Calculator Mode
Enter Ratio
Results
Original
12 : 18
Simplified
2 : 3
Decimal
0.6667
Percentage
66.6667%
Fraction
2/3
Parts Total
5
Common Ratios
Golden Ratio
1:1.618
Design, Art
Screen 16:9
16:9
HD Video
Screen 4:3
4:3
Classic TV
Photo 3:2
3:2
35mm Film
Square
1:1
1/3 Rule
1:2
Design
Cement:Sand
1:3
Mortar
Coffee:Water
1:15
Pour Over
Common Ratio Calculations
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Practice Ratio Problems
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Practice with 5 problems to test your understanding.
Ratio Results
Simplified Ratio
2 : 3
?How Do You Calculate Ratios?
A ratio compares two or more quantities. To simplify a ratio, divide all parts by their GCF. For example, 12:8 simplifies to 3:2 (divide by 4). To solve a proportion (a:b = c:x), use cross-multiplication: a*x = b*c, so x = (b*c)/a. Equivalent ratios have the same relationship (2:3 = 4:6 = 6:9).
What is a Ratio?
A ratio is a comparison between two or more numbers that shows their relative sizes. Written as a:b or a/b, ratios express the relationship between quantities without specifying actual values. Ratios are used in cooking, construction, finance, map scales, aspect ratios, and anywhere relative proportions matter.
Key Facts About Ratios
- A ratio compares two or more quantities (parts to parts or part to whole)
- Simplify by dividing all parts by their GCF: 12:8 = 3:2
- Equivalent ratios: multiply or divide all parts by the same number
- Proportion: two equal ratios (a:b = c:d). Cross multiply: ad = bc
- Ratio to fraction: a:b means a/(a+b) of whole is first part
- Common ratios: 1:1 (equal), 2:1 (double), 1.618:1 (golden ratio)
- Scale ratio: multiply all parts by scale factor
- Ratios can have more than two parts: 1:2:3 means parts in that proportion
Quick Answer
A ratio compares two or more quantities. To simplify a ratio, divide all parts by their GCF. For example, 12:8 simplifies to 3:2 (divide by 4). To solve a proportion (a:b = c:x), use cross-multiplication: a*x = b*c, so x = (b*c)/a. Equivalent ratios have the same relationship (2:3 = 4:6 = 6:9).
Frequently Asked Questions
What is a ratio?
A ratio compares two or more quantities. It shows the relative size of two values. For example, a ratio of 2:3 means for every 2 units of the first quantity, there are 3 units of the second. Ratios can be written as 2:3, 2/3, or "2 to 3".
How do I simplify a ratio?
To simplify a ratio, divide both numbers by their greatest common factor (GCF). For example, 12:18 has a GCF of 6, so dividing both by 6 gives 2:3. The simplified ratio has the same relationship but uses smaller numbers.
What is a proportion?
A proportion is an equation stating that two ratios are equal. For example, 1:2 = 3:6 is a proportion. Cross multiplication can be used to verify: if a:b = c:d, then a×d = b×c. Proportions are used to solve for unknown values.
How do I solve for an unknown in a proportion?
Use cross multiplication. For a:b = c:x, cross multiply to get a×x = b×c, then solve for x = (b×c)/a. For a:b = x:d, you get b×x = a×d, so x = (a×d)/b.
What are equivalent ratios?
Equivalent ratios have the same value when simplified or converted to decimals. Examples: 1:2, 2:4, 3:6, and 50:100 are all equivalent (they all equal 0.5). Multiply or divide both parts by the same number to find equivalent ratios.
How are ratios used in real life?
Ratios appear everywhere: recipes (2:1 flour to sugar), maps (1:50000 scale), finance (P/E ratio), mixing (3:1 paint dilution), aspect ratios (16:9 screens), and probability (1:6 odds). They're essential for scaling, comparing, and proportioning.
Last updated: 2026-01-15
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How this works
Formulas follow standard definitions from the NIST Digital Library of Mathematical Functions and classical textbook derivations. Calculations run entirely in your browser. Where a closed-form solution exists, it is used; where an iterative or numerical method is required, the implementation is named on the page.
Sources
- [1]NIST Digital Library of Mathematical FunctionsAcademicdlmf.nist.govAccessed Apr 21, 2026
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