Ratio Calculator
Calculate and simplify ratios instantly. Simplify ratios to lowest terms, find missing values in proportions, scale ratios up or down, convert ratios to percentages, and compare if two ratios are equivalent. Perfect for math problems, cooking recipes, design work, and more.
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Usage Examples
Simplify Ratio
Enter 8:12 to get 2:3. The tool finds the GCD (4) and divides both parts by it.
Find Missing Value
If a recipe uses 3 cups of flour for every 4 cups of water, and you have 15 cups of flour, find how much water you need. Ratio: 3:4, Known value (A): 15, Result: 20 cups of water.
Scale Ratio
Scale 2:3 by a factor of 5 to get 10:15. Useful for scaling recipes or designs.
Convert to Percentage
Convert 3:7 to percentages: 30% and 70%. Useful for understanding proportions in data analysis.
Compare Ratios
Check if 2:4 and 3:6 are equivalent (they are, both equal 1:2).
Table of Contents
What is a Ratio?
A ratio is a comparison between two or more quantities, showing how many times one value contains or is contained within another. Ratios are expressed using a colon (:) or as fractions, and they describe proportional relationships between quantities.
Ratios are fundamental to understanding proportional relationships in math, cooking, design, finance, and many other fields. Unlike absolute values, ratios describe relationships — for example, "3 parts flour to 2 parts sugar" describes a proportion that can be scaled up or down.
Key characteristics of ratios:
- Proportional relationship — Ratios describe how quantities relate to each other
- Order matters — The ratio 3:4 is different from 4:3
- Simplest form — Ratios can be simplified to lowest terms (like fractions)
- No units required — Ratios are pure numbers, independent of units
- Multiplicative — Ratios can be scaled up or down proportionally
Example: If a recipe calls for a 2:3 ratio of flour to sugar:
- For every 2 parts flour, you need 3 parts sugar
- If you use 4 cups of flour, you need 6 cups of sugar (scaled by 2)
- The ratio 2:3 is already in simplest form
How Ratio Calculations Work
Ratio calculations involve several fundamental mathematical concepts:
Greatest Common Divisor (GCD)
The GCD is the largest number that divides evenly into both parts of a ratio. It's used to simplify ratios:
- GCD(144, 216) = 72
- Both 144 and 216 are divisible by 72
- 144 ÷ 72 = 2, 216 ÷ 72 = 3
- Simplified ratio: 2:3
Proportions
A proportion is an equation stating that two ratios are equal. Cross multiplication is used to solve proportions:
- If 3:4 = 15:?, then 3 × ? = 4 × 15
- Solving: ? = 60 ÷ 3 = 20
- Result: 3:4 = 15:20
Scaling
Scaling maintains the ratio while changing the actual values:
- Original: 2:3
- Scaled by 5: (2 × 5):(3 × 5) = 10:15
- The relationship (2/3) remains the same
Percentage Conversion
Converting to percentages shows the distribution:
- Ratio 3:7 represents 3 parts out of 10 total (30%) and 7 parts out of 10 total (70%)
- Total = 3 + 7 = 10
- Part A % = (3 ÷ 10) × 100 = 30%
- Part B % = (7 ÷ 10) × 100 = 70%
- Always sums to 100%
Calculation Types
1. Simplifying Ratios
Reduces a ratio to its simplest form by dividing both parts by their Greatest Common Divisor (GCD).
Example: Simplify 144:216
GCD(144, 216) = 72
144 ÷ 72 = 2, 216 ÷ 72 = 3
Result: 2:3
2. Finding Missing Values
Uses proportions to find an unknown value when you know the ratio and one actual value.
Example: Ratio 3:4, Known A = 15, Find B
3:4 = 15:?
3 × ? = 4 × 15
? = 60 ÷ 3 = 20
Result: B = 20
3. Scaling Ratios
Multiplies or divides both parts of a ratio by the same factor.
Example: Scale 2:3 by factor 5
2 × 5 = 10, 3 × 5 = 15
Result: 10:15
4. Converting to Percentages
Shows what percentage each part of the ratio represents of the total.
Example: Convert 3:7 to percentages
Total = 3 + 7 = 10
Part A = (3 ÷ 10) × 100 = 30%
Part B = (7 ÷ 10) × 100 = 70%
Result: 30% : 70%
5. Comparing Ratios
Determines if two ratios are equivalent by comparing their values (A ÷ B).
