We develop a theory for scaling properties of quantum transport in nano-field effect transistors. Our starting point is a one-dimensional effective expression for the drain current in the Landauer-Büttiker formalism. Assuming a relatively simple total potential acting on the electrons the effective theory can be reduced to a scale-invariant form yielding a set of dimensionless control parameters. Among these control parameters are the characteristic length l and -width w of the electron channel which are its physical length and -width in units of the scaling length . Here is the Fermi energy in the source contact and is the effective mass in the electron channel. In the limit of wide transistors and low temperatures we evaluate the scale-invariant i-v characteristics as a function of the characteristic length. In the strong barrier regime, i. e. for long-channel behavior is found. At weaker barriers source-drain tunneling leads to increasingly significant deviations from the long-channel behavior.