Since you only give one measurement, one must assume that it is a girdle diameter measurement.
If the stone in question is a round diamond, at this measurement it can be estimated that the diamond weighs between 4 and 5 carats.
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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.
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 measurement across the girdle is between 5.9 mm, which weighs approximately .75 carats, and 6.2 mm, which weighs approximately .85 carats. If the diamond is a different cut, there is not enough information in your question to answer it: other cuts require more than one measurement.
A 2 mm round diamond weighs about .03 carats, so a 1.5 mm round diamond would be smaller than .03 carats. A .01 carat diamond is about as big as a grain of sand.
Forty-five carats is large for any diamond. For reference, a five carat princess cut diamond measures 9.5 x 9.5 mm.