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?"
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?"