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As I understood, this tool normally shows distance in the project CRS units, not the geodetic meters (despite it actually says the distance is in meters).

However, now I read (Section III, 4 - Measure some distances) that in the Measure Tool Options you can change the "Ellipsoid for distance calculation":

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Does it mean it can actually finally compute correct geodetic distance?

However, I don't see this option in the QGIS ver 1.9.0-Master.