A new method for mass flow measurement of fluids in pipes is presented; its novelty lies in the capability for intrinsic calibration. The method is founded on a concept, where two independent analytic expressions for the flow rate are formed from the same direct measurement readings (input parameters). If the input parameters were error-free, the two expressions would yield identical results, by definition. This fact can be used as goal function in a minimization routine that removes systematic errors of the inherently error-prone input parameters. The uncertainty of the mass flow measurement is then only influenced by statistical effects and is typically less than 1% with regard to the measured value. The new method is explained by a proof-of-principle that is based on measurements in a large-scale cryogenic system. The intrinsic calibrations can be executed in situ at any moment during operation of a plant, and with no need for a reference standard. While the new method is applicable in any system involving single-phase fluid flow, it offers particular advantages in cryogenic application.