The magnetisation and electron spin resonance (ESR) spectrum of two specimens of tetrahedral amorphous carbon (ta-C), deposited from a filtered cathodic arc, were measured over a wide temperature range. The magnetisation was found to consist of superparamagnetic, paramagnetic and diamagnetic contributions. The superparamagnetic contribution resembled that recently found in carbon prepared from the tetrahedrally bonded substance adamantane. We found that the superparamagnetic contribution in ta-C correlated with low-level ferromagnetic contamination and that the properties were well described by the classical Langevin function with a temperature dependent magnetic moment. ESR measurements combined with the magnetisation results for the paramagnetic contribution gave consistent values of the electron spin density which showed a very high level unpaired electrons in ta-C. This high spin density shows that a large fraction of the residual sp2 sites in ta-C are isolated in the sp3 network.