New dimensions and loss of weight obtained by recutting damaged brilliants are arrived at by the same methods as used for recutting oldcuts. Depending on the damage of the diamond, the total height or the girdle diameter of the stone must be adjusted.
Brilliants with damage to their girdle because of nicks, fractures, or cleavage cracks have been reduced in their diameter. Therefore the height has become too large in proportion to their diameter.
A new height must be established:
The girdle diameter is measured in millimeters up to begin of damage (Fig 398); this measurement AB = 100 % is used to calculate the new height according to the formula:
Height = R Ø _{(up to damage)} X 0.62 

Fig 398 Diagram showing the repair of a brilliant with damaged girdle 
Then the weight is calculated according to known formula, The loss of weight depending on dimension and size of damage and existing proportions of the damaged stone amounts to about 1025%.
Brilliants with a damaged culet show too small a total height in proportion to their girdle diameter; the latter must be reduced to obtain again ideal proportion.
A new girdle diameter must be established
The total height in millimeters
from the table to the begin of the damaged culet is measured
(Fig 399). This measurement AB = 58 % is taken to calculate a
new girdle diameter according to the formula: R Ø = height_{(up to damage)} x 100/58 

Fig 399 Diagram showing the repair of a brilliant with damaged culet 
The loss of weight is about 1030 % depending on dimensions of damage. The loss of weight is calculated according to the formula:
loss of weight x100 / old weight
Example  
old weight  2.80 ct  
new weight  1.90 ct  0.90 ct / 2.80 ct x100 = 32.1% 
loss of weight  0.90 ct 
On the following page the possibilities of recutting and repairing are summarized in table form.
In the case of fancy cuts the damage usually occurs on the culet or at the pointed end of the girdle caused by setting or knocking during wear; recutting is essential. Frequently other shapes are then cut instead of just repairing the stone. A drop or navette damaged at the point of the girdle becomes a brilliant, a damaged emerald cut as a carré or trapeze. It is very difficult therefore to calculate the recutting, and it is advisable to first consult a diamond cutter.
Modernizing Old Cut  Diamond imitations 