A planar antenna for a radio frequency identification tag which receives or transmits an electromagnetic signal is provided. The planar antenna comprises a dielectric slab and a fractal dipole antenna. The height of the fractal dipole antenna is 0.3 to 0.7 times of the half wavelength of the electromagnetic signal, and the width of the fractal dipole antenna is 0.7 to 1.1 times of the half wavelength of the electromagnetic signal. The planar antenna achieves miniaturization and a good matching by utilizing the optimal size of the fractal dipole antenna.