Ratio Calculator
Simplify ratios, solve proportions, and scale recipes with step-by-step solutions
Ratio Calculator
:
Result
Simplified Ratio
2 : 3
Original: 12 : 18
GCD: 6
Decimal Form
0.666667
Percentage
40.0% : 60.0%
Equivalent Ratios
2 : 3
4 : 6
6 : 9
Simplification
Divided both parts by GCD of 6
What is Ratio Calculator?
What is a Ratio Calculator?
A ratio expresses the relationship between two or more quantities, showing how many times one value contains another. Ratios are written as A:B (read as "A to B") or as fractions A/B.
Types of Ratio Calculations
1. Simplifying Ratios
Reduce a ratio to its lowest terms by dividing both parts by their greatest common divisor:
- Find the GCD of both numbers
- Divide both parts by the GCD
- The result is the simplified ratio
Example: 12:18 → GCD = 6 → 12÷6 : 18÷6 = 2:3
2. Solving Proportions
When two ratios are equal, they form a proportion. Find missing values using cross multiplication:
- Set up the proportion: A:B = C:X
- Cross multiply: A × X = B × C
- Solve for X: X = (B × C) ÷ A
Example: 3:4 = 9:X → 3×X = 4×9 → X = 36÷3 = 12
3. Scaling Recipes
Multiply ingredients by a scale factor to increase or decrease recipe size:
- Choose your scale factor (2 = double, 0.5 = half, etc.)
- Multiply each ingredient by the factor
- Maintain the same proportions
Applications
- Recipe scaling and cooking measurements
- Map scales and architectural drawings
- Financial ratios and business analysis
- Mixing solutions and chemical concentrations
- Gear ratios in mechanical systems
- Aspect ratios in photography and video
FAQ - Ratio Calculator
A ratio compares quantities of the same type (like 3:4 apples to oranges), while a fraction represents part of a whole (like 3/4 of a pizza). However, ratios can be written as fractions for calculations.