Ratio Calculator
Calculate and simplify ratios with our free online calculator. Convert ratios to fractions, decimals, and percentages with detailed explanations.
Ratio Calculator
Ratio Calculator
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What is a Ratio?
A ratio is a comparison between two or more quantities, showing how many times one value contains another. It's expressed as a:b or a/b, where a and b are the quantities being compared.
Types of Ratios:
- Simple Ratio: Compares two quantities (e.g., 3:4)
- Compound Ratio: Compares more than two quantities (e.g., 2:3:5)
- Part-to-Part: Compares parts of a whole (e.g., boys:girls)
- Part-to-Whole: Compares a part to the total (e.g., boys:total students)
Ratio Properties:
- Simplification: Divide both terms by their GCD
- Equivalent Ratios: Ratios that represent the same relationship
- Proportion: Two ratios that are equal (a:b = c:d)
- Cross Multiplication: a × d = b × c in proportions
Common Examples:
- 12:8 = 3:2 (simplified by dividing by 4)
- 1:2 = 0.5 = 50%
- 3:4 = 3/4 = 0.75 = 75%
- Golden ratio: 1:1.618 (approximately 5:8)
Applications:
- Recipe scaling and cooking
- Financial analysis and ratios
- Architecture and design proportions
- Statistics and probability
- Engineering and technical calculations
- Art and photography composition
Frequently Asked Questions
How do I simplify a ratio?
Divide both numbers by their greatest common divisor. For example, 12:18 divides by 6 to become 2:3, the simplest form.
How do I solve a proportion?
Set the two ratios equal and cross-multiply. If 2:3 = x:9, then 3x = 18, so x = 6. The calculator solves for the missing value.
What is an equivalent ratio?
An equivalent ratio expresses the same relationship using different numbers, found by multiplying or dividing both sides by the same value. 1:2, 2:4, and 5:10 are all equivalent.
How do I scale a recipe or mixture with ratios?
Multiply every part of the ratio by the same factor. To double a 2:1 mix, use 4:2 — the proportion stays the same while the quantity grows.