An 8mm x 8mm cushion cut is about 2.5 carats. But a jeweler or gemologist is better able to weigh the stone physically so that you have an accurate weight.
According to Wikipedia: " ...cushion antique brilliant [cut] with a faceted girdle and extra facets on the pavilion."
A large square cut stone is commonly known as a "cushion cut" or "princess cut" depending on the shape of the stone.
Your answer depends on the type of stone and the cut. The measurements you give are approximate to a sort-of princess cut, but the measurements you give are not 'true' for the ratios defined by the cut. Your local jeweler or certified gemologist can weigh the stone for you and give you its carat weight and type.
A 3.1 carat diamond is approximately 0.62 grams in weight. In terms of size, it would measure around 9-10mm in diameter for a round brilliant cut diamond. The actual size may vary depending on the specific shape and cut of the stone.
The value of 1.45 carats of diamonds will depend on weather you have one single diamond or more. Do you have 145 diamonds with a total weight of 1.45 carats or 2 0.5 carat diamonds and a 0.45 carat diamond? Large diamonds are many many times more valuable than small ones and a single 1.45 carat diamond will be worth far more than tree diamonds with a total carat weight of 1.45 carats
The mm size of a diamond stone relative to its weight in carats is directly related to the cut and the excellence of the cut. For example, a round brilliant stone measuring 8 mm in diameter at the girdle weighs about two carats. A different cut will have a different weight in carats.
This diamond may weigh between 1.75 (7.8MM) and 2.00 carats (8.2MM). The millimeter measurement is the diameter of the girdle, and depending on the cut, this diamond may weigh more or less than indicated, above.
Your answer depends on the cut you are measuring. If the gem is a round cut, the carat weight will be about .10 carats.
Since cushion cut is a rather square cut, one must assume that your diamond measures 7mm x 7mm. In this case, it weighs approximately two carats.
A round cut diamond weighing .25 carats measures 4.1mm at the girdle.
If the cut is round, this weight may rate in the just under 7 carats range. If it is a different cut, the weight will be different.
A round cut diamond weighing .25 carats measures 4.1mm at the girdle.
Your jeweler is better equipped to help you figure out the answer to your question. With a round mounting and a square diamond, your question reads like you're trying to drive a square peg into a round hole.
This diamond could weigh about six carats if its measurement is 10mm x 10mm.
Cushion cut because it is a less popular cut
Cushion Cut refers to a way that diamonds are cut. The Cushion cut is an antique cut that was most common in the nineteenth century, though recently cushion cut engagement rings have become popular once more.
If the diamond is a round cut, a stone weighing a little over 3 carats would have the 9.5mm measurement at the girdle.