Abstract: Through the basic way and no use of Stokes＇ formula,the calculation formula of the surface density of circulation of the vector field is derived. It is pointed out that at the same point the surface density of circulation of the vector field f（ r,t） surrounding the different axis is different,the size ofΔ× f is equal to the maximum of the surface density of circulation,the direction of theΔ× f is along thus a axis when the loop winds this axis,the surface density of circulation maximize,the surface density of circulation that winding the axis n is equal to the weight of theΔ× f along axis n. Thus a vector fieldΔ× f is called the curl of f（ r,t）. A mistake is pointed out,that ones often make when they calculate the line integral which vector field is along a infinite short line segment.

Key words: vector field, the surface density of circulation, curl