-by-step algebraic breakdown and equality verification check.

About this Tool

The Proportion Calculator solves direct proportion equations of the form A/B = C/D. By applying the cross-multiplication principle (A × D = B × C), it isolates and computes whichever term is unknown. All arithmetic runs in real time inside your browser with complete precision and support for decimal values.

Frequently Asked Questions

Common questions about Proportion Calculator – Find the Missing Value, accuracy, and browser-side security.

Cross-multiplication states that if A/B = C/D, then A × D = B × C. For example, if 2/3 = x/12, cross-multiplying gives 2 × 12 = 3 × x, so 24 = 3x, leading to x = 8.

Yes, decimal inputs (such as 2.5/5 = x/10) are fully supported. The calculator performs exact floating-point calculations without premature rounding.

Division by zero is mathematically undefined. In A/B = C/D, neither B nor D can equal zero. The calculator validates your inputs and flags any zero denominators before solving.

In a direct proportion, as one quantity increases, the other increases at a constant rate (y = kx). In an inverse proportion, as one quantity increases, the other decreases (y = k/x). This calculator solves standard direct proportions.

Divide A by B and divide C by D. Both sides must yield identical decimal values (for example, 2 ÷ 3 = 0.6667 and 8 ÷ 12 = 0.6667).