A method is developed for computing the sizes of surface
cracks in magnetic materials. The method is applicable to a crack with varying width along the crack depth, and is based on measuring leakage magnetic field by Hall element probe. New analytical expressions are derived for the z-component of the intensity of the leakage magnetic field of a surface
crack with linearly varying width. Computations are performed for sizing of several such cracks with complex cross-sections, and unknown shapes. The computed results show that reasonably precise sizing can be achieved for all of the investigated cracks.