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Ratio Calculator

Easily solve ratio problems. Find missing values in a proportion or scale ratios up and down.

Ratio Calculator

Solve ratio problems and scale ratios up or down.

Solve for D in the proportion A : B = C : D

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Understanding Ratios

A ratio is a quantitative relationship between two numbers that describes how many times one value can contain another. Ratios are used to make comparisons between quantities. For example, a ratio of 1:2 means the second value is twice as large as the first.

Solving Proportions (A : B = C : D)

A proportion is an equation stating that two ratios are equal. To solve for a missing value (D), we use cross-multiplication.

A / B = C / D
A * D = B * C
D = (B * C) / A

Scaling Ratios

Scaling a ratio means to multiply or divide all parts of the ratio by the same number. This creates a new, equivalent ratio. For example, scaling the ratio 1:2 by 10 gives the equivalent ratio 10:20.

This calculator finds the scaling factor for you. If you have a ratio A:B and provide a new value for A (let's call it A'), it finds the new value for B (B') that maintains the same relationship.

B' = A' * (B / A)

Making Sense of Ratios and Proportions

A ratio is a way to compare two quantities. Whether you're scaling a recipe, resizing an image, or working with architectural plans, ratios are everywhere. I built this calculator to handle two common ratio tasks: finding a missing value in a proportion and scaling a ratio.

How to Use the Ratio Calculator

This tool has two modes to solve different kinds of problems:

1. Find Missing Value (A : B = C : D)

This mode solves a proportion. A proportion is an equation stating that two ratios are equal. If you have a ratio A : B and you know one part of an equivalent ratio (C), this tool will find the missing part (D).

The math is based on cross-multiplication: A * D = B * C. The calculator solves for D: D = (B * C) / A.

2. Scale Ratio

This mode helps you scale a known ratio up or down. For example, if you have a recipe with a ratio of 2 parts flour to 1 part sugar (2 : 1) and you now want to use 10 parts of flour, how much sugar do you need?

Enter your original ratio (2 and 1). Then, enter the new value for one of the parts (10 for flour), and the calculator will find the corresponding value for the other part (5 for sugar) to maintain the same ratio.

Real-World Example: Scaling an Image

Let's say you have an image that is 1920 pixels wide by 1080 pixels high (a 16:9 ratio). You want to resize it to be 800 pixels wide. What should the new height be?

  • Go to the "Scale Ratio" tab.
  • Enter the original ratio: A = 1920, B = 1080.
  • Enter the new value for A: A' = 800.
  • The calculator will solve for B', giving you the new height: 450 pixels.

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