For the tritium assay at the Tritium Laboratory Karlsruhe (TLK) which started operation in Nov. 94 an isothermal shield calorimeter was built. The calibration of the calorimeter was performed with an electrically heated simulator covering the range between 1 mW and about 2 W. After the calibration tritium activities in four Amersham uranium getter containers were determined The excellent reproducibility and high precision of the measurements with the KfK-calorimeter was shown.The tritium activity inventories could be determined with relative standard deviations from the average value of the order of 0.01% to 0.1% depending on the activity level.These results demonstrate the suitability of the KfK-calorimeter as a nondestructive method for a careful assay of tritium.