A lathe is a machine tool that can creates a symmetrical workpiece by spinning it on an axis while performing various task such as cutting, knurling, sanding and drilling. A Morse taper is a part that makes it easier to fit the tapered spindle, which mounts tools such as arbors, drill chucks and lathe centres. They come in standard sizes determined by numbers starting from zero, with most lathes using sizes 1 or 2. You can determine its size by the size of its tail stock.
Remove the Morse taper from the lathe by firmly pulling it from its holder.
Hold a ruler marked with millimeters across the end of the tail stock's opening.
Place the start of the ruler on one side of the opening and note the distance to the other side of the opening. A tail stocks that is about 12 mm would be a No. 1 Morse taper. If it's about 18 mm, its a No. 2 Morse taper.
Ensure you correctly measure the size of the tail stock, as not all Morse tapers fit all lathes.