Ratio Calculator
Print| Missing Value (D) | 800 |
| Simplified Ratio Shape | 3 : 4 |
| Decimal Value (A / B) | 0.75 |
A ratio is a quantitative relationship between two or more numbers that describes how many times one value is contained within another. Ratios can be expressed as numbers separated by a colon (e.g., 2:1), as the word “to” (e.g., 2 to 1), or as a standard mathematical fraction (e.g., 2/1). The concept is highly intuitive and is utilized daily in map scales, baking recipes, betting odds, and digital screen dimensions.
Our free Ratio Calculator features two modes: a Ratio Solver to find the missing fourth value in the proportion equation A:B = C:D using cross-multiplication, and a Ratio Scaling Calculator to expand or shrink any ratio by a desired multiplier.
Solving Proportions (A:B = C:D)
A proportion is an equation stating that two ratios are equal. To solve for a missing value (for instance, finding D when A, B, and C are known), you can convert the ratios into equivalent fractions and perform cross-multiplication:
A / B = C / D
Multiply the diagonally opposite terms:
A × D = B × C
Solve for D:
D = (B × C) / A
Example: If 3:4 is equal to 600:D, solve for the missing term D:
D = (4 × 600) / 3
D = 2400 / 3 = 800.
The completed proportion is 3:4 = 600:800.
Ratio Scaling: Expanding and Shrinking
Scaling a ratio involves multiplying or dividing all terms in the ratio by the same constant factor (the scale multiplier). This changes the absolute values while preserving the proportional relationship between the terms.
- Expanding (Scaling Up): Multiply all terms by the scaling factor. If a baking recipe requires a
1:2:3ratio of butter:sugar:flour, scaling it up 5 times yields5:10:15. - Shrinking (Scaling Down): Divide all terms by the scaling factor. If you want to shrink the ratio
250:280by a factor of2.5, divide both numbers:250 / 2.5 = 100280 / 2.5 = 112The scaled-down ratio is
100:112.
Screen Resolutions & Aspect Ratios
In geometry and display design, the aspect ratio describes the proportional relationship between a shape’s width and height. Below is a curated index of standard screen aspect ratios and their corresponding pixel resolutions:
| Resolution Name | Aspect Ratio | Width (Pixels) | Height (Pixels) |
|---|---|---|---|
| 480p (SD) | 3:2 | 720 | 480 |
| 720p (HD) | 16:9 | 1280 | 720 |
| 1080p (FHD) | 16:9 | 1920 | 1080 |
| 2160p (4K UHD) | 16:9 | 3840 | 2160 |
| 4320p (8K UHD) | 16:9 | 7680 | 4320 |
| SVGA | 4:3 | 800 | 600 |
| XGA | 4:3 | 1024 | 768 |
| WQXGA | 16:10 | 2560 | 1600 |
Solve fraction conversions using our Fraction Calculator or examine decimal equations with the Percentage Calculator.
Frequently Asked Questions (FAQ)
What is the difference between a ratio and a fraction?
A ratio compares two quantities to one another (e.g., a ratio of 3:4 of red to blue marbles means for every 3 red marbles there are 4 blue ones). A fraction compares a part to the whole (e.g., the red marbles represent 3/7 of the total collection of marbles).
How do you simplify a ratio?
To simplify a ratio, divide all numbers in the ratio by their greatest common factor (GCF). For example, the ratio 15:20 can be simplified by dividing both terms by 5, resulting in the simplified ratio 3:4.
What is the most common video aspect ratio?
The standard aspect ratio for modern televisions, computer monitors, and streaming platforms is 16:9. Historically, older television sets and CRT screens used a boxier 4:3 aspect ratio.
How do you use cross-multiplication to solve proportions?
Cross-multiplication states that if A / B = C / D, then the cross-products are equal: A × D = B × C. If one of the values is unknown, you can solve for it by dividing the product of the known diagonal by the remaining third value.