Heat Flow Density Calculator
Find crustal heat flow density from a rock's thermal conductivity and the local geothermal gradient, with a plain-language tectonic-setting classification.
🔥 What is Heat Flow Density?
Heat flow density, also called terrestrial heat flux, is the rate at which thermal energy from Earth's interior conducts outward through the crust, measured per unit surface area. Geophysicists report it in milliwatts per square meter (mW/m2), and it is one of the most fundamental measurements used to characterize a region's thermal and tectonic state.
Heat flow surveys underpin geothermal energy exploration, where high heat flow values point to promising drilling targets. Petroleum geologists use crustal heat flow to model the maturation of organic material into oil and gas over geologic time. Volcanologists and seismologists use regional heat flow maps to trace the thermal signature of subduction zones, rifts, and mantle plumes. Academic geophysicists use compiled global heat flow datasets to test models of mantle convection and plate cooling.
A common point of confusion is treating heat flow density and geothermal gradient as interchangeable. Geothermal gradient (degC/km) describes only how fast temperature rises with depth, while heat flow density (mW/m2) is the actual rate of thermal energy transport, which also depends on how well the local rock conducts heat. Two sites can share an identical gradient yet have very different heat flow if their rock's thermal conductivity differs.
This calculator applies Fourier's law of heat conduction directly to the crust, converting a rock's thermal conductivity and the local geothermal gradient into heat flow density, and adds a plain-language classification of whether the result looks like typical continental crust, an elevated tectonically active setting, or a very high volcanic or ridge-like setting.
📐 Formula
Both q versus G (at fixed k) and q versus k (at fixed G) are straight proportional lines under this direct multiplication, so this page does not include a chart, per the same reasoning used for other single-multiplication relationships on this site: a straight-line "vs" plot adds no shape a reader couldn't already see from the formula itself.
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Typical Continental Crust
k = 2.5 W/m·K (granite/gneiss), G = 30 °C/km
Example 2 — Elevated, Tectonically Active Region
k = 3.0 W/m·K, G = 60 °C/km
Example 3 — Very High, Volcanic/Ridge Setting
k = 2.0 W/m·K, G = 160 °C/km
❓ Frequently Asked Questions
🔗 Related Calculators
What is heat flow density in geophysics?
Heat flow density (or heat flux) is the rate at which thermal energy conducts outward through Earth's crust per unit area, usually reported in milliwatts per square meter (mW/m2). It's the standard measurement geophysicists use to characterize a region's thermal state and tectonic activity.
What is the formula for heat flow density?
Heat flow density follows Fourier's law of heat conduction applied to the crust: q = k x G, where k is the rock's thermal conductivity in W/m*K and G is the local geothermal gradient in degrees C per kilometer. The result comes out directly in mW/m2.
Why does q = k times G work directly in mW/m2 without extra conversion?
It's a convenient unit cancellation. Converting G from degC/km to degC/m divides by 1000, giving q in W/m2. Converting that q to mW/m2 multiplies by 1000. The two factors of 1000 cancel exactly, so q in mW/m2 equals k in W/m*K times G in degC/km with no leftover conversion factor.
What is a typical continental heat flow value?
Typical continental heat flow ranges from roughly 40 to 120 mW/m2, with old stable cratons near the low end and tectonically active regions, rift zones, and areas with elevated radiogenic heat production running higher within that band or above it.
Why is heat flow much higher near mid-ocean ridges?
Mid-ocean ridges are where new oceanic crust forms from upwelling magma, placing hot material very close to the seafloor. Heat flow there can exceed 300 mW/m2, several times the continental average, and it decreases steadily as the crust ages and moves away from the ridge.
What thermal conductivity should I use for common rock types?
Granite and gneiss typically run 2.5 to 3.5 W/m*K, basalt around 1.5 to 2.5 W/m*K, and shale or unconsolidated sediment often below 2 W/m*K. Use a lab-measured value for your specific rock sample when precision matters, since conductivity also varies with porosity and water content.
Is heat flow density the same as geothermal gradient?
No. Geothermal gradient (degC/km) measures how fast temperature rises with depth, while heat flow density (mW/m2) is the actual rate of thermal energy transport, which also depends on the rock's thermal conductivity. Two locations can share the same gradient but have very different heat flow if their rock conductivities differ.
How is heat flow density measured in the field?
Geophysicists measure a borehole's temperature gradient with downhole sensors, then measure or estimate the rock's thermal conductivity from core samples in the lab, and multiply the two per Fourier's law, exactly the calculation this calculator performs.
Why do old cratons have low heat flow?
Ancient continental cratons have had hundreds of millions to billions of years to cool and lose their original formation heat, and their thick, stable lithosphere insulates the surface from deeper mantle heat, so measured heat flow there often falls toward the low end of the continental range.
Can heat flow density be negative?
In this simple conductive model, no, heat flow density is always positive since it assumes heat flows outward from a hotter interior to a cooler surface. In reality, highly localized measurements can occasionally show apparent negative flux due to convective or transient effects, but the steady-state conductive model used here always returns a positive value for positive conductivity and gradient.