Hmm, I though he meant Formula Data References because getting the value of an attribute with a FDR is not as obvious.
While you could have an Adhoc Analysis, where a value is calculated but not persisted, I think you are asking about calculated values that are persisted back to a PIPoint. Once a calculated value has been written to a PIPoint, stop thinking of it in terms of an Analysis or a Calculation. Think of it as a PIPoint and/or hopefully an AFAttribute referencing that PIPoint. So now your question is reduced to "How to retrieve values for an AFAttribute or PIPoint using PI Web API?"
I believe Rick_Davin_3.0 answered the first part of the question. With PI Web API, Attribute and PI Point data is available through the Stream and the StreamSet controller with the methods offered by the latter allowing access to multiple streams at a time while the Stream controller offers access to individual streams. Please note that there is read and write methods listed.