Amethyst and Quartz have the same specific gravity so their face-up size
depends on the weight, shape and proportions of the cut. Face-up area is a measure of the size of the gem when viewed from above (as set in a ring).
It tells you how big the gem is at the girdle plane.
0.5 Ct Amethyst (Cushion)
1 Ct Quartz (Round)
5.09×5.09 mm →
36.96 mm² ← 6.86×6.86 mm
0.5ct Amethyst Cushion (5.09×5.09mm)
1ct Quartz Round (6.86×6.86mm)
Difference: 58% (13.64 mm²)
1ct Quartz Round (6.86×6.86mm) has approx. 58% more face-up area than 0.5ct Amethyst Cushion (5.09×5.09mm).