Diamonds do not cost a constant price per carat. Because large diamonds are far rarer than small diamonds, a larger diamond costs more per carat than a smaller diamond. That is what this graph shows.
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To come up with this graph, I used prices from Zales.com. I measured prices of round diamonds, because they are the most common shape. I focused on a cut, color, and clarity that appears nearly perfect to the unaided human eye. I looked at diamonds that had a clarity of SI2 or better, a color of I or better, and a cut of Good or better. To minimize the potential impact of price outliers, the graph measures the per carat price of the second cheapest diamond at a given carat size.
Apparently, the median size of newly-purchased engagement ring diamonds today is 1 carat. However, if someone is considering springing for a slightly larger rock, the actual price per carat of a 1.5 carat diamond is slightly cheaper than the trend line says it should be—at least at Zales.
For those on a budget, the half carat diamond is by far the best deal of all the diamonds measured by this graph. Not only do you buy half as much diamond as someone buying a 1 carat diamond, you also spend less than half as much per carat, resulting in a diamond price that is less than a quarter of the price of a 1 carat diamond.