A princess cut of one carat measures 5.5mm x 5.5mm; one half carat of this cut measures 4.4mm x 4.4mm. Your diamond is about half way in between these weights, and may weigh about .75 carat.
A certified gemologist can give you an exact weight.
This diamond could weigh about six carats if its measurement is 10mm x 10mm.
Forty-five carats is large for any diamond. For reference, a five carat princess cut diamond measures 9.5 x 9.5 mm.
If the diamond measures 7.5 x 7.5 mm, the diamond may weigh about two carats. You can ask a certified gemologist to weigh the diamond for an exact carat weight.
Carats measure the weight of the diamond, regardless of its cut. A trustworthy gemologist will remove the stone from its setting, weigh it, and remount it, for a fee.
A round cut diamond weighing .25 carats measures 4.1mm at the girdle.
A round cut diamond weighing .25 carats measures 4.1mm at the girdle.
Your answer depends on the cut you are measuring. If the gem is a round cut, the carat weight will be about .10 carats.
If the diamond is a round cut, a stone weighing a little over 3 carats would have the 9.5mm measurement at the girdle.
One kilo equals 5,000 carats regardless of the colour or cut of diamond.
If the diamond is a round brilliant cut, this measurement at the girdle indicates that it could weigh between .20 carats (3.8 mm) and .25 carats (4.1 mm). If the diamond is of a different cut, a jeweler can remove the diamond and give you the exact carat weight.
If the diamond is a round brilliant cut, the 3mm measurement at the girdle indicates that the diamond weighs about 1/10th of a carat, or .10 carats.
Both Asscher cut and Princess cut diamonds have at least one measurement that is 5mm, and both with this perimeter weigh in the one carat range. ('Square' diamond is a description for a rather generic cut.) A certified gemologist can give you an exact weight for your diamond.