A ratio is a way of comparing two or more quantities. It shows the relative size of the quantities. For example, if a recipe calls for 2 cups of flour and 1 cup of sugar, the ratio of flour to sugar is 2:1.

How do you simplify a ratio?

To simplify a ratio, you find the greatest common divisor (GCD) of all the numbers in the ratio and then divide each number by the GCD. For example, the ratio 12:18 simplifies to 2:3 because the GCD of 12 and 18 is 6.

How do you solve a proportion like A:B = C:D?

This is a proportion problem. The fundamental rule is that the product of the means equals the product of the extremes (A * D = B * C). You can use this cross-multiplication principle to solve for any missing value. Our calculator does this automatically.

Ratio Calculator (Solve & Simplify)

How Does This Calculator Work?

This calculator can perform two main functions: solving for a missing value in a proportion and simplifying a ratio.

Solving Ratios (A:B = C:D): This is a proportion problem. The rule of proportions states that the product of the means equals the product of the extremes. In other words, A × D = B × C. To solve for any missing value (e.g., D), you can rearrange this formula. For example, to find D, the formula becomes D = (B × C) / A.
Simplifying Ratios (A:B): To simplify a ratio, the calculator finds the Greatest Common Divisor (GCD) of the numbers. The GCD is the largest number that divides into both numbers without leaving a remainder. Both parts of the ratio are then divided by the GCD to get the simplest form. For example, in the ratio 16:24, the GCD is 8, so the simplified ratio is 2:3.

The Surprising History of the Golden Ratio

One of the most famous and mystifying ratios in history is the Golden Ratio, approximately equal to 1.618. It's often represented by the Greek letter phi (Φ). The ancient Greeks, particularly mathematicians like Euclid, were fascinated by it, believing it represented perfect harmony and beauty.

They found this ratio in the geometry of a pentagram and in "golden rectangles." For centuries, it has been claimed that the Golden Ratio appears everywhere, from the proportions of the Parthenon in Athens and the Great Pyramids of Giza to the spirals of seashells and the structure of human DNA. While some of these claims are debated by modern scholars, the Golden Ratio's enduring legacy in art, architecture, and nature shows the timeless human fascination with finding mathematical order in the world around us.

Explore More Related Tools

While you're here, check out some of our other popular math and science calculators:

Percentage Calculator: Compare quantities using percentages.
Fraction Calculator: Ratios are often expressed as fractions.
Scientific Calculator: For advanced mathematical calculations.
Exponent & Root Calculator: Explore powers and roots.
Logarithm Calculator: The inverse of exponentiation.
Standard Deviation Calculator: A key tool for statistics.
Unit Converter: Convert between units while maintaining ratios.
Age Calculator: Calculate ratios of ages or time spans.
GPA Calculator: An essential tool for students.
Quadratic Equation Solver: Solve for unknowns in equations.

Frequently Asked Questions (FAQ)

How do I solve for a missing value (e.g., 'x')?

Simply leave the box for the value you want to find empty. For example, to solve 2:3 = 10:x, you would enter 2 in 'A', 3 in 'B', 10 in 'C', and leave 'D' blank. The calculator will automatically solve for the empty field.

What's the difference between a ratio and a fraction?

They are very similar concepts for comparing parts. A ratio compares parts to parts (e.g., 2 boys : 3 girls), while a fraction typically compares a part to the whole (e.g., 2/5 of the group are boys). A ratio like A:B can be written as the fraction A/B.

Can I simplify a ratio with more than two numbers?

This calculator is designed to simplify a ratio with two numbers (A:B). To simplify a ratio with more numbers, like A:B:C, you would need to find the Greatest Common Divisor (GCD) for all three numbers and then divide each number by it.

Ratio Calculator

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