Ratio Calculator – Simplify, Scale & Solve Proportions
Simplify ratios, solve proportions, and compare ratios
Table of Contents
How to Use
- Select the type of calculation you need
- Enter the required values
- Click calculate to see the result
- View the simplified ratio or solution
What is a Ratio?
A ratio is a comparison of two or more quantities. It shows how much of one thing there is compared to another. Ratios can be written in several ways: a:b, a to b, or a/b.
For example, if there are 3 apples and 5 oranges, the ratio of apples to oranges is 3:5.
Simplifying Ratios
To simplify a ratio, divide both parts by their greatest common divisor (GCD). A simplified ratio has no common factors other than 1.
Example: 12:18 → GCD is 6 → 12÷6 : 18÷6 = 2:3
Proportions
A proportion is an equation stating that two ratios are equal: a:b = c:d. This can also be written as a/b = c/d.
The cross-product property states: if a:b = c:d, then a×d = b×c. This is useful for solving for unknown values.
Real-World Applications
- Cooking and recipes (scaling ingredients)
- Maps and scale drawings
- Financial calculations (exchange rates, interest)
- Mixing solutions and chemicals
- Photography (aspect ratios)
- Construction and architecture
Frequently Asked Questions
- What's the difference between a ratio and a fraction?
- While ratios and fractions look similar, a ratio compares two separate quantities (like apples to oranges), while a fraction represents a part of a whole (like 3/8 of a pizza). Ratios can also compare more than two quantities.
- How do I know if two ratios are equivalent?
- Two ratios a:b and c:d are equivalent if their cross products are equal (a×d = b×c). You can also simplify both ratios to their lowest terms and check if they're the same.
- Can ratios have decimals?
- Yes, ratios can have decimal values. However, it's often cleaner to express them as whole numbers. Multiply both parts by a power of 10 to eliminate decimals, then simplify.
- What is a golden ratio?
- The golden ratio is approximately 1:1.618 (or φ ≈ 1.618). It appears frequently in nature, art, and architecture and is considered aesthetically pleasing.