Ratio Calculator

Easily calculate, compare, and simplify ratios with our Ratio Calculator. Whether you're working on math homework, adjusting recipes, or analyzing data, this tool helps you find equivalent ratios, simplify proportions, and solve ratio-based problems accurately — in just seconds.

Our calculator supports ratios with any number of terms, including decimals, fractions, and mixed values. It’s fast, reliable, and built to make complex ratio operations simple.

What Is a Ratio?

A ratio is a way to compare two or more quantities that show how much of one thing exists relative to another. Ratios are commonly written using a colon (:) or as a fraction.

For example:
3:2 means “3 parts of one thing for every 2 parts of another.”

It can also be expressed as a fraction:
3/2 = 1.5

Ratios are everywhere — in recipes, maps, finance, science, and statistics. They help us understand proportions and relationships between quantities.

Ratio Calculator — Fast, Accurate, and Easy to Use

The Ratio Calculator from Digital Calculator makes ratio computation effortless. It can:

• Simplify ratios to their lowest terms
• Find equivalent ratios
• Compare two ratios
• Convert fractions or decimals to ratios
• Solve proportions (e.g., a/b = c/d)

How to Use:

1. Enter the terms of your ratio (e.g., 24:16).
2. Click Calculate.
3. Instantly get the simplified ratio, equivalent forms, and step-by-step breakdown.

Example Inputs

Formula for Simplifying Ratios

To simplify a ratio, divide all terms by their greatest common divisor (GCD).

Formula:

Simplified Ratio = (a ÷ GCD, b ÷ GCD)

Example:

Simplify 18:24

Step 1: Find GCD(18, 24) = 6
Step 2: Divide both terms by 6
18 ÷ 6 = 3
24 ÷ 6 = 4

Simplified Ratio = 3:4

Step-by-Step Example Calculations

Example 1: Simplify a Basic Ratio

Simplify 40:100

GCD(40, 100) = 20
Divide each term by 20:
40 ÷ 20 = 2
100 ÷ 20 = 5

Result: 2:5

Example 2: Simplify a Multi-Term Ratio

Simplify 12:18:24

Step 1: Find GCD(12, 18, 24) = 6
Step 2: Divide each by 6
12 ÷ 6 = 2
18 ÷ 6 = 3
24 ÷ 6 = 4

Simplified Ratio = 2:3:4

Example 3: Convert a Fraction to a Ratio

Convert 3/5 to a ratio.

Since 3/5 = 3:5

Result: 3:5

Example 4: Convert a Decimal to a Ratio

Convert 0.25 to a ratio.

0.25 = 25/100 = 1/4

Result: 1:4

Example 5: Find an Equivalent Ratio

Find an equivalent ratio of 2:3 where the first term is 10.

Use proportion:
2/3 = 10/x
Cross-multiply:
2x = 30 → x = 15

Equivalent Ratio = 10:15

Understanding Ratio and Proportion

A proportion shows that two ratios are equal.

Example:
2:3 = 4:6 (because 2/3 = 4/6)

Proportions help solve for unknown values in direct relationships, such as scaling recipes, map distances, or business models.

Formula for Solving Proportions:

a/b = c/d
Then, cross multiply:
a × d = b × c

Applications of Ratios in Real Life

Ratios appear everywhere — from the classroom to real-world problem solving.

1. Education and Mathematics

Students use ratios to solve problems involving geometry, probability, and algebraic relationships.

2. Cooking and Recipes

Ratios ensure consistent taste and quantity when scaling recipes up or down.
Example: A 2:1 ratio of flour to sugar ensures the same sweetness at any batch size.

3. Finance and Business

Ratios measure profitability, efficiency, and liquidity.
Example: Debt-to-equity ratio = Total Liabilities / Shareholder Equity.

4. Science and Engineering

Used in chemical mixtures, mechanical design, and scaling models.
Example: A 1:4 fuel-to-oil ratio.

5. Photography and Design

Aspect ratios define image dimensions (e.g., 16:9 widescreen or 4:3 standard).

6. Everyday Life

Used to calculate discounts, compare speeds, or analyze survey data.

Ratio vs. Fraction: What’s the Difference?

While both show comparisons, their meanings differ slightly:

Example:
If there are 2 boys and 3 girls, the ratio is 2:3.
But if there are 2 boys out of 5 students total, the fraction is 2/5.

Ratio Simplification Table

How to Simplify Ratios Manually

If you’d like to simplify ratios without a calculator, follow these steps:

1. Write the ratio as two or more numbers separated by colons.
   Example: 16:24
2. Find the GCD of all terms.
   GCD(16, 24) = 8
3. Divide each term by the GCD.
   16 ÷ 8 = 2
   24 ÷ 8 = 3
4. Write the simplified ratio: 2:3

This method ensures accuracy when working with small numbers. For larger or decimal ratios, our calculator does the work instantly.

Working with Decimal Ratios

If a ratio includes decimals, multiply all terms by a power of 10 to make them whole numbers before simplifying.

Example:

Simplify 0.8 : 1.6

Multiply both terms by 10 → 8 : 16
Simplify → divide by 8 → 1:2

Our Ratio Calculator automatically performs this conversion for you.

Comparing Ratios

To compare ratios and determine which is greater, convert them into fractions or decimals.

Example:

Compare 2:3 and 3:5

2:3 = 2/3 = 0.6667
3:5 = 3/5 = 0.6

Since 0.6667 > 0.6, 2:3 is greater.

Solving Ratio Word Problems

Example 1:

A class has 15 boys and 20 girls. Find the ratio of boys to girls.
15:20 → divide by 5 → 3:4

Example 2:

A car travels 180 miles on 6 gallons of fuel. What is the mileage ratio (miles per gallon)?
180:6 → divide by 6 → 30:1

How to Use the Ratio Calculator Effectively

Our Ratio Calculator simplifies all ratio-related tasks in seconds.

Steps:

1. Enter two or more numbers separated by colons (e.g., 24:36:48).
2. Click Calculate to see the simplified form.
3. Optionally, view equivalent ratios or solve proportions.
4. Reset and try new values easily.

You can also input decimals, fractions, or mixed numbers directly — the calculator converts and simplifies automatically.

Why Use the Digital Calculator Ratio Calculator?

We designed our Ratio Calculator to make mathematical comparisons quick, intuitive, and educational.

Key Features:

• Simplifies any ratio instantly
• Handles multiple terms (2-term, 3-term, etc.)
• Works with decimals, fractions, and negatives
• Step-by-step results with explanations
• Fully responsive — works on all devices
• 100% free, no registration needed

Use it for academic, professional, or personal calculations and ensure every ratio you use is accurate and easy to understand.Try the Ratio Calculator now and simplify ratios effortlessly.

Real-World Ratio Examples