A method for producing a bent pipe from thermoplastic material with end cross-sections, central points of which have in relation to one another a positional tolerance on the basis of LN xy/JAR xy/FAR xy in relation to one another. A straight pipe element is introduced into a tool and a portion of the straight pipe element is heated that is located in the bending region to a temperature which lies above a glass transition temperature of the thermoplastic material by a first temperature value. The straight pipe element is bent about the heated bending region of the tool by a freely selectable bending angle, which has a spatial alignment in an XYZ system of coordinates that is fixed with respect to the pipe. The pipe is then cooled below the glass transition temperature by a second temperature value.