The spindle taper is the tapered socket in the spindle that locates and holds the toolholder. The taper self-centers the tool and transmits cutting torque. Common milling standards are CAT (a.k.a. V-flange, common in North America), BT (metric, common in Asia/Europe) and HSK (a hollow taper that contacts both the taper and the spindle face for higher speed and rigidity).
The number after the letters gives the size — CAT40 and BT40 for general work, CAT50/BT50 for heavy cutting, HSK-A63/A100 for high-speed and 5-axis. Toolholders and spindles must match taper type and size.
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