How to Calculate Ratio

Ratio Calculator

Enter two quantities below to calculate their ratio in decimal, simplified, and percentage forms.

Understanding and Calculating Ratios

Ratios are fundamental mathematical tools used to compare two or more quantities. They express how much of one quantity there is relative to another. Whether you're baking, mixing chemicals, scaling a recipe, or analyzing data, understanding ratios is crucial for making accurate comparisons and predictions.

What is a Ratio?

A ratio is a way to show the relationship between two numbers or quantities. For example, if you have 3 apples and 2 oranges, the ratio of apples to oranges is 3 to 2. This can be written in several ways:

• Using a colon: 3 : 2
• Using the word "to": 3 to 2
• As a fraction: 3/2

It's important that the order of the numbers in a ratio corresponds to the order of the quantities being compared. A ratio of 3:2 is different from 2:3.

Why are Ratios Important?

Ratios are used in countless real-world scenarios:

• Cooking and Baking: Recipes often use ratios for ingredients (e.g., 1 part sugar to 2 parts flour).
• Maps and Models: Scale ratios (e.g., 1:1000) indicate that 1 unit on the map represents 1000 units in reality.
• Finance: Debt-to-equity ratios, price-to-earnings ratios, and other financial metrics use ratios to assess a company's health.
• Science and Engineering: Ratios are used in mixtures, concentrations, gear ratios, and more.
• Sports: Win-loss ratios, assist-to-turnover ratios, etc., help evaluate performance.

How to Calculate and Express Ratios

Calculating a ratio involves taking two quantities and expressing their relationship. Our calculator above helps you do this in three common ways:

1. Decimal Ratio (A ÷ B)

This is simply the first quantity divided by the second quantity. It tells you how many times the first quantity fits into the second, or what fraction of the second quantity the first quantity represents. For example, if you have 10 apples and 25 oranges, the decimal ratio of apples to oranges is 10 ÷ 25 = 0.4.

Example: If a class has 12 girls and 18 boys, the decimal ratio of girls to boys is 12 ÷ 18 = 0.6667 (approximately).

2. Simplified Ratio (A : B)

Often, ratios are simplified to their lowest terms, just like fractions. This means dividing both parts of the ratio by their greatest common divisor (GCD). The GCD is the largest number that divides both quantities without leaving a remainder.

Steps to Simplify a Ratio:

1. Identify the two quantities (A and B).
2. Find the Greatest Common Divisor (GCD) of A and B.
3. Divide both A and B by their GCD.

Example: Let's simplify the ratio 10 : 25.

• Quantities are 10 and 25.
• The divisors of 10 are 1, 2, 5, 10.
• The divisors of 25 are 1, 5, 25.
• The GCD of 10 and 25 is 5.
• Divide both by 5: 10 ÷ 5 = 2, and 25 ÷ 5 = 5.
• The simplified ratio is 2 : 5.

This means for every 2 apples, there are 5 oranges.

3. Percentage (A is what % of B)

A ratio can also be expressed as a percentage, showing what proportion the first quantity is of the second quantity, out of 100. To convert a decimal ratio to a percentage, you simply multiply by 100.

Formula: (A ÷ B) × 100%

Example: Using our 10 apples and 25 oranges example:

• Decimal ratio = 0.4
• Percentage = 0.4 × 100% = 40%

This means the number of apples is 40% of the number of oranges.

Using the Ratio Calculator

Our Ratio Calculator simplifies these calculations for you. Simply enter your "First Quantity (A)" and "Second Quantity (B)" into the respective fields. Click "Calculate Ratio," and the tool will instantly provide:

• The decimal value of A divided by B.
• The simplified ratio of A to B.
• The percentage representing A as a proportion of B.

This tool is perfect for students, professionals, or anyone needing quick and accurate ratio calculations for various applications.