For a given Dirac operator we use the noncommutative residue to define certain functionals of differential forms which yield such tensors as: metric, Einstein, and torsion. We generalise these concepts in non-commutative geometry and show e.g. that for the conformally rescaled noncommutative 2-torus the Einstein and the torsion functionals vanish. Also the Hodge-de Rham, Einstein-Yang-Mills, and quantum SU(2) group spectral triples are torsion free, while the almost commutative 2-sheeted manifold has torsion. Based on Adv.Math. 427, 1091286 (2023); Commun.Math.Phys. 130 (2024) and JNCG DOI 10.4171/JNCG/573 (2024) with A. Sitarz and P. Zalecki.