Ratio Calculator
Reduce 2- and 3-part ratios to lowest terms, scale display resolutions and other aspect ratios, split a total by ratio, and solve A:B = C:D with step-by-step working.
Quick Answer & Key Proportion Formula
Direct Answer: A proportion states that two ratios are equivalent: A / B = C / D. By cross-multiplication, the product of the extremes equals the product of the means: A × D = B × C. To solve for any unknown variable, isolate it by dividing by the paired coefficient: D = (B × C) / A. To simplify ratios, divide all integers by their Greatest Common Divisor (GCD).
How to Master Ratios, Proportions, and Scaling
Ratios are fundamental mathematical expressions comparing two or more quantities. Whether sizing images for digital media, adjusting culinary recipes, or dividing business equity, understanding these core principles ensures precision.
1. Cross-Multiplication Method
When dealing with equivalent ratios formatted as fractions, cross-multiplication eliminates the denominators:
For example, if 2 / 3 = 4 / X, then 2 × X = 3 × 4 = 12. Dividing both sides by 2 yields X = 6.
2. Euclidean GCD Reduction
A ratio is in its simplest form when its terms are integers with no common positive factors other than 1:
For the resolution 1920:1080, the GCD is 120. Dividing both numbers by 120 produces the standard 16:9 aspect ratio.
Solving a proportion for x?
The proportion calculator solves A / B = C / D with worked examples, checks whether two ratios are proportional and handles inverse proportions.
Common Aspect Ratio Reference Table
| Aspect Ratio | Decimal (W ÷ H) | Standard Resolutions | Primary Use Case |
|---|---|---|---|
| 16:9 | 1.7778 | 1920×1080 (FHD), 3840×2160 (4K) | YouTube, TV, modern computer monitors |
| 4:3 | 1.3333 | 1024×768, 1440×1080 | Classic television, iPad screens, Micro Four Thirds |
| 1:1 | 1.0000 | 1080×1080, 2048×2048 | Square social media posts, profile pictures |
| 9:16 | 0.5625 | 1080×1920 | TikTok, Instagram Reels, YouTube Shorts, mobile video |
| 21:9 | 2.3333 | 2560×1080, 3440×1440 | Ultrawide gaming displays, cinema anamorphic format |
| 3:2 | 1.5000 | 3000×2000, 6000×4000 | 35mm photography, Microsoft Surface laptops |
Frequently Asked Questions
How do you simplify a ratio to lowest terms?
To simplify a ratio A:B, first eliminate any decimals by multiplying all terms by 10, 100, or 1,000. Next, calculate the Greatest Common Divisor (GCD) of all terms using the Euclidean algorithm, and divide each term by this GCD. For example, 1920:1080 has a GCD of 120, which simplifies to 16:9.
What is the difference between a ratio and a proportion?
A ratio compares two quantities, such as 3:4. A proportion is an equation stating that two ratios are equal, such as 3:4 = 9:12. A ratio describes a relationship; a proportion lets you find a missing value when that relationship stays the same.
What is an aspect ratio and how is it calculated?
An aspect ratio is the proportional relationship between the width and height of an image, video, or display screen. It is expressed as Width:Height (such as 16:9 for widescreen HD video or 1:1 for square posts). To scale dimensions while preserving aspect ratio, divide the new target width by the original width to get a scale factor (k), and multiply the original height by k.
How do you convert a ratio to a percentage?
Divide each part by the sum of all parts and multiply by 100. A 3:1 ratio has 4 parts, so the shares are 3 ÷ 4 = 75% and 1 ÷ 4 = 25%. To express A as a percentage of B instead, compute A ÷ B × 100: in a 3:4 ratio, 3 is 75% of 4.
How do you divide an amount into a given ratio?
Add all parts of the ratio together to find the total number of shares. Divide the total sum by this total number of shares to determine the value of one part. Finally, multiply each ratio term by this single part value.