How to Calculate GE of Sbox? How to count Gate Equivalent (GE) of Sbox used in block Cipher. For example how much area does the Sbox of Block Cipher Prince take? And How is it calculated?
This basically boils down to find a "good" implementation of the S-box and then compute the GE by weighting the operations used (e.g. XOR = 1GE), that is, as you already commented, synthesize the implementation.

Note that the resulting GE greatly depend on the optimization of your implementation, the technology library used etc.

Wikipedia lists some software for this:


https://en.wikipedia.org/wiki/Logic_synthesis#Commercial_tools_for_logic_synthesis
https://en.wikipedia.org/wiki/Logic_synthesis#Free_tools


I've never used a tool to design an ASIC, I have only some basic experience with FPGA development, so cannot tell you more about the different tools.