The relation between the technological parameters of cutting and the tool life is important information that has been described by several functions since the publication of the Taylor formula. Although the vc-T cutting speed-tool life curve has local extremes, the Taylor formula can describe correctly only its monotone decreasing phase, and this is typical also for the vc-T function proposed by different researchers. This paper describes the results of studies aimed at analysing the relationship proposed by Kundrák and applicable throughout the interval of the vc-T curve. It introduces cutting speed ranges, analyses their boundaries and explores the relationship between constants of the new vc-T formula and the exponent k of the Taylor formula valid for section III. These findings were verified by experiments executed on hardened steel type 100Cr6 (HRC 60 ± 2) by K10 type CBN tool.