Ratio Calculator
What Is a Ratio?
A ratio compares two or more quantities, showing how much of one thing there is relative to another. Ratios are written with a colon (3:1) or as a fraction (3/1). They appear everywhere: in cooking recipes, map scales, financial analysis, and machine gear ratios.
A proportion states that two ratios are equal. If A:B = C:D, then A × D = B × C. This cross-multiplication property is the foundation for solving proportions and finding unknown values.
How to Solve a Proportion
Given a proportion A:B = C:D where one value is unknown:
Cross-multiply: A × D = B × C
If solving for A: A = (B × C) / D
If solving for B: B = (A × D) / C
If solving for C: C = (A × D) / B
If solving for D: D = (B × C) / A
How to Simplify a Ratio
To simplify a ratio to its lowest terms:
- Find the Greatest Common Divisor (GCD) of both numbers.
- Divide both numbers by the GCD.
- The result is the simplified ratio.
Example: Simplify 24:36
GCD(24, 36) = 12
24 ÷ 12 = 2, 36 ÷ 12 = 3
Simplified ratio: 2:3
Common Ratio Applications
- Cooking: Scaling recipes up or down (2:1 ratio of water to rice).
- Photography: Aspect ratios (16:9, 4:3, 1:1).
- Finance: Debt-to-income ratio, price-to-earnings ratio.
- Maps: Scale ratios (1:100,000 means 1 cm = 1 km).
- Mechanics: Gear ratios for bicycles and vehicles.
- Chemistry: Mole ratios in chemical reactions.
Frequently Asked Questions
How do I solve a proportion?
For A:B = C:D, cross-multiply: A×D = B×C. If one value is unknown, solve for it: D = (B×C)/A, etc.
How do I simplify a ratio?
Find the greatest common divisor (GCD) of both numbers, then divide both by the GCD. 12:18 simplifies to 2:3 because GCD(12,18) = 6.
What are common uses for ratios?
Cooking (2:1 water to rice), photography (16:9 aspect ratio), finance (debt-to-income), maps (scale ratios), and chemistry (mole ratios).