Aspect Ratio Calculator

How to use the aspect ratio calculator

Leave the ratio on free and the tool works backwards: you give it two sides, it divides both by their greatest common divisor and tells you the shape. Lock a ratio instead and it works forwards, solving whichever side you did not just type so the shape holds.

A ratio has no unit. Both sides only have to be measured in the same thing, so pixels, millimetres, inches and printer points all behave identically. That is why a 6000 by 4000 photograph and a 3 by 2 inch print are the same shape and crop into each other without loss.

Reducing a ratio is the same operation as reducing a fraction, and it uses the same tool: Euclid algorithm for the greatest common divisor. Keep replacing the pair with the smaller number and the remainder until the remainder is zero, and what is left is the largest number that divides both.

1. 1

   Start with 1920 and 1080

   1920 divided by 1080 leaves a remainder of 840.

2. 2

   Replace and repeat

   1080 and 840 leaves 240. Then 840 and 240 leaves 120.

3. 3

   Stop at a remainder of zero

   240 and 120 divides exactly, so the answer is 120.

4. 4

   Divide both sides

   1920 over 120 is 16, and 1080 over 120 is 9.

Cinema quotes ratios as a decimal instead of a pair, which is the same information written differently. The modern anamorphic scope standard is 2.39:1, and that is exactly 239:100 because 239 is prime and shares no factor with 100. Standard widescreen, 1.85:1, reduces to 37:20.

What a monitor sold as 21:9 actually measures

There is no 21:9 panel. The name is a marketing shorthand that sits nicely beside 16:9, and the two common ultrawide resolutions reduce to something else entirely. Enter either into the calculator above and it will tell you the same thing.

The 64:27 figure is not arbitrary. It is 16:9 cubed in the sense that matters to broadcast: 4:3 stretched to 16:9 stretched again by the same factor, which is why it turned up in the standards as an extended television ratio rather than out of nowhere.

The practical consequence is small but real. Content mastered for 2.39:1 cinema does not fill either panel exactly, and content mastered for a literal 21:9 fills neither. If you are compositing to a fixed frame, use the resolution rather than the name.

Why the ratio never tells you the resolution

A ratio is a shape and a resolution is an amount. 1280x720 and 3840x2160 are both 16:9, and one holds nine times as many pixels as the other. Knowing the shape tells you whether an image will letterbox; it tells you nothing about whether it will look sharp.

This is the confusion behind most bad exports. Someone asks for 16:9 and receives a 640x360 file, which is correctly shaped and useless on a large screen. The two numbers have to be specified together, and the calculator shows both because neither is sufficient alone.

The formula, worked line by line

The whole tool is one idea. A ratio is a fraction, a fraction has a canonical form, and you reach that form by dividing both sides by their greatest common divisor. Everything else on the page is that operation run forwards instead of backwards.

Euclid algorithm finds the divisor without factorising anything. Divide the larger number by the smaller, keep the remainder, and repeat with the smaller number and the remainder until the remainder is zero. Whatever you were dividing by at that moment is the answer.

gcd(a, b) = gcd(b, a mod b), repeated until b = 0
reduced ratio = width / gcd : height / gcd
gcd(1920, 1080) = 120, so the ratio is 16:9
missing height = width x (ratio height / ratio width)
missing width = height x (ratio width / ratio height)
megapixels = width x height / 1,000,000

Reducing works the same way on decimals once you scale them up. The cinema ratio 2.39:1 becomes 239:100 by multiplying both sides by 100, and 239 is prime so nothing cancels. 1.85:1 becomes 185:100, which does cancel by 5, leaving 37:20.

A ratio also fixes the diagonal. Two rectangles with the same ratio, laid corner to corner, share one straight diagonal line, and that is the geometric statement of what having the same shape means. It is also the quickest way to check a resize by eye.

Cropping is where ratios cost something. Moving a 3:2 photograph to 16:9 means the shape has to change, so either the image loses height or it gains bars. The calculator will tell you the target size; deciding what leaves the frame is still a judgement call.

Questions people ask