Decompression melting of the upper mantle produces magmas and volcanism at the Earth's surface. Experimental petrology demonstrates that the presence of CO2 and H2O enhances peridotite melting anywhere within the upper mantle down to approximately 200–300 km depth. The presence of mantle melts with compositions ranging from carbonate-rich to silicate-rich unavoidably affects the geophysical signals retrieved from Earth's mantle. Geochemical investigations of erupted intraplate magmas along with geophysical surveys allow for constraining the nature and volume of primary melts, and a sound formalism is required to integrate these diverse datasets into a realistic model for the upper mantle including melting processes. Here, we introduce MAGLAB, a model developed to calculate the composition and volume fraction of melts in the upper mantle, together with the corresponding electrical conductivity of partially molten mantle peridotites at realistic pressure-temperature conditions and volatile contents. We use MAGLAB to show how the compositions of intraplate magmas relate to variations in lithosphere thickness. Progressive partial melting of a homogeneous peridotitic mantle source can in theory create the diversity of compositions observed among the spectrum of intraplate magma types, with kimberlite melts beneath thick continental shields, alkaline magmas such as melilitite, nephelinite and basanite beneath thinner continents and relatively old plus thick oceanic lithospheres, and ‘regular’ basalts beneath the youngest and thinnest oceanic lithospheres as well as beneath significantly thinned continental lithospheres. MAGLAB calculations support recent experimental findings about the role of H2O in the upper mantle on producing primary kimberlitic melts in addition to CO2. We demonstrate the robustness of MAGLAB calculations by reproducing the compositions of erupted melts as well as associated mantle electrical conductivities beneath the Society hotspot in the Pacific Ocean. A comparison of our simulations with magnetotelluric surveys at various oceanic settings shows that the heterogeneities in electrical conductivity of Earth's upper mantle are related to variations in volatile content via the presence of small (generally <<1 wt%) and heterogeneously distributed fractions of CO2-H2O-bearing melts.