Ratio Calculator

Calculate ratios, proportions, and solve ratio problems. Perfect for cooking, mixing, scaling, and mathematical applications.

Calculator Input

:

Results

Simplified Ratio
3:2
Reduced to lowest terms
Original Ratio:12:8
Decimal Form:1.5000
GCD:4

Visual Representation

First Part
12.00 (60.0%)
Second Part
8.00 (40.0%)

Step-by-Step Calculation

Step 1: Find the GCD of 12 and 8
GCD(12, 8) = 4
Step 2: Divide both parts by the GCD
12 ÷ 4 = 3
8 ÷ 4 = 2
Step 3: Simplified ratio = 3:2

How to Use

Basic Steps

  1. Select the type of ratio calculation you need
  2. Enter the known values in the appropriate fields
  3. For proportions, enter three known values to find the fourth
  4. Use quick examples to see common ratio applications
  5. Review the simplified ratio and step-by-step solution

Calculation Types

  • Simplify: Reduce ratios to lowest terms
  • Equivalent: Find proportional ratios
  • Proportion: Solve for unknown values
  • Scale: Adjust recipe or formula quantities
  • Compare: Determine which ratio is larger
  • Percentage: Convert ratios to percentages

Understanding Ratios

What is a Ratio?

A ratio is a comparison of two or more quantities, showing how many times one value contains another. Ratios can be written as:

  • 3:2 (colon notation)
  • 3 to 2 (word form)
  • 3/2 (fraction form)
  • 1.5 (decimal form)

Simplifying Ratios: Divide both parts by their greatest common divisor (GCD).

Proportions

A proportion states that two ratios are equal: a:b = c:d

Cross Multiplication: a × d = b × c

If 3:4 = x:12, then 3 × 12 = 4 × x

36 = 4x, so x = 9

Common Applications

Cooking & Recipes

Scale ingredients proportionally when changing serving sizes or batch quantities.

Maps & Scale

Convert between map distances and real-world distances using scale ratios.

Finance & Business

Calculate profit margins, debt-to-equity ratios, and other financial metrics.

Example Calculations

Example 1: Recipe Scaling

Problem: A recipe serves 4 people and calls for 2 cups of flour. How much flour for 6 people?

Original ratio: 4 people : 2 cups
Scale factor: 6 ÷ 4 = 1.5
New amount: 2 × 1.5 = 3 cups

Answer: You need 3 cups of flour for 6 people.

Example 2: Paint Mixing

Problem: Mix paint in a 3:2 ratio of blue to white. How much white paint for 9 liters of blue?

Ratio: 3 blue : 2 white
If blue = 9 liters, scale factor = 9 ÷ 3 = 3
White needed: 2 × 3 = 6 liters

Answer: You need 6 liters of white paint.

Example 3: Proportion Problem

Problem: If 5 apples cost $3, how much do 8 apples cost?

Set up proportion: 5 apples : $3 = 8 apples : $x
Cross multiply: 5 × x = 3 × 8
5x = 24
x = $4.80

Answer: 8 apples cost $4.80.

Frequently Asked Questions

How do I simplify a ratio?

Find the greatest common divisor (GCD) of both numbers and divide both parts by it. For example, 12:8 becomes 3:2 after dividing both by 4.

What's the difference between a ratio and a fraction?

A ratio compares two separate quantities (like 3 boys to 2 girls), while a fraction represents part of a whole (like 3/5 of the class). Ratios can be converted to fractions and vice versa.

Can ratios have more than two parts?

Yes! Ratios can have multiple parts, like 2:3:5 for mixing three ingredients. The same principles apply - you can scale all parts proportionally.