Geothermal Gradient Calculator

The geothermal gradient is the rate at which rock temperature rises with depth, so temperature at depth is surface temperature plus gradient times depth in kilometres: 12 degrees C at surface with a gradient of 35 degrees C/km reaches 152 degrees C at 4,000 m. The continental average is 25 to 30 degrees C/km. The gradient is not a property of depth alone but the ratio of heat flow to thermal conductivity, G = q/k, so a shale-filled basin with conductivity near 1.5 W/m/K develops a much steeper gradient than a quartzite section near 6 W/m/K carrying exactly the same heat flux. Roughly half of that flux comes from radiogenic decay of uranium-238, thorium-232 and potassium-40 in the crust and mantle, the remainder from primordial and core heat. Gradients cluster by tectonic setting: 10 to 20 degrees C/km on ancient shields such as the Canadian and West African cratons, 20 to 30 in normal continental crust, 30 to 50 in rifts and thinned crust like the Basin and Range, and above 50, occasionally above 100, in volcanic provinces such as Iceland and the Taupo zone. That distinction drives economics, because conventional flash power plants want resource temperatures above about 150 degrees C, binary organic Rankine units work down to roughly 90 degrees C, and anything cooler is limited to direct-use heating. The linear model has clear limits: gradients flatten with depth as conductivity and radiogenic content change, groundwater circulation can locally invert them, and shallow borehole readings stay disturbed for months after drilling.

Miners knew deep workings were hot long before anyone measured them properly. Systematic borehole and mine-shaft temperature observations across Europe in the eighteenth and nineteenth centuries converged on an increase of roughly 1 degree C per 30 metres. Joseph Fourier supplied the mathematics in his 1822 Theorie analytique de la chaleur, which gave conduction the differential equation still underlying gradient interpretation. William Thomson, later Lord Kelvin, used the observed gradient in 1862 to estimate the age of the Earth by treating the planet as a body cooling from an initially molten state, arriving at figures of tens to a few hundred million years. Kelvin's answer was wrong, and the reason - radioactivity supplying heat continuously - emerged after 1903, when the heat output of radium was measured, and through R.J. Strutt's surveys of radioactive element concentrations in rocks from 1906. That reframed the gradient as a steady-state balance rather than a relic of cooling. Exploitation followed quickly: Piero Ginori Conti generated electricity from natural steam at Larderello in Tuscany in 1904, and a commercial plant opened there in 1913. Reykjavik began piping geothermal water for district heating in the 1930s, and The Geysers field in California started generating in 1960. Petroleum drilling later supplied bottom-hole temperatures in bulk, and Horner-plot corrections for drilling disturbance became standard practice for extracting true formation gradients from them.