A tire pressure calculator for race and triathlon bikes. Based on the Frank Bertho calculator. I get the impression that the pressure is a bit on the low side but that’s for your own optimization. Adding a bit for more speed and lowering for more comfort is a common approach.
This is based on the assumption that the tire should compress about 15% in height. To me it is not (yet) clear what this means for tubeless or tires with inner tubes. Some sources mention that the pressure with tubeless tires is even lower. So, this cannot be considered as the final and optimal calculator. The weigth of the bike should be including the water bottles and such and the rider needs to be with all his/her gear. So don’t use the nett bike weight and the unclothed rider.
Recommended pressure (bar)  
Rear5.3 
Front6.2 
Weight 

kg  kg 
Weight distribution 

%  % 
Tyre size 

Rear  Front 
The code to create the above calculator is largely based on the work of Joakim Roubert. All of these calculations are based on the graphs below. Note that the wheel load is presented on the xaxis so the pressue is depending on the weight distribution. On my triathlon bike I measured it to be 45% of the weight on the rear wheel and 55% on the front wheel. Hence the default value of the form above.
These are the relations between load and pressure, using simple linear eqations y = a·x + b where y represents the pressure in bar and x the wheel load. With this you can create your own overview if you like.
width a b
20 0.206850 0.68958
23 0.175000 0.80000
25 0.150000 0.75000
28 0.116670 0.10000
32 0.092917 0.30417
37 0.055158 0.50000
References
Herse, Rene, Science and Bicycles 1: Tires and Pressure