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This paper presents new and simplified formulas for the armature leakage reactance of synchronous machines, and compares the results obtained with tests on 100 machines of varied types. The new formulas are characterized by novel expressions for the end leakage and for the ``air-gap'' or ``differential leakage'' reactances. Formulas for zero phase-sequence reactances are also given. The definitions of armature leakage and armature reaction reactances used are those proposed by Doherty and Nickle in 1926, and as a result the leakage reactance has a much smaller value than has heretofore been assigned to it, thus requiring a rather fundamental revision of the ordinary conceptions of the flux densities existing in the various parts of a loaded synchronous machine.