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Proportion Calculator – Sigma Calculator
⚙️ Enter Any Three Values — We'll Find the Fourth

Leave one field blank (the unknown) and fill the other three. The calculator auto-solves as you type.

A — Numerator 1
B — Denominator 1
=
C — Numerator 2
D — Denominator 2

Yellow = unknown field  |  Green = solved answer

RESULT
📊 Percentage Proportion

Solve any proportion involving percentages in three different modes.

RESULT
📏 Scale / Ratio Calculator

Scale a value proportionally from one reference size to another.

Formula used: A / B = D / C → solves for D

SCALED VALUE (D)
➗ Ratio Simplifier

Reduce a ratio A : B to its simplest form using the GCD.

:
SIMPLIFIED RATIO

📚 What Is a Proportion?

A proportion is an equation stating that two ratios are equal: A / B = C / D. It describes a consistent relationship between four numbers. Proportions appear everywhere — from scaling recipes to map measurements, currency conversions, and engineering drawings.

A / B = C / D   →   A × D = B × C

The core rule is cross multiplication — the product of the means equals the product of the extremes. Knowing any 3 of the 4 values always lets you find the 4th.

🧮 Formulas Used

  • Finding A:   A = (B × C) ÷ D
  • Finding B:   B = (A × D) ÷ C
  • Finding C:   C = (A × D) ÷ B
  • Finding D:   D = (B × C) ÷ A

All four formulas derive directly from cross multiplication. This calculator auto-detects which variable is missing and applies the correct formula instantly.

❓ Frequently Asked Questions

What is a proportion in math? +
A proportion is an equation showing two ratios are equal, such as 1/2 = 3/6. It means the relationship on the left is identical to the relationship on the right — both simplify to 0.5.
How do you solve a proportion step by step? +
Write your proportion as A/B = C/D. Cross-multiply to get A×D = B×C. Then isolate your unknown by dividing both sides. For example, finding D: D = (B × C) ÷ A.
What is the difference between ratio and proportion? +
A ratio compares two quantities (e.g., 3:4). A proportion is an equation stating two ratios are equal (e.g., 3:4 = 6:8). A ratio is a single comparison; a proportion links two equal ratios.
What is the golden ratio? +
The golden ratio (φ ≈ 1.6180) is a special proportion where (A+B)/A = A/B. It appears widely in nature, art, and architecture and is considered aesthetically ideal in many design traditions.
Can denominators in a proportion be zero? +
No. Division by zero is undefined, so B and D (the denominators) must never equal zero. Our calculator will display an error and prevent incorrect results if this occurs.
What is an inverse proportion? +
In an inverse proportion, as one value increases the other decreases by the same factor, so A × B = C × D (a constant product rather than a constant ratio). The Scale Ratio tab can help model this.
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