Simplify Ratio Calculator
Reduce any ratio to its simplest form by finding the GCD and dividing both parts.
Our calculator shows each step of the simplification process, perfect for learning and verification.
Ratio Calculator
Our free ratio calculator helps you simplify ratios, solve proportions, find equivalent ratios, calculate aspect ratios, and convert between ratios, fractions, and percentages. Perfect for students, teachers, designers, and anyone working with proportional relationships.
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4.9
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Updated: July 2026
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Ratio Calculator calculator
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Leave one empty to solve for it
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Method
Divide both by GCD (Greatest Common Divisor)
Simplified Ratio
2 : 3
GCD = 12
Conversions
Fraction
2/3
Decimal
0.667
Percentage
66.67%
Parts of B
1.5
Steps
1. Find GCD of 24 and 36 = 12
2. Divide both: 24÷12 : 36÷12
3. Result: 2 : 3
lightbulb Tips
- •Simplify: divide both by GCD
- •a:b = a/b as fraction
- •Cross multiply: a×d = b×c
- •16:9 = widescreen aspect ratio
balance Reference
Aspect Ratios
Widescreen
16:9
Standard
4:3
Photo
3:2
Square
1:1
Tips
a:b = a/b = (a/b)×100%
GCD divides both evenly
How to Use the Ratio Calculator
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Choose Type
Select simplify, solve proportion, find equivalents, convert, compare, or scale.
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Enter Values
Input the ratio values (A:B or A:B:C for three-part ratios).
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Set Options
Configure additional options based on calculation type.
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View Results
See simplified ratio, conversions, and step-by-step solution.
The Formula
Ratios compare two quantities. To simplify, divide both parts by their GCD. To solve proportions, use cross multiplication: a × d = b × c.
a : b = c : d (cross multiply: a × d = b × c)
lightbulb Variables Explained
- a : b First ratio (antecedent : consequent)
- c : d Second ratio (equivalent or proportion)
- GCD Greatest Common Divisor for simplification
tips_and_updates Pro Tips
1
To simplify a ratio, divide both numbers by their GCD
2
Ratios can be written as fractions: a:b = a/b
3
Cross multiplication solves proportions: if a:b = c:d, then a×d = b×c
4
Aspect ratios like 16:9 describe width to height relationships
5
Equivalent ratios have the same simplified form
6
To scale a ratio, multiply both parts by the same number
Calculate ratios instantly with our free online ratio calculator. Simplify ratios, solve proportions, find equivalent ratios, and convert between ratios, fractions, and percentages with detailed step-by-step solutions.
Ratio and Proportion Calculator
Solve proportion problems using cross multiplication.
Find the missing value in any proportion equation with complete working shown.
Aspect Ratio Calculator
Calculate aspect ratios for images, videos, and screens.
Find equivalent dimensions while maintaining the same proportions for any resolution.
Ratio Converter
Convert ratios to fractions, decimals, or percentages.
Transform between different representations of proportional relationships.
Equivalent Ratios Calculator
Generate lists of equivalent ratios by multiplying or dividing by common factors.
Useful for scaling recipes, maps, and designs.
Three-Part Ratio Calculator
Work with ratios involving three or more quantities.
Simplify and compare complex ratios with multiple parts.
What Is a Ratio and How Does It Work?
A ratio is a comparison of two or more quantities that shows how many times one value contains another. Written as a:b (read "a to b"), it expresses the relative size of two amounts, such as 2:3 or 16:9.
According to Encyclopaedia Britannica, a ratio is a quotient of two numbers or quantities that indicates their relative magnitude. Ratios can also be written as fractions (a/b), with colons, or with the word "to."
They stay unchanged when both parts are multiplied or divided by the same nonzero number, which is why 2:3, 4:6, and 6:9 are all equivalent and describe the same proportional relationship.
How to Simplify a Ratio Using the GCD Formula
To simplify a ratio, divide every part by the greatest common divisor (GCD) of all the numbers. The formula is: simplified ratio = (a ÷ GCD) : (b ÷ GCD).
For example, to reduce 24:36, first find that the GCD of 24 and 36 is 12; dividing both gives 24÷12 : 36÷12 = 2:3, the lowest-terms form.
Wolfram MathWorld defines the GCD as the largest positive integer that divides each value without a remainder. The Euclidean algorithm—repeatedly replacing the larger number with the remainder of dividing the two—is the standard method for finding it, and it underlies how this calculator reduces ratios to their simplest form.
Where Are Ratios Used in Real Life?
Ratios appear across cooking, finance, design, and science.
- In recipes, a 2:3 flour-to-water ratio scales cleanly: 6 cups of flour needs 9 cups of water.
- In screens and video, aspect ratios like 16:9 and 4:3 define shape—1920×1080 simplifies to 16:9 because their GCD is 120.
- In finance, the debt to income ratio and price-to-earnings ratios guide decisions, while maps use scale ratios such as 1:50,000.
- The golden ratio, roughly 1.618 and studied at length by Wolfram MathWorld, guides proportions in art and architecture.
Khan Academy highlights ratios and rates as foundational to unit pricing, mixing, and speed problems, making them one of the most practical topics in everyday math.
How to Convert Between Ratios, Fractions, and Percentages
A ratio a:b converts directly to the fraction a/b, and from there a fraction calculator can reduce or combine it, while you convert to a decimal by dividing a by b, or to a percentage by multiplying that decimal by 100. For example, the ratio 3:4 becomes the fraction 3/4, the decimal 0.75, and the percentage 75%.
To go the other way, a percentage like 40% becomes 40:100, which simplifies to 2:5. Decimal ratios such as 1.5:2 can be cleared by multiplying both parts by 10 to get 15:20, then reduced to 3:4.
Khan Academy treats these conversions as different representations of the same proportional relationship, so choosing a format depends only on context, not on the underlying value.
Common Mistakes When Working With Ratios
- The most frequent error is confusing a part-to-part ratio with a part-to-whole fraction: in a 2:3 mix the first quantity is 2/5 of the total, not 2/3.
- Another mistake is adding ratios directly—3:4 plus 1:2 cannot be summed term by term.
- People also forget order matters, so 16:9 is not the same as 9:16.
- When simplifying, dividing by a common factor that is not the full GCD leaves the ratio unreduced (e.g., 24:36 divided by 2 gives 12:18, still reducible).
- Finally, avoid using zero as the second term, since a:0 implies division by zero and is undefined, a rule reflected in this calculator's input validation.
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