The coupling of an electromagnetic plane wave to a thin conductor depends on the sheet conductance of the material: a poor conductor interacts weakly with the incoming light, allowing the majority of the radiation to pass; a good conductor also does not absorb, reflecting the wave almost entirely. For suspended films, the transition from transmitter to reflector occurs when the sheet resistance is approximately the characteristic impedance of free space (Z 0 = 377 Ω). Near this point, the interaction is maximized, and the conductor absorbs strongly. Here we show that monolayer graphene, a tunable conductor, can be electrically modified to reach this transition, thereby achieving the maximum absorptive coupling across a broad range of frequencies in terahertz (THz) band. This property to be transparent or absorbing of an electromagnetic wave based on tunable electronic properties (rather than geometric structure) is expected to have numerous applications in mm wave and THz components and systems.