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What exactly is 720p, 1080i and 1080p
The term 720p, 1080i and 1080p are terms all associated with High Definition Television (HDTV). HDTV is the highest form of digital television. It has a 16:9 aspect ratio, which is similar to a movie theater screen.
The characters 'p' and 'i' stand for 'progressive' and 'interlaced' respectively.
In case of a progressive type, all the pixels in a screen are lit.
In case of interlaced type, pixels only in the odd numbered rows are lit, then after 1/60th second, even numbered rows are lit. after that, its back to back with each 1/60th second.
Note : A pixel is a dot in the screen, which, when lit, can be of any color or shade irrespective of its location.
720p
720p is a High definition picture frame made of 720 rows of pixels with 1280 pixels in each row. 720p puts 921,600 pixels on the screen. There arent as many pixels are 1080i or 1080p, so static detail is far less compaired to those. It is also refreshed every 1/60th second.
720p which has a resolution of 1280x720, supports 3 native resolutions
- 1024×768 (XGA) which has a pixel count of 786,432. Its a 0.8 Megapixel picture with image and pixel aspect ratio of 4:3. It is a general PC resolution (XGA) and native resolution on many entry-level plasma TVs.
- 1280×720 (WXGA) with 921,600 pixels on screen. Its a 0.9 megapixel image with image aspect ratio of 16:9 and pixel aspect ratio of 1:1. It is a standard high definition, generally a PC resolution (WXGA). It is also used by high-end video projectors.
- 1366×768 (WXGA) with as many as 1,049,088 pixels. It is a 1.0 megapixel image with image aspect ratio of 16:9 and pixel aspect ratio of 1:1. It is generally used by in PC's and HD-Compatible LCD TV's.
1080i
It has 1,080 rows of pixels with 1,920 pixels with 1,920 pixels in each row. It consists of 2,073,600 pixels in the screen, which is alternatively lit, so, 1,036,800 pixels are lit on every screen refresh. The odd-numbered rows are lit up on the first screen refresh; then, on the second, just the even-numbered rows. It takes two 1/60-second refreshes to illuminate all the pixels. So, it takes 2x(1/60) = 1/30 seconds to lit up all pixels.
- 1080i has a native resolution of 1920×1080 with 2,073,600. Its a 2.1 megapixel image with aspect ratio of 16:9 and pixel aspect ratio of 1:1. It is used in standard High Definition video resolutions. It can also be used as PC resolution lower than WUXGA.
1080p
1080p is a high-def picture made of 1,080 rows of pixels with 1,920 pixels in each row. It consists of 2,073,600 pixels in a screen. All the rows of pixels are lit up on each and every screen refresh operation. Every pixel on the screen is refreshed each 1/60 second.
- 1080p has a native resolution of 1920×1080 with 2,073,600. Its a 2.1 megapixel image with aspect ratio of 16:9 and pixel aspect ratio of 1:1. It is used in standard High Definition video resolutions. Genrally used by Full-HD and HD-Compatible LCD, Plasma and Rear Projection TVs.
This chart shows the most common display resolutions, 720p, 1080i & 1080p shown in blue.

Which HDTV Format Is Better -- 720p, 1080i, or 1080p ?
Progressive image is better than an interlaced type, because it processes the image at twice the speed.
The difference between 720p and 1080i is negligible but 720p is used far more than 1080i. So, buying a 720p HDTV is recommended over a 1080i HDTV.
1080p is undoubtedly the best resolution in use.
So, if you can afford, go for a 1080p. If you cant, dont go for 1080i which costs in between both, instead 720p would be better.