Using measurements, not pixels, to resize an object in an image

What @TheDigitalDog said matters a lot, so remember the dpi (ppi) determines the image size. I'm in CS6, but here's how I do it:

File>New brings up the panel where you select the image size. The dropdown menu gives you a choice between inches, pixels, cm, etc. When you choose inches, it tells you what that is in pixels.  It also makes you enter a DPI, so pay attention to that because it determines and will change the dimensions of the image:

@Markusdark wrote:

In other products, if I had an object in an image that I wanted to resize into a specific measurement, I could click on the object and select something like "Numeric Transform"

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If by “object” you mean a selected layer (not the entire image), choose Edit > Free Transform, then right-click a measurement field up in the options bar and choose a unit of measure.

Another way to do that, without right-clicking, is to simply type it in with an abbreviation. For example, if it’s in pixels but you want 4 centimeters, enter "4 cm".

???

When you resample a images you should be able to use whatever unites you  want to use.  While using Transform the size width and height resize is shown in percentage when you use the resizing box. However  I can easily use units there as well.  Here  I changed a layer's width to 4 inches and photoshop had no peoblem resizing the layers width to 4 inches.

You can also right click on a field and chose what unites you want the field displayed with.

Exactly 2.125" tall by 1.337" at WHAT PPI? Gotta define that! 

Without a fixed number of pixels over a metric like inch or mm, there is no size. 

The math is simple and outlined in this very, very old article on resolution that hasn't changed since its writing:

http://digitaldog.net/files/Resolution.pdf