Adding the field to a form design makes it available for all new documents. It will not be on existing documents until they are saved by a user or refreshed by an agent.
Look in the help database to find information about document collections (to select the documents you want to act on) and ComputeWithForm (to evaluate the value based on the field’s formula on the form), then save the documents with the new values.
To be more selective, you could create an agent to select all the documents you want to have the new value and include an agent to compute and populate that one field and save the document. This is generally safer and would have fewer unintended impacts.