Aspect ratios, solved

How to use

1. In “Simplify a size”, type a width and height, for example 1920 and 1080.
2. Read the reduced ratio, its decimal form and the closest common ratio with its typical use.
3. In “Solve the missing side”, type or pick a ratio, say whether you know the width or the height, and enter it.
4. The other side appears immediately, rounded to whole pixels, with the exact value shown if rounding was needed.

How it works

A ratio is simplified by dividing both sides by their greatest common divisor, found with Euclid's algorithm: repeatedly replace the pair (a, b) with (b, a mod b) until b is zero; the remaining a is the GCD. Decimal inputs such as 1.85 are first scaled to whole numbers (185 : 100).

Solving uses cross-multiplication: height = width × ratioH / ratioW, or width = height × ratioW / ratioH. The decimal ratio is simply width ÷ height. To find the nearest common ratio, the tool compares that decimal with a list of standard ratios and reports the smallest relative difference; within 0.5% counts as a match.

Worked example

1920 × 1080: 1920 mod 1080 = 840; 1080 mod 840 = 240; 840 mod 240 = 120; 240 mod 120 = 0, so the GCD is 120 and the ratio is 1920/120 : 1080/120 = 16:9 (decimal 1.7778).

A so-called 21:9 monitor at 2560 × 1080 actually reduces to 64:27 (2.370), which is why the tool reports it as “closest to 21:9” rather than an exact match. And a 16:9 video 1280 px wide needs a height of 1280 × 9 / 16 = 720 px.

Limitations

• Results are rounded to whole pixels, so a solved size can be a fraction of a pixel away from the exact ratio.
• The list of common ratios is a curated selection, not exhaustive.
• Decimal inputs are limited to six decimal places.

FAQ