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Calculate and simplify ratios, scale proportions, find missing values, convert ratios to fractions, decimals, and percentages, and compare ratios.
Simplified 4:8 to 1:2 by dividing both terms by 4
a:b = (a÷GCD):(b÷GCD)4:8GCD = 44 ÷ 4 : 8 ÷ 4= 1:2This calculator provides mathematical calculations for educational and informational purposes.
Results are rounded for display but calculations use full precision.
A ratio calculator is a mathematical tool that helps you work with ratios and proportions. Ratios compare two quantities and are written as a:b or a/b. They are used extensively in cooking, construction, finance, map scales, and everyday problem-solving. Our calculator supports five different modes to handle any ratio-related problem.
Our ratio calculator offers five powerful calculation modes:
Simplify - Reduce ratios to lowest terms (e.g., 4:8 becomes 1:2)
Scale - Enlarge or reduce ratios proportionally (e.g., 1:2 scaled to ?:10 = 5:10)
Find Missing - Solve proportions for unknown values (e.g., 2:3 = 4:? means ? = 6)
Convert - Transform ratios to fractions, decimals, and percentages
Compare - Determine if two ratios are equivalent or which is larger
a:b = (a÷GCD):(b÷GCD)Example: 12:8 = (12÷4):(8÷4) = 3:2
a:b scaled to ?:c means multiply both by c/bExample: 2:3 scaled to ?:12 = (2×4):(3×4) = 8:12
If a:b = c:d, then a×d = b×cExample: 2:3 = 4:? means 2×? = 3×4, so ? = 6
a:b = a÷bExample: 3:4 = 3÷4 = 0.75
a:b = (a÷b)×100%Example: 1:4 = (1÷4)×100 = 25%
A ratio is a comparison of two quantities. It shows how many times one value contains another. Ratios are written as a:b (read as 'a to b') or as a fraction a/b. For example, if there are 2 apples and 3 oranges, the ratio of apples to oranges is 2:3.
To simplify a ratio, find the greatest common divisor (GCD) of both terms and divide each term by it. For example, to simplify 12:18, find GCD(12,18)=6, then divide: 12÷6=2 and 18÷6=3, giving you 2:3.
A ratio compares two quantities (e.g., 2:3), while a proportion states that two ratios are equal (e.g., 2:3 = 4:6). Proportions are useful for finding missing values when you know three of the four terms.
Use cross-multiplication. If a:b = c:d and you need to find d, calculate d = (b×c)÷a. For example, if 2:3 = 4:?, then ? = (3×4)÷2 = 6.
Yes, ratios can include decimals. However, they are often converted to whole numbers for simplicity. To convert 1.5:2.5 to whole numbers, multiply both by 2 to get 3:5.
Divide the first term by the second term and multiply by 100. For example, 3:4 = (3÷4)×100 = 75%. This represents the first term as a percentage of the second term.
Equivalent ratios represent the same relationship but with different numbers. For example, 1:2, 2:4, and 3:6 are all equivalent ratios. You can find equivalent ratios by multiplying or dividing both terms by the same number.
Ratios are used everywhere: in cooking (recipe scaling), maps (scale ratios like 1:100000), finance (debt-to-income ratios), photography (aspect ratios like 16:9), construction (mixing concrete), and many other applications.