A closed-form approximate expression for the optical conductivity of graphene is developed, which generates results with less than 0.8% maximum absolute error for λ>250 nm. The expression takes wavelength, temperature, chemical potential, and hopping parameter into account and provides a fast, easy, and reliable alternative to well-known methods that include singular integrals. Numerical results confirm that the effective complex electrical permittivity derived from the optical conductivity successfully represents this one atom thick material in three-dimensional electromagnetic simulations and analyses.