Example: Compare 2:4 and 3:6
Ratio 1: 2 ÷ 4 = 0.5
Ratio 2: 3 ÷ 6 = 0.5
Result: Equivalent (both equal 1:2 when simplified)
Common Uses
- Cooking and Recipes: Scaling recipes for different serving sizes, maintaining ingredient proportions, and mixing ratios for cocktails or marinades
- Design and Architecture: Working with aspect ratios (16:9, 4:3), scale drawings (1:100), and applying the golden ratio in design
- Finance and Business: Analyzing financial ratios (debt-to-equity, price-to-earnings), resource allocation, and performance metrics
- Math and Education: Solving algebra problems, working with similar figures in geometry, and analyzing data in statistics
- Science and Engineering: Understanding chemical formulas and mole ratios, preparing solutions with specific concentrations, and calculating gear ratios
- Everyday Life: Mixing paint colors, calculating fuel efficiency (miles per gallon), and understanding proportions in various contexts
Real-World Examples
Example 1: Scaling a Recipe
Problem: A recipe serves 4 people and uses a 3:2 ratio of flour to sugar (3 cups flour, 2 cups sugar). You need to serve 12 people. How much flour and sugar do you need?
Solution:
- Original ratio: 3:2
- Scaling factor: 12 ÷ 4 = 3
- Scale the ratio: 3:2 × 3 = 9:6
- Result: 9 cups flour, 6 cups sugar
Example 2: Finding Missing Dimension
Problem: A scale drawing uses a 1:50 ratio. If a wall in the drawing is 3 cm long, how long is the actual wall?
Solution:
- Ratio: 1:50
- Known value (drawing dimension): 3 cm
- Set up proportion: 1:50 = 3:?
- Cross multiply: 1 × ? = 50 × 3
- Solve: ? = 150 cm = 1.5 meters
Example 3: Converting to Percentages
Problem: A survey shows a 7:3 ratio of positive to negative responses. What percentage of responses are positive?
Solution:
- Ratio: 7:3
- Total = 7 + 3 = 10
- Positive % = (7 ÷ 10) × 100 = 70%
- Negative % = (3 ÷ 10) × 100 = 30%
- Result: 70% positive, 30% negative
Frequently Asked Questions
A ratio compares two quantities and can be simplified like a fraction, but ratios are typically used to show relationships, while fractions represent parts of a whole. The ratio 3:4 means "3 parts to 4 parts," while the fraction 3/4 means "3 out of 4 parts of a whole." Ratios can have more than two parts (e.g., 1:2:3), while fractions typically compare one part to a whole.
Yes! Ratios can have three or more parts (e.g., 1:2:3 for cement:sand:gravel in concrete). The calculator currently handles two-part ratios, but the principles extend to multi-part ratios. For multi-part ratios, you would apply the same simplification, scaling, and calculation methods to all parts.
You can enter decimal values in the calculator. For simplification, the tool will find whole number ratios when possible, or you can work with the decimal ratios directly. If you have decimals like 1.5:2.5, you can simplify by multiplying both parts by 2 to get 3:5, or work with the decimals directly in scaling and percentage calculations.
A ratio cannot have both parts equal to zero (0:0 is undefined). If one part is zero, that's valid (e.g., 0:5 means no amount of the first part for every 5 of the second). However, when calculating percentages or comparing ratios, having zero in the denominator would cause division by zero, which is undefined.
Absolutely! The calculator is perfect for scaling recipes. Enter your original ingredient ratio, then use the "Scale" or "Missing Value" mode to adjust quantities. For example, if a recipe uses 3:2 flour to sugar and serves 4, but you need to serve 12, scale by factor 3 to get 9:6.
Ratios can be converted to percentages by dividing each part by the total and multiplying by 100. Use the "Percentage" mode in the calculator to do this automatically. For example, 3:7 converts to 30% and 70% (since 3 + 7 = 10, and 3/10 = 30%, 7/10 = 70%).
No. All calculations happen entirely in your browser using JavaScript. Your ratios, values, and results are never sent to any server. This ensures complete privacy and security for your data.
The golden ratio (φ ≈ 1.618 or approximately 1:1.618) is a special mathematical ratio that appears in nature, art, and design. It's considered aesthetically pleasing and is often used in design compositions. You can use the calculator to work with the golden ratio by entering values like 1.618:1 or 1618:1000.