Vanadium exists in multiple valence states in silicate and oxide systems, namely V(2+), V(3+), V(4+) and V(5+). This special characteristic has been exploited in several ways to estimate the redox conditions of high-temperature planetary processes, such as partial melting and core formation. However, the use of V as a universal redox indicator (i.e. suitable for the entire range of oxygen fugacities found in the inner Solar System) requires precise knowledge of the partitioning of all of its several valence states. Here we report the results of a series of 1 atm (1300 degrees C) and high-pressure (1-3 GPa, 1315-1450 degrees C) experiments carried out over a range of redox conditions sufficiently large (from QFM-13 center dot 3 to QFM+11 center dot 4, where QFM is the quartz-fayalite-magnetite oxygen buffer) to constrain the full panoply of V chemical behaviour. Partition coefficients between the major upper-mantle minerals (olivine, clinopyroxene, orthopyroxene, spinel and garnet) and silicate melt were precisely measured with laser ablation inductively coupled plasma mass spectrometry for V and other selected heterovalent and homovalent elements (Al, P, Ca, Sc, Ti, Cr, Fe, Ga, Y, Zr and Nb). The particularly large range of redox conditions investigated here enabled concentrations of V(2+) and V(5+) to be constrained along with V(3+) and V(4+), allowing modelling of the change in bulk V partition coefficient with oxygen fugacity to be performed in a robust thermodynamic fashion. As in previous studies, we found a trend of increasing incompatibility from V(3+) to V(4+) to V(5+) for all phases. Partition coefficients for V(2+) can be either higher or lower than for V(3+), depending on the phase. Additionally, we found evidence for changes in the oxidation state of Cr (Cr(2+) Cr(3+)), Fe (Fe(2+) Fe(3+)) and Ti (Ti(3+) Ti(4+)). There is also indication that P may behave as a heterovalent element, occurring as a trivalent cation at very reducing conditions (P(3+) P(5+)). For all other trace elements, the oxidation state remained constant. The data presented here can be used to implement methods of estimating the redox state of mantle and mantle-derived planetary samples from bulk-rock concentration and crystal/melt partitioning with only minor extrapolation and bias, allowing better precision and accuracy than previously possible. The method of estimating the redox conditions of basalt suites from bulk-rock V concentrations relative to homovalent elements with similar compatibility (e.g. V/Sc and V/Ga) was tested using databases for mid-ocean ridge, ocean island and island arc basalts. Within the many assumptions involved in forward trace-element modelling (e.g. degree and style of melting, source composition, constant partition coefficients), we show that the redox states of the source regions of these different types of terrestrial basalts are indistinguishable from each other, having relative oxygen fugacities at similar to QFM +/- 1. The fact that arc magmas have higher Fe(3+)/Fe(2+) ratios than other types of basalts, making them appear to be more oxidized, may be due to late-stage processes rather than derivation from a more oxidized part of the asthenosphere.