We derive physics-based formula of current-voltage characteristic for resonant tunneling diodes (RTDs) by using the Voigt function. The Voigt function describes the mixing condition of homogeneous and inhomogeneous broadenings of peak energy width in transmission probability, which is sensitively reflected to nonlinear negative differential resistance of RTDs. The obtained formula is applicable to the SPICE model of RTD without performing numerical integrals. We indicate validity of the formula by comparing to measured data for double-barrier and triple-barrier RTDs.