Solve proportions instantly — find any missing value in A/B = C/D,
scale ratios, simplify, and solve percentage proportions with step-by-step solutions.
⚡ Instant Results✅ 100% Free📐 Step-by-Step🔁 Auto-Solve🔒 Private📱 Mobile Friendly
⚙️ 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 1B — Denominator 1
=
C — Numerator 2D — Denominator 2
Yellow = unknown field | Green = solved answer
RESULT
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🕓 Recent Calculations
📊 Percentage Proportion
Solve any proportion involving percentages in three different modes.
RESULT
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📏 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)
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➗ Ratio Simplifier
Reduce a ratio A : B to its simplest form using the GCD.
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SIMPLIFIED RATIO
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📚 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.