In the critical state model, the critical current, Ic, of a superconductor defines the upper limit of dissipation-free current flow. However conventional transport Ic measurements of practical superconductors rely on the detection of a voltage drop along the length of the conductor. This requires that the superconductor has entered the dissipative regime, and hence inherently over-estimates the current at which geometric saturation occurs. Nonetheless, the convenience of the 1 µV cm⁻¹ criterion means that it has become the widely adopted definition of transport Ic. Here, we present an alternative definition for the transport critical current of a superconducting tape under self-field conditions, which is based on the concept of geometric current saturation across the full cross-sectional area. This saturation threshold can be experimentally determined through simple Hall sensor measurements of the evolving perpendicular magnetic field at the tape surface. The surface field exhibits a signature transition when the transport current increases beyond the current-saturation threshold. We present an analytical model which describes this effect and defines the critical saturated current as a function of d^2 B⊥/d It^2. This definition is first validated using finite element (FE) modelling, and then experimentally demonstrated through measurements on a variety of commercial REBCO and Bi-2223 tapes of differing widths. It is found that the 1 µV cm⁻¹ criterion consistently leads to an overestimation of the saturated critical current by ~15% in REBCO tapes, and up to 30% in a Bi-2223 tape. FE modelling indicates that this overestimate is most prominent in superconductors exhibiting a low n-value (i.e. n ≲ 20). A key advantage of the measurement approach presented here is that it allows the unambiguous measurement of a transport Ic value to be completed at lower currents, without entering the dissipative region in which sample damage can occur. There are also implications as to the correct choice of Ic value which should be employed within the well-known Norris and Brandt equations for AC loss.