is a bigger resolution slower?

i have a widescreen monitor,
i want to use the whole screen,
but not at the cost of it being slower.

current resolution:1024x768 [not widescreen]
biggest resolution:1920x1080 [Only widescreen resolution]

p.s. i know how to change the resolution.
 
No. It all depends on resolution, not screen size. If you increase resolution, the number of pixels the graphics card has to draw will increase, which will decrease frames per second. However, if you increase the screen size, nothing changes, according to the computer, as size isn't tied with pixel count.

from here

Yes, Screen resolution has a massive impact on performance, obviously the more pixels the GPU has to render the longer it will take to render the entire frame so you will end up with less FPS (Frames per second).

Higher resolutions (Like 1080P+) require more VRAM (Video Random Access Memory) to store all the textures in the game, the HD4670 you linked to has 1GB of VRAM which is good, but unfortunately doesn't really have the raw power to be able to play the latest games at decent in-game settings.

from here

A 1920x1080 monitor has 2073600 pixels. A 1366x768 monitor has 1049088 pixels, or roughly half as many. That's a MUCH lighter load for the graphics card. If you go from the smaller monitor to the larger one, your FPS could drop by close to half also, although it will also depend on how demanding the game is on your CPU. If it is at all like BF3, expect BF4 multiplayer to depend a lot on the CPU for performance too.
If you're concerned about the larger monitor sapping performance too much, you could: 1) run it at less than its native resolution for games, although that could introduce some fuzziness or unintended blurring, 2) get a 1600x900 (1440000 pixels) or 1680x1050 (1764000 pixels) monitor instead, 3) turn some settings down, or 4) get a more powerful graphics card, like a HD7970 or GTX770 instead.

from here

Hope these will answer your question. :)
 
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