Ratio Calculator
Calculate ratios, proportions, and solve ratio problems. Perfect for cooking, mixing, scaling, and mathematical applications.
Calculator Input
Results
Visual Representation
Step-by-Step Calculation
How to Use
Basic Steps
- Select the type of ratio calculation you need
- Enter the known values in the appropriate fields
- For proportions, enter three known values to find the fourth
- Use quick examples to see common ratio applications
- 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?
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?
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?
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.