Salesforce formula fields are 'read only' fields, which means that their direct values are not restorable or replicable.
The value (the result) of the formula fields is excluded in the Data backup and instead the "how-to" as a separate item is captured within the Metadata backup.
When restoring or replicating the object’s records which have formula fields, the metadata responsible for the calculation will recreate the result automatically upon insert. You can restore these metadata XMLs with a 3rd party IDE tool (such as Workbench).
Sometimes you may need to access the actual formula from the metadata backup for various reasons such as comparing an older calculation to a recent change or simply for audit purposes.
To access it, simply navigate to the Metadata backup history, select ‘CustomObject’ and download the zip.
Within each object, you will find the formula field calculation in the XML.
In this example, we show a formula calculated on a field in the Case object to determine Case age.