Comment by mannykannot

This is not quite the same situation, as you are calculating a value having a dimension (that of power, or energy per second) three different ways using a single consistent system of units, and getting a result demonstrating / conforming to the conservation of energy. If you were to perform one of these calculations in British imperial units (such as from pressure in stones per square hand and rate of flow in slugs per fortnight) you would get a different numerical value (I think!) that nonetheless represents the same power expressed in different units. The article, however, is discussing a dimensionless ratio between a dimensionless constant and a physical measurement that is specific to one particular planet.