The invention relates to a tool adapter which can be fixed to tool machines in a detachable and interchangeable manner, the tool machines being drilling and milling or similar cutting tool machines comprising at least one rotating work spindle. The tool machines are used to receive and position cutting tools, whereby the tool adapter (1) which is made of a spherical section (4) and a cylindrical band (3) is secured to a tool receiving element (2) and the tool receiving element (2) comprises, preferably, a central bore (5) for supplying a coolant. Opposite lying traversal bores (8, 9) which are used to receive clamping bolts (10, 11) are provided in the tool adapter (1) in a tool-sided cylindrical band (3) which is adjacent to the spherical section (4) the band being, preferably, diametrical and comprising a planar system arranged on a tool-sided receiving area and pointing to the tool receiving element (2).