Ratio Calculator Simplify ratios, solve proportions, and compare ratios — with visual representations and real-world appl...

Ratio Calculator

Simplify ratios, solve proportions, and compare ratios — with visual representations and real-world applications.

Simplify Ratio

Solve Proportion

Compare Ratios

Scale Ratio

First Term

Second Term

Format Fraction (a/b) Decimal Percentage

A

B

C

D (Unknown)

First Ratio A

First Ratio B

Second Ratio A

Second Ratio B

Original A

Original B

Scale Factor

—

— = —

—

Simplified Ratio

—

Decimal Value

—

Percentage

—

Relationship

Ratio Visualization

What is a Ratio?

A ratio compares two quantities by division, showing how much of one thing there is compared to another.

Ratio Notation**:

• Colon notation**: a:b (e.g., 3:4)
• Fraction notation**: a/b (e.g., 3/4)
• Word notation**: "3 to 4"

Simplifying Ratios**:

To simplify a ratio, divide both terms by their Greatest Common Divisor (GCD).

Example**: 8:12 = 8÷4 : 12÷4 = 2:3

✅ Key Concept**: Ratios can compare parts to parts, parts to whole, or whole to parts.

Ratio Calculation Pitfalls

⚠️ Common mistakes to avoid:

• Adding instead of multiplying**: To scale a ratio, multiply both terms by the same factor
• Confusing ratio with difference**: 2:3 is not the same as "2 less than 3"
• Incorrect proportion setup**: Always maintain the same order (a/b = c/d, not a/b = d/c)
• Zero values**: Ratios cannot have zero as the second term (division by zero)
• Mixed units**: Ensure both quantities use the same units before calculating

✅ Best Practices**:

• Always simplify ratios to their lowest terms
• Use cross-multiplication to verify proportions: a×d = b×c
• When scaling, apply the same factor to all terms in the ratio
• For decimal ratios, multiply by powers of 10 to eliminate decimals before simplifying

Real-World Applications

Ratios are essential in:

• Cooking**: Recipe scaling (2 cups flour : 1 cup sugar)
• Photography**: Aspect ratios (16:9, 4:3, 3:2)
• Finance**: Financial ratios (debt-to-equity, price-to-earnings)
• Medicine**: Drug dosage ratios (5mg per kg of body weight)
• Construction**: Mix ratios (1 part cement : 2 parts sand : 3 parts gravel)

📊 Example Use Cases**:

• Recipe scaling**: Original ratio 2:3, scale by 4 → 8:12
• Map scale**: 1:50,000 means 1cm on map = 50,000cm in real life
• Business**: Profit margin ratio of 0.25 = 25% profit
• Photography**: 16:9 aspect ratio for widescreen displays

How to Use This Calculator

➡️ Simplify Ratio

"Simplify 8:12" → 2:3 (0.6667, 66.67%)

➡️ Solve Proportion

"3:4 = 9:D" → D = 12

➡️ Compare Ratios

"2:3 vs 4:6" → Equivalent (both equal 0.6667)

➡️ Scale Ratio

"Scale 5:8 by factor 3" → 15:24

Note: All calculations handle decimal inputs and automatically simplify results. For proportions, the calculator solves for the missing fourth term using cross-multiplication.