A tool interface that is easy to produce but also precise, for coupling a tool head to a tool shank in a centered manner in respect of a shank axis, comprises a first interface part that is connected to the tool shank or to the tool head, and a second interface part that is connected to the respectively other tool part, namely, to the tool head or to the tool shank. The two interface parts have interface surfaces that substantially complement each other and are intended to bear flatly on each other. The interface surface of the first interface part comprises an inner cone surface and an outer cone surface, which surrounds the latter on the outside and coaxially. The interface surface of the second interface part comprises an outer cone surface, which corresponds with the inner cone surface of the first interface part, and an inner cone surface, which corresponds with the outer cone surface of the first interface part. In the case of a first invention variant, an annular web formed between the inner cone surface and the outer cone surface of the first interface part is slotted by at least one recess. In the case of a second invention variant, the second interface part has a central bore surrounded coaxially by its outer cone surface, an annular web formed between the outer cone surface and this bore being in this case slotted by at least one recess.