Proportion Calculator

Our ratio calculator is designed to find a missing value in a given proportion. In other words, it effortlessly converts an existing ratio into an equivalent ratio based on one known value in the new set.

Directions for use

Ratio calculator

Use this proportion calculator when you need to solve for a single missing value. The tool computes the unknown variable from the following equation:

A : B = C : D

To use the ratio solver, simply enter any three known values (A, B, C, or D) and click “Calculate.” The tool will instantly return the missing value. Additionally, it provides several visual representations of the completed ratio, including a pie chart, a bar chart, and a rectangle with side lengths proportional to the given numbers. These visual aids correspond to the ratio where both numbers were initially provided.

For instance, if you input values for A, B, and C, the ratio finder will calculate D and display visual representations of the A : B ratio. Conversely, if you enter B, C, and D, the calculator will solve for A and display graphs for the C : D ratio.

Ratios and Proportions

Ratio definition

A ratio is a mathematical method for comparing two values, representing how many times one value is contained within another. Typically, ratios are written as two numbers separated by a colon (e.g., 1 : 3 or 5 : 9). They can also be expressed as fractions or by using the word “to.” Below are a few common ways to write ratios:

9:4

1 to 3

4/5 or \$\frac{4}{5}\$

Ratios can be easily visualized using pie charts or bar graphs. For example, the ratio of 1 to 3 can be written as 1 : 3 or 1/3, and represented visually as follows:

Scaling ratios

Ratios can easily be scaled up or down. To scale a ratio up, multiply both numbers by the same multiplier. For example, to enlarge a 1 : 3 ratio by 4 times, multiply both 1 and 3 by 4:

1 : 3 = (1 × 4) : (3 × 4) = 4 : 12

Note that this final ratio is equivalent to the original because the fraction 4/12 simplifies perfectly back to 1/3. Conversely, to scale a ratio down, divide both numbers by the same divisor. For example, to shrink a 25 : 70 ratio by a factor of 5, divide both 25 and 70 by 5:

25 : 70 = (25/5) : (70/5) = 5 : 14

Again, the final ratio is perfectly equivalent to the initial one, as the fraction 25/70 simplifies down to 5/14.

Example 1

Scaling ratios is a practical skill often used in cooking, especially when adjusting a recipe to serve a different number of guests. Imagine a pancake recipe that feeds one person requires half a cup of flour and one cup of milk. If you need to make pancakes for a family of 8, how would you scale the ingredients?

Solution

The initial ratio of flour to milk is written as:

0.5 : 1

Since you are cooking for 8 people, you must scale up the given ratio 8 times. To do this, simply multiply both numbers of the original ratio by 8:

0.5 : 1 = (0.5 × 8) : (1 × 8) = 4 : 8

The final equivalent ratio is 4 : 8. You will need 4 cups of flour and 8 cups of milk.

Proportions

A proportion is a mathematical statement equating two ratios. For example:

1 : 2 = 2 : 4

5 : 6 = 30 : 36

Proportions possess a highly useful property for calculating unknown ratios: the cross-product property. This rule states that the product of the means (the inner numbers of the proportion) is always equal to the product of the extremes (the outer numbers of the proportion).

Take the proportion 5 : 6 = 30 : 36. Here, 6 and 30 are the means, while 5 and 36 are the extremes. According to the cross-product property, 6 × 30 = 5 × 36. We can verify this easily: 6 × 30 = 180, and 5 × 36 = 180.

Example 2

Ratios—specifically aspect ratios—are frequently used in technology to describe screen sizes and video dimensions.

For instance, a standard 480p camera resolution is typically characterized by a 4 : 3 aspect ratio. The height of the video is smaller than the width and is exactly 480 pixels. What is the exact width of the video in pixels?

Solution

We know the aspect ratio is 4 : 3, which serves as the first half of our proportion. We also know the height is the smaller value. Therefore, the height will be the second value in the equivalent ratio. Using this data, we can set up the following proportion:

4 : 3 = Width : Height

4 : 3 = Width : 480

We can solve for the missing width by applying the cross-product property:

3 × Width = 4 × 480

Width = (4 × 480)/3 = 1920/3 = 640

A 480p resolution video with a 4 : 3 aspect ratio will have a width of 640 pixels and a height of 480 pixels.

Note that some devices use different aspect ratios to define their 480p resolution, resulting in varying video widths. For example, the iPod Touch 4 uses a 480p (3:2) resolution, translating to a width of 720 and a height of 480 pixels. Meanwhile, the Samsung Galaxy S II uses a 480p (5:3) resolution, yielding 800 × 480 pixels for video width and height, respectively.