Geothermal Gradient Calculator
Enter two temperatures and depths to get the geothermal gradient (ΔT/Δz), or a gradient to get the temperature at depth, then turn the gradient into heat flow with a rock's thermal conductivity.
The geothermal gradient is the temperature rise per unit depth: gradient = ΔT / Δz = (T_deep − T_shallow) / (z_deep − z_shallow).
Use the Geothermal Gradient Calculator
Calculator Inputs
Solve for
Mean annual surface temperature at the location
0 for the surface, or the depth of a shallower log reading
Typical continental crust ≈ 25–30 °C/km
Temperature you want to reach at depth
Measured or known temperature at depth (e.g. bottom-hole temperature)
Gradient presets (°C/km)
Result
Enter values and click Calculate to see the result.
Subsurface Temperature
Formula applied
Heat Flow from the Gradient (q = k × ΔT/Δz)
Uses the gradient above. Pick a rock or type your own thermal conductivity k.
Conductive heat flow
—
Temperature at Depth by Gradient (15 °C surface)
T = 15 °C + gradient × depth. Values in °C, with °F in brackets.
| Depth | 20 °C/km 1.10 °F/100 ft | 25 °C/km 1.37 °F/100 ft | 30 °C/km 1.65 °F/100 ft | 40 °C/km 2.19 °F/100 ft | 60 °C/km 3.29 °F/100 ft |
|---|---|---|---|---|---|
| 1 km (3,281 ft) | 35 (95) | 40 (104) | 45 (113) | 55 (131) | 75 (167) |
| 2 km (6,562 ft) | 55 (131) | 65 (149) | 75 (167) | 95 (203) | 135 (275) |
| 3 km (9,843 ft) | 75 (167) | 90 (194) | 105 (221) | 