"Real" output is calculated, not measured

Real GDP cannot be measured. It must be calculated.

I found a great statement to that effect from Statistics Canada. It's got a technical tone to it, but the meaning is clear:

Growth in the gross domestic product (GDP) or any other nominal value aggregate can be decomposed into two elements: a "price effect", or the part of the growth linked to inflation, and a "volume effect", which covers the change in quantities, quality and composition of the aggregate. The volume effect is presented in the National Accounts by what is referred to as the "real" series (such as the real GDP).
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Statistics Canada uses the chain Fisher index as a measure of real GDP. Following the same sequence that we used with Equation (4), chaining Equation (6) gives us:

(7)

This is the formula used as the basis of the calculations of real GDP at both the national and provincial levels.

In case you were wondering.