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Ratio Calculator

Created by Piotr Małek and Julia Żuławińska
Reviewed by Jack Bowater
Last updated: Apr 22, 2024


The ratio calculator will help you compute identical ratios given three of the four parts of the two ratios. A ratio is a relationship between two quantities, very often represented as a fraction. It displays how much of one part is contained in another part, basically representing a fractional or percentage amount of the whole.

Before we can use the calculator, we need to understand how to do ratios and how to find a ratio.

How to do ratios?

A ratio is made up of two parts, the same as how a fraction is made up of two parts. There is the numerator (the top number of the fraction) and the denominator (the bottom number of the fraction).

For example, suppose there is a pie cut into eight slices and three of the eight slices have been eaten. If we want to know the ratio of slices eaten compared to the entire pie, then we have to put the number eaten as the numerator and the total number of pieces as the denominator; 3/8.

That is the most basic of ratios since no simplification is involved. But what if we want to simplify or scale up the ratio to a larger, yet equivalent ratio? The next section on how to find a ratio will explain the process.

How to find a ratio?

Suppose we have the same ratio of 3/8, but we want to scale it up to a larger, equivalent ratio with a denominator of 72. The way to do this is to set up a proportion, which is two ratios equal to each other and solve for the missing part. We can do this as follows:

  1. Write both ratios in terms of fractions, labeling the missing part with an x.
  2. Set the fractions equal to each other, forming a proportion.
  3. Use the process of cross-multiplication to isolate the variable.
  4. Solve for the variable.
  5. Use the ratio calculator to check your answer.

In the above example, the steps would look as follows:

  1. 3/8 = x/72;
  2. 8 · x = 72 · 3;
  3. 8x = 216;
  4. x = 27.

For more complex ratios involving larger numbers or decimals, the ratio calculator is much more convenient to use. The proportion calculator, which does the same thing, may also be used to solve problems such as the one above.

The golden ratio

Golden ratio line

The golden ratio is a special ratio that is achieved when two quantities have the same ratio as the ratio of their sum to the larger of the two quantities. If we denote the two quantities at a and b, then the golden ratio is (a+b)/a = a/b. The value of this ratio is approximately 1.618. The golden ratio calculator is handy for computing this ratio.

It has been said that the rectangle that is most aesthetically pleasing to the eye is the golden rectangle. This is a rectangle with length a + b and width a. The rectangle is golden if (a+b)/a = a/b. The golden rectangle calculator will compute the length and width necessary to achieve the perfect golden rectangle.

The ratio calculator is also helpful in the geometric application of similar triangles. If the sides of one triangle are in proportion with the sides of another triangle, the two triangles are said to be similar. This applies to other polygons as well.

FAQ

What is the golden ratio?

The golden ratio is a special number, approximately 1.618, found by dividing a line into two parts so that the longer part divided by the smaller part is equal to the whole length divided by the longer part. It's often seen in nature, art, and architecture, creating aesthetically pleasing proportions.

How do I find the ratio of two numbers?

To find the ratio of two numbers, follow these simple steps:

  1. Choose any two numbers you're interested in.
  2. Divide both numbers by their greatest common divisor.
  3. After dividing, write down the result separated by a colon (e.g., 3:4).
  4. The result is your ratio!

For example, to find the ratio of 10 and 15, first find the GCD, which is 5. Divide both numbers by 5.

The ratio is 2:3.

What are 3 ways to find a ratio?

Here are three ways to find a ratio:

  • Direct comparison - Simply compare two numbers directly. For example, if you have 4 apples and 8 oranges, the ratio is 4:8. You can simplify it to 1:2.

  • Scale Factor - Find a common factor that can scale both numbers to a simpler form. For example, for 10 and 20, divide both by 10, giving the ratio of 1:2.

  • Greatest Common Divisor (GCD) - Divide both numbers by their GCD to simplify the ratio. For example, the GCD of 14 and 28 is 14, so the ratio is 1:2 after dividing both numbers by 14.

What is the ratio of 3 to 5?

The ratio of 3 to 5 means that for every 3 units of one quantity, there are 5 units of another. It's like comparing two things; for example, if you have 3 apples, you would have 5 oranges. This ratio can be written as 3:5 or as a fraction, 3/5.

Piotr Małek and Julia Żuławińska
Ratio of...
two numbers - A:B
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find an equivalent of a ratio.
A : B = C : D
A
B
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