Nugget diameters are published for various materials and thicknesses in many locations.
The American Welding Society AWS C1.1 - “Recommended Practices for Resistance Welding” is one of these. Weld schedules including nugget diameters are listed for various materials. How to measure a nugget is also shown in the AWS C1.1 standard.
This blog also describes the method to measure a nugget:
HOW DO YOU MEASURE WELD NUGGETS?
WHAT IS THE FORMULA TO CALCULATE NUGGET DIAMETER IN RESISTANCE WELDING?
There is no formula to calculate a weld nugget.
If one examines the available charts, it is apparent that the weld nugget varies with the size of the electrode weld face and the material thickness. The nugget size varies between about 75 – 90% of the electrode weld face. This is not a formula just an observation.
There is no exact formula to calculate or accurately predict a nugget diameter prior to welding. It can be estimated as pointed out above but there are many variables in every machine set up that can have an effect upon the resultant nugget size.
For a complete understanding of the above values purchase the full AWS Standard with all of the notes and explanations and other material values.
References: AWS – AWS Standard C1.1 “Recommended Practices for Resistance Welding”