from Megapixels and Aspect Ratio

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What are the maximum image dimensions that can fit in X megapixels?

What do I get if I buy a 50 megapixel camera? Or in any 50 megapixel image?

(It depends on the aspect ratio)

A few standard aspect ratios (1:1, 4:3, 3:2, 16:9) are automatically shown below.

If you enter the other aspect field, it will be shown too, first. Aspect ratio can be entered in format like 5:4 or 4:3 or 11:14, or it can be the corresponding divided number like 0.8 or 1.3333 or 1.7778 (to 1).

The result output lines are repeated to show the calculation is precise out to several decimal places. However images cannot be dimensioned in fractions of pixels. One pixel is the smallest possible unit, so rounded integers are necessary. Rounding loses precision. To add or subtract one pixel to width or height can be thousands of pixels in the other dimension. Those steps affect the megapixel total slightly (shown above), and it explains the second rounded result.

The goal is to compute maximum dimensions of a specific aspect ratio that matches the specified megapixels. Megapixels is sensor Area (in units of pixels). Pixels are the only units used. We don't need to know actual pixel size, because all computed Units are "pixels", units of one pixel. The calculator computes the WxH image dimensions of various aspect ratios that match the megapixels that you specify. Because of rounding, dimensions might vary slightly over or under the exact megapixels, but your camera takes bigger liberties approximating megapixels and aspect ratio.

This calculation does describe our sensor sizes of given megapixels and aspect ratio. Any small variation will only be because your camera rounds its values of megapixels and/or aspect ratio. Compute and use the camera's actual precise values, and they will be exactly matched. An example: an image size of 5000x3750 pixels is exactly 5000x3750 = 18.75 mp and exactly 5000/3750 = 1.33333 : 1 aspect (4:3). Note that megapixels are regular multiples of 1000 (NOT of 1024).

The blue image here shows the aspect concept visually. 4:3 is taller, but 3:2 is wider. Technically, aspect can change the diagonal slightly, but not much. The sensor area is the same WxH (megapixels), but 3:2 and 4:3 diagonals vary by 2%, and 16:9 and 4:3 vary from each other by 6%. This small diagonal variation can change pixel size slightly, by
√ 6% . But the plan is, nothing very significant changes except the aspect ratio of the sensor.

This of course includes 16:9 video camcorder sensors, but an exception are 16:9 video frames which are contained within existing 4:3 or 3:2 sensors. These of course cannot be the full diagonal (that width cannot be wider than the sensor width). And their width could be even smaller (which does reduce field of view), but of course, 16:9 movies will be resampled to 1920x1080 or 1280x720 anyway. The assumption here is that 16:9 in a 4:3 or 3:2 sensor will be as wide as those dimensions allow, but is more true of still cameras taking movies than of camcorders taking still photos. See More about video frame sizes relative to still pictures.

Math is precise, but Real World, not so much: If checking the calculator against your camera, realize that cameras round the specifications. For example, a Microsoft cell phone with 2592 x 1456 pixels specifies 3.77 MP and 16:9 aspect, which computes slightly different dimensions (3 pixels less width). This is because 2592x1456 is actually 3.774 megapixels, and 2592/1456 is actually 1.78 aspect (16:9 is 1.7778). If you enter those actual correct numbers, the calculator shows the exact dimensions (in bold on top line).

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