Carat is often confused with size where as in fact it is actually a measure of weight. Some times a larger diamond gives the impression that it is more brilliant than a smaller one. This is only because light travels a greater difference through the larger diamond, this result is known as the prism effect that your eyes register as more brilliance and fire
A one carat diamond is approximately equivalent to 200 milligrams. You can also divide a One carat diamond into 100 "points". A .50 carat diamond is the same as .50 points or 1/2 -carat diamond.
It would be wrong to conclude that a 1 carat diamond would be twice the amount of a ½ carat diamond assuming colour, clarity and cut remain the same. Larger diamonds are found less frequently in nature and only 1% of all diamonds mined weigh more than 1 carat.
The cut of the diamond as well as the mounting can make a diamond look larger or smaller.