Pixel VS DPI - Need to have a quick question cleared up!

Hello Adobe Forums!
I would consider myself an experienced designer, but I have a question that might seem rather mundane. To be completely honest, I just think I have overthought/overanalyzed it to a point where I confused myself!
In Photoshop, I have a 300 DPI psd image, that image size is 2"x1" and is 600x300px.
Now, my question is: is there a way to reduce the DPI in an effort to increase the pixels?
My goal is to have a larger amount of pixels at 72dpi for a web image. The theory makes sense in my head, but when put into practice, my image loses its quality. I need it to be sharp.
Aside from all of this, if I do have to end up resampling, are there other programs that resample more effectively than Photoshop?
Thanks in advance!

Exactly. Web images have no PPI, only the pixel dimensions. Your image is 600px x 300px; ignore the 300 PPI, ignore the 2" x 1". Focus only on the 600px x 300px. When you use this image in a web layout, it will take up exactly 600px x 300px. Whether or not that size works for what you're trying to do is up to you, it is what it is. But the image is not 72 PPI or 300 PPI or any other PPI, since you're not printing it.
In fact, even images destined for print don't have a specific PPI until you set the size at which they will be printed. Photoshop provides the PPI of the image based on a particular output size for convenience, but the only true measure of the resolution of a digital image are the pixel dimensions, period.
Here's a short article I wrote for our customers w/ digital cameras, to explain digital resolution and print resolution:
WHAT IS RESOLUTION?
The resolution of a digital image is the number of pixels it  contains, plain and simple. If you open an image into Photoshop and go  to Image > Image Size, the top section of the dialog box shows you  the total number of pixels in your image. This is the actual resolution  of the image, independent of the size you plan to use it.
For example, a photo taken with a Canon Digital Rebel XSi might have a  resolution of 4272 x 2848. This means there are 4272 pixels across, and  2848 pixels down, that make up the image.
Most digital cameras are rated as a certain number of "megapixels." A  megapixel is one million pixels, and camera manufactures calculate the  megapixels by multiplying the maximum width by the maximum height that  their camera can capture. In the example above, the Digital Rebel XSi is  a 12 megapixel camera (4272 times 2848 = 12,166,656 pixels).
HOW  BIG IS A PIXEL?
A pixel has no size of its own, it is simply the smallest single  "unit" in a digital image. In fact, the word pixel derives from the term  "picture element." If you zoom in close enough in Photoshop you can see  all the individual pixels that make up an image. (In Photoshop CS4  there is also a pixel grid that you can enable to make it easier to  see.)
SO  WHAT ABOUT PPI?
You've probably heard a lot about pixels per inch (PPI) or dots per inch (DPI), but what does that actually mean?
Pixels per inch is a relative measurement of resolution, that takes into account the size you're going to print the image. Now there's a  mouthful! Don't let that confuse you, though, it's actually really simple to calculate: take the total number of pixels and divide by the size you plan to use it.
So for example, if you take that 4272 x 2848 image I mentioned  earlier and print it 10 inches wide, the resolution would be 427.2 PPI  (4272 divided by 10).
For optimum print quality, we look for 300 PPI at print size, and a  similar calculation will tell you how big you can print your images.  Using that same image, take 4272 and divide by 300. The result is 14.24,  so you can print that image as large as 14.24" without the image  looking low-res or pixellated, or without doing any resampling in  Photoshop.
Oh, and the proper unit of measurement for the resolution of a digital  image at a particular print size is PPI. The proper unit of measurement of the resolution of  an output device is DPI. The two are not synonymous nor  interchangeable -- images never contain dots, only pixels, and printers never print with pixels, only dots.
OK,  SO YOU'RE SAYING RESOLUTION AND PPI ARE NOT THE SAME THING?
Right. They're related, but not the same. The easy way to think about  this is that PPI is the "print resolution" of the image.
Let's look at another example: say you have an image that is 1500  pixels x 1500 pixels, and you print it at 5" wide. 1500 divided by 5 is  300 PPI. If you print the same image at 10" wide, 1500 divided by 10 is  150 PPI. The print resolution has changed because you're using the image  at a much larger size, but the actual resolution of the image (1500 x  1500) has not changed.
CAN'T  I JUST INCREASE THE RESOLUTION IN PHOTOSHOP?
You can, but it's not the same as if the image had the correct  resolution to start with.
If you ask Photoshop to increase the resolution of an image, it needs  to calculate how to add all those new pixels you're asking for. It uses  some pretty complex algorithms to do this, but it's still "inventing"  pixels that were never there. There is a limit to how much you can  artificially increase the resolution of an image without it being  visible (either as blurriness or jaggedness). And don't forget: a  low-resolution original doesn't contain as much detail as a high-res  image. Photoshop can only interpolate from the data that exists in the  file, so it won't magically add in all that missing detail.
A good rule of thumb is if your image would be less than 225 PPI or  so at the size you want to use it, you would be better off retaking the  photo than upsampling in Photoshop. Anything less than that and it will  almost certainly appear low-res when printed, and you would see  artifacts if you upsample it.

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