A simply and analytical formula of the axial light intensity distribution behind a circular aperture is derived by using the Helmhotz-Kirchhoff integral theorem and the Kirchhoff' s boundary conditions. It is studied the nonparaxial on-axis intensity distribution throughout the whole space behind a circular aperture. An accurate formula to calculate the Fresnel number of circular aperture is presented and the validity of usual Fresnel number formula is reexamined. By using the analytical formula and diffraction integral formula,some numerical simulation comparisons are done,and it is shown that the results of the two methods are completely coincident.