  Key questions for any superconductor include: what is its maximum
dissipation-free electrical current (its `critical current') and can this be
used to extract fundamental thermodynamic parameters? Present models focus on
depinning of magnetic vortices and implicate materials engineering to maximise
pinning performance. But recently we showed that the self-field critical
current for thin films is a universal property, independent of microstructure,
controlled only by the penetration depth. Here we generalise this observation
to include thin films, wires or nanowires of single- or multi-band s-wave and
d-wave superconductors. Using extended BCS theory we consider dissipation-free
self-field transport currents as Meissner-London currents, avoiding the concept
of pinning altogether. We find quite generally, for type I or type II
superconductors, the current is limited by the relevant critical field divided
by the penetration depth. Our fits to 62 available data sets, from zinc
nanowires to compressed sulphur hydride with critical temperatures of 0.65 to
203 K, respectively, are excellent. Extracted London penetration depths,
superconducting energy gaps and specific heat jumps agree well with reported
bulk values. For multiband or multiphase samples we accurately recover
individual band contributions and phase fractions.
