The Crop tool only works in aspect ratio. You resize the image to the desired pixel dimensions on exporting.
So crop the image to what aspect ratio you want 1200 long/wide (width number always comes first) by 1600 high/tall which is 4-3 (or 3-4) (3 units in one direction and 4 units in the other direction). Then when you export the image you set the pixel dimension.
Thanks for your effort. I know that LR can crop to almost whatever aspect ratio you want but it is not what I want to do.
If Lightroom were to offer at least a display on what the current size of the crop is, I'd be almost there. A possibility to enter dimensions would be perfect.
I think you confused image capture ratio and pixel numbers of the sensor with final output size.
Sensors are of certain aspect ratios, 3/2, 4/3, 16/9, 1/1, which are ratios of the long side to the short side of the sensor. They can be of any number, 3000 to 2000, 4000 to 3000 and so on (3/2, 4/3) or in the real world 6879 to 4586 (3/2) or 6880 to 5160 (4/3) pixels.
The crop tool allows you to crop out parts of an image you don't want or to a different Aspect Ratio, like going from 1/1 to 3/2 or 3/2 to 4/3 or 4/3 to 3/2 or 1/1, and what is left is what you want in the image and the number of pixels will change when doing that. It is in the Final Output you specify the reduced number of pixels you want the image to be along with the number of pixels per inch.
In your example 1200 to 1600 is a 4/3 (or 3/4) ratio. So using the 3/2 ratio give you the same effect as typing in 1200 to 1600.
Please not that LR never changes the original image. Even if you crop an image to a much smaller size, reducing the number of available pixels being displayed, the original images is never touched and the crop can be removed to reveal the original image in it's original size and aspect ratio.
It is only when Exporting images can they be reduced in the number of available pixels, to reduce the size in MBs of the image, and the number of pixels per inch to either reduce or increase the size of the image in inches and or mm.
No possibility to set target pixel dimensions in the crop tool, however you can display the current crop dimensions in the Info Overlay. The "I" key toggles the overlay (off - Info 1 - Info 2). Go to View > View Options and set one or more of the six available fields to Cropped Dimensions. When you crop the pixel dimensions will be displayed after you release the mouse.
Trying to drag the crop box to an exact size will quickly send you to the madhouse. A better technique is to get close - for instance, 1206x1608 - and then resize to the desired numbers at export.
I hope this better explains what I am talking about and what you are asking.
This image is from B&W film shot with a Leica M3 that is 3/2 ratio. Note the number of pixels on the long and short sides.
Cropped to the 4/3 ratio. Note the number of pixels on the long and short sides.
Then that image reduced to your 1200 by 1600 size (or as close as I can come to it using a mouse).
The bright area is what is left of the image when cropping to 1600 by 1200 Pixels.
Is that what you want? I don't think so.
That same image, cropped to the 4/3 ratio size then Reduced on Export to a JPG file.
This is what I think you are after. IE to reduce the File size in MBs and Pixel dimensions but retain most of the original image.
Thanks to everybody who wrote an answer. All your comments were right in their proper ways.
Nevertheless, the answer is simple: it cannot be done directly.
Of course, I can set a ratio, crop and export to the desired pixel dimensions, still this is not the thing I'm after. I'll have to do it outside of Lightroom. GraphicConverter (Mac only) can do it, possibly Photoshop and others. But not Lightroom.
...this is what I suspected and it is the answer to my question.
Someone else marked a different answer as correct.
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The Any Crop plugin will show you the current crop dimensions in pixels in real time as you adjust it with the crop tool, and it will let you crop to an exact pixel dimension.
Thanks for hinting at the plugin. It lets me do what I want to do as far as I can see from a few minutes of testing.