What is a Ratio?
A ratio is a quantitative relationship between two numbers that describes how many times one value can contain another. Applications of ratios are fairly ubiquitous, and the concept of ratios is quite intuitive. This could likely be demonstrated by giving a child half as many cookies as his sister. While the child may not be able to voice the injustice using ratios, the raucous protestations that would most likely ensue should make it immediately obvious that he is well aware he has received a 1:2 ratio of cookies conceptually, if not mathematically.
As shown above, ratios are often expressed as two numbers separated by a colon. They can also be written as "1 to 2" or as a fraction (½). The ratio represents the number that needs to be multiplied by the denominator in order to yield the numerator. This is clearer if the first number is larger than the second; i.e., with the ratio 2:1, 2 can contain 1, 2 times. It is also possible to have ratios that have more than two terms.
Ratios are common in many daily applications including: aspect ratios for screens, describing maps and models as a scaled-down version of their actual size, in baking and cooking, when discussing the odds of something occurring, or to describe rates, such as in finance. If, for example, a person wanted to make 5 cakes, each of which required a 1:2:3 ratio of butter:sugar:flour, and wanted to determine the total amount of ingredients necessary, it would be simple to compute. Increasing the ratio by five times yields a 5:10:15 ratio.
How to Use This Calculator
This tool is divided into two primary functions depending on your goal: solving for a missing value, or scaling an existing ratio.
- Solve Missing Value Mode: Use this when you have a known proportion (like 3:4) and you want to match it to a new scale (like 600:X). Simply enter the three known numbers and leave the one you want to solve for blank. The calculator will cross-multiply and solve it instantly.
- Scale Ratio Mode: Use this when you have a base ratio (like 250:280) and you want to scale the entire ratio up (enlarge) or down (shrink) by a specific multiplier (factor).
The Formula
When solving for a missing value in a proportional ratio set (A : B = C : D), the calculator uses cross-multiplication. The product of the extremes (A and D) equals the product of the means (B and C).
A × D = B × C
Solving for D:
D = (B × C) / A
If you are instead scaling a ratio, the formula simply multiplies or divides both A and B by the scaling factor.
Typical Aspect Ratios and Sizes of Screens
The aspect ratio is the ratio of a geometric shape's sizes in different dimensions. In the case of a rectangle, the aspect ratio is that of its width to its height. Although widely used in paper sizing and photography, frequent uses involve computer and phone screens.
| Name | Aspect Ratio | Width (px) | Height (px) |
|---|---|---|---|
| 720p | 16:9 | 1280 | 720 |
| 1080p (FHD) | 16:9 | 1920 | 1080 |
| 2160p (4K UHD) | 16:9 | 3840 | 2160 |
| SVGA | 4:3 | 800 | 600 |
| WXGA | 16:10 | 1280 | 800 |
| UXGA | 4:3 | 1600 | 1200 |
| WUXGA | 16:10 | 1920 | 1200 |
| WQHD | 16:9 | 2560 | 1440 |
Frequently Asked Questions
To find a missing number in a ratio (for example A:B = C:D, where D is missing), you set them up as equivalent fractions: A/B = C/D. Then you cross multiply (A * D = B * C) and divide by the known number that is grouped with your missing variable. In this case, D = (B * C) / A.
A ratio of 1:1.5 means that for every 1 unit of the first item, there are 1.5 units of the second item. If you want to use whole numbers, you can scale both sides by multiplying by 2, which turns 1:1.5 into an equivalent ratio of 2:3.
A fraction represents a part of a whole (like 3 slices out of an 8-slice pizza, or 3/8). A ratio compares two distinct parts to each other. For example, if there are 3 boys and 5 girls, the ratio of boys to girls is 3:5, but the fraction of boys compared to the *whole* group is 3/8.
Simplifying a ratio is similar to simplifying a fraction. You find the greatest common divisor (GCD) of both sides of the ratio and divide them both by that number. For instance, the ratio 15:20 can be simplified by dividing both sides by 5, resulting in 3:4.
Equivalent ratios are ratios that express the same proportional relationship between numbers, even if the numbers themselves are different. For example, 1:2, 2:4, and 10:20 are all equivalent ratios because the second number is always twice the first.