Aspect Ratio Calculator

Three of the four numbers give you the fourth. The arithmetic is one division, and everything that goes wrong afterwards is about what happens when the answer is not a whole number, or when the shape you have and the shape you need do not match.

The whole calculation

width / height = ratio

1920 / 1080 = 1.7778
divide both by 120  ->  16 : 9

new height = new width / ratio
1000 / 1.7778 = 562.5

which is half a pixel, and nothing accepts half a pixel.

Simplifying is just dividing both numbers by their greatest common divisor. 1920 and 1080 share 120, which is where 16:9 comes from.

Fractional answers are flagged above, and never rounded off without saying so. Round them yourself and pick a direction: rounding down loses a row of pixels, rounding up gains one, and either way the result is no longer exactly the ratio you asked for. For video it matters more than for images, because encoders usually want dimensions divisible by two and sometimes by sixteen.

Fit or fill

A 16:9 picture into a square box

fit inside     the whole picture, bars top and bottom
fill it        edges cropped, nothing left over

Same picture, same box, and the difference is
whether you lose the edges or lose the space.

Two ways to put a picture in a box that is the wrong shape. Fit inside keeps everything and leaves bars. Fill it keeps the box full and throws away whatever hangs over the edges.

In CSS these are object-fit: contain andobject-fit: cover. Cover is the right default for a hero image and the wrong one for a logo. The numbers above tell you how much you lose, which is the part worth checking before somebody's head goes missing from a banner.

21:9 is a lie, and so is 4K

21:9 is not 21:9

2560 / 1080 = 2.370
21 / 9       = 2.333
64 / 27      = 2.370

The monitor box says 21:9 because it is easier to say.

Ultrawide monitors are sold as 21:9 and are actually 64:27, which is 16:9 multiplied by 4:3. Close enough to say out loud, not close enough to calculate with, which is why 2560 by 1080 instead of the 2520 by 1080 that a true 21:9 would give.

4K is worse. Cinema 4K is 4096 pixels wide and consumer 4K is 3840, which makes it a 3.8K sold under a rounder name. The consumer number is the one that keeps 16:9.

Anamorphic, where the pixels are not square

Everything here assumes square pixels, which is true of every screen made this century and not true of a lot of older video. DVD stores 720 by 576 and displays it as 16:9 by stretching each pixel sideways, so the stored shape and the shown shape are different numbers.

If you are working with source that has a pixel aspect ratio, multiply the stored width by it before doing anything here.

The A series is the interesting one

A4 is 1 to the square root of 2, and that ratio is the only one where halving gives you the same shape again. A4 folded is A5, folded again is A6, and all of them are 1:1.414. That is the whole design, and it is why photocopiers have a 71% button.

It also means A-series paper never lands on whole pixels at any useful size, so the sizes list stays empty for it.

Where the common sizes come from

The list is generated, not looked up. It takes the heights and widths that hardware actually uses and keeps only the pairs where both sides come out as whole pixels at your ratio. A ratio with an irrational side, like the A series or the golden ratio, produces nothing, which is the honest answer.