Ratio Calculator
Simplify ratios and calculate proportions. Find the greatest common divisor and convert ratios to decimal values instantly.
Result
- Simplified Ratio
- 0
- Decimal Value (A/B)
- 0
Formula & Guide
Formula
:
Simplified Ratio
A:B = (A÷GCD):(B÷GCD)
Divide both numbers by their greatest common divisor
=
Decimal Value
A/B = Decimal
Divide the first number by the second
Formula Variables
A
First Value
The first number in the ratio
B
Second Value
The second number in the ratio
GCD
Greatest Common Divisor
The largest number that divides both A and B evenly
Step-by-Step Scenario
Example Scenario
Value A
8
Value B
12
1
Find the Greatest Common Divisor
- GCD of 8 and 12: The factors of 8 are 1, 2, 4, 8. The factors of 12 are 1, 2, 3, 4, 6, 12. The GCD is 4.
The GCD is the largest number that divides both numbers evenly
2
Simplify the Ratio
- 8:12 = (8 ÷ 4):(12 ÷ 4)
Additional Examples
Simple Ratio
Value A: 6
Value B: 9
GCD
GCD(6, 9) = 3
Simplified
6:9 = 2:3
Decimal Conversion
Ratio: 3:4
Decimal
3 ÷ 4 = 0.75
Meaning
3 is 75% of 4
Characteristics of Ratios
Comparison Tool
Ratios provide a clear way to compare two quantities, making it easy to understand relationships between values.
Scalable
Ratios maintain their relationship when scaled. If 2:3 is doubled, it becomes 4:6, which simplifies back to 2:3.
Universal Application
Used in cooking (recipe scaling), construction (mixing materials), finance (financial ratios), and maps (scale).
Simplified Form
Ratios are typically expressed in their simplest form, making them easier to understand and work with.
Important Notes
- Ratios should be simplified to their lowest terms by dividing both numbers by their GCD.
- Ratios can be written as A:B or A/B, but A:B is more common for comparisons.
- The order matters in ratios: 2:3 is different from 3:2.
- Ratios with the same simplified form are equivalent (e.g., 4:6 = 2:3 = 8:12).
- When converting ratios to decimals, be aware that some ratios produce repeating decimals.
Frequently Asked Questions
Find answers to common questions about ratio calculations.
A ratio is a comparison of two quantities showing how many times one value contains or is contained within the other. It's expressed as A:B or A/B, where A and B are the two numbers being compared.
To simplify a ratio, divide both numbers by their greatest common divisor (GCD). For example, 8:12 simplifies to 2:3 by dividing both by 4 (the GCD of 8 and 12).
A ratio compares two quantities and can be written as A:B or A/B. A fraction represents a part of a whole. While similar, ratios emphasize comparison while fractions emphasize division.
Yes, ratios can be expressed as decimal values. For example, the ratio 3:2 equals 1.5 when expressed as a decimal (3 ÷ 2 = 1.5).
Ratios are used in many fields including cooking (recipe scaling), construction (mixing materials), finance (financial ratios), maps (scale), and everyday comparisons.
To convert a ratio A:B to a percentage, calculate A/(A+B) × 100 for the first part, or B/(A+B) × 100 for the second part. For example, 3:2 means 60%:40%.