Heat Flow From Gradient and Conductivity Calculator

Terrestrial heat flow is the conductive flux of thermal energy escaping through the Earth surface, and it follows Fourier law of heat conduction: the flux equals thermal conductivity multiplied by the temperature gradient. The negative sign in the physics convention simply records that heat moves down the temperature gradient, and it is dropped here because the geothermal gradient is defined as positive downward. The unit arithmetic is convenient: conductivity in watts per meter per kelvin multiplied by a gradient in degrees C per kilometer yields the answer directly in milliwatts per square meter, since the factor of 1000 for kilometers cancels the factor of 1000 for milliwatts. Continental heat flow averages roughly 65 mW/m2 and oceanic heat flow roughly 100 mW/m2, giving a global mean near 87 mW/m2 and a total planetary heat loss of about 46 terawatts. The two inputs carry very different uncertainty. Gradients are measured directly in boreholes and are usually reliable to a few percent, while conductivity must be measured on recovered core with a divided-bar or needle-probe apparatus and can vary by a factor of four across lithologies: about 1.5 to 2.5 W/m/K for shale and basalt, 2.5 to 3.5 for granite, and 5 to 7 for quartzite, because quartz is an exceptionally good conductor. Shales are also anisotropic, conducting better parallel to bedding than across it. The calculation assumes steady-state pure conduction, which fails where groundwater advection redistributes heat, where recent sedimentation or erosion has not thermally equilibrated, or where surface temperature has changed. Pleistocene glaciation still perturbs profiles above roughly 300 m, so reliable determinations use deeper intervals.

Interest in the Earth thermal gradient predates heat flow as a discipline. Mine and borehole temperature observations through the eighteenth and nineteenth centuries established that temperature rises with depth, and in 1862 William Thomson, later Lord Kelvin, used the gradient together with a cooling-sphere model to argue that the Earth was only 20 to 400 million years old. That estimate collapsed after Becquerel discovered radioactivity in 1896 and R. J. Strutt showed in 1906 that radiogenic heat production in crustal rocks supplies a continuous internal source Kelvin had not accounted for. Measuring the flux rather than the gradient required pairing borehole temperatures with conductivity measurements on the same rocks. Edward Bullard made pioneering determinations in South African boreholes published in 1939, and comparable British measurements followed shortly after. The oceanic revolution came around 1950 to 1954, when Bullard, together with Roger Revelle, Arthur Maxwell and later Richard Von Herzen, developed probes that could be lowered into soft seafloor sediment to record gradient and conductivity in situ. The resulting discovery that heat flow is high at mid-ocean ridges and declines with crustal age became strong evidence for seafloor spreading. The International Heat Flow Commission was established in 1963 under the International Union of Geodesy and Geophysics and has curated the global database ever since. In 1968 Roy, Blackwell and Birch demonstrated the linear relation between surface heat flow and near-surface radiogenic heat production that still underpins crustal thermal modeling.