When cameras come with a hike in resolution, we think about image size gains in megapixels or percentages, but actual image dimensions follow the inverse square law, so that if resolution increases by 37.5%, as in the case of the new Sony A7C II vs the existing A7C, the actual image width and height only increase by 17%.
The smaller the increase in megapixels, the smaller the gain in image pixel dimensions. So while the 25MP sensor in the new Panasonic Lumix G9 II has 25% more megapixels than the 20MP Lumix G9 before it, the actual gain in image width and height is just 12%
The diagram at the top of this article compares the image size in pixels created by the Sony A7C II versus the Sony A7C. Considering it has 37.5% more resolution, the A7C II’s images don’t seem that much larger.
The maths are pretty simple, though. That gain in megapixels has to be split between the increased width and the increased height. In fact the gain in width or height is the square root of the percentage gain in megapixels. The square root of 1.375 (the increased resolution as a multiplication factor) is near enough 1.17, so you get images 1.17x wider and 1.17 times higher. Not that much, is it?
Let’s take a more extreme example. The Sony A7CR has 61 million pixels versus the 24 megapixels of the original A7C. That should yield a huge jump in image sizes, right?
Well let’s work it out. The A7CR has 2.54x the megapixels of the A7C, but the square root of that gives a horizontal and vertical size factor of 1.59x. So although the A7CR has more than twice the resolution, its images are only 59% wider and taller.
So the next time a camera maker launches a new model with 50% more resolution, twice the resolution or more, just remember the inverse square law – you’re not going to get images 50% wider and taller or 100% wider or taller. Maths can be cruel sometimes!