Solve proportions (A:B = C:D) by entering any three values, scale ratios up or down, simplify ratios, and explore typical aspect ratios for screens and videos.
The Ratio Calculator is a practical mathematical tool designed to simplify, expand, compare, and solve ratios and proportions. A ratio represents the quantitative relationship between two or more values, showing how many times one value contains or is contained within another. Proportions are equations stating that two ratios are equal (e.g., a/b = c/d). Ratios are used in business, cooking, design, and science.
Simplifying a ratio involves dividing all terms in the ratio by their Greatest Common Divisor (GCD). For example, a ratio of 12:18 can be simplified to 2:3 by dividing both terms by 6. The ratio calculator automates this step, instantly reducing any input ratio to its simplest form. It also allows users to expand ratios by multiplying the terms by a constant factor, which is useful when scaling recipes or models.
Solving proportions is another core feature. If a proportion has an unknown value—for example, finding x in the equation 3/5 = x/20—the calculator uses cross-multiplication to solve for the unknown. Cross-multiplying yields 3 * 20 = 5 * x, leading to 60 = 5x, and x = 12. This method is fundamental for solving scaling problems in geography (maps scale), chemistry (solution concentrations), and engineering.
Ratios are also widely used in digital screens and photography, commonly referred to as aspect ratios. An aspect ratio is the proportional relationship between the width and height of an image or screen. Common aspect ratios include 16:9 for widescreen videos, 4:3 for older TVs, and 1:1 for social media posts. The ratio calculator helps designers scale layouts without distorting the dimensions.
In financial analysis, ratios are used to evaluate a company's performance, such as the price-to-earnings (P/E) ratio, debt-to-equity ratio, or current ratio. In daily life, ratios are used for mixing fuel, diluting cleaning concentrates, and adjusting baking recipes. The ratio calculator provides an easy and accurate way to manage these proportional adjustments, preventing mixing errors.
How it Works & Formula
A proportion is true when the cross-products are equal: A × D = B × C. To solve for any one value, rearrange: D = (B × C) / A.
Practical Examples
Scaling a 16:9 photo to a width of 1080px yields a height of (9 × 1080) / 16 = 607.5px.
Frequently Asked Questions
How do you simplify a ratio?
Divide both terms of the ratio by their Greatest Common Divisor (GCD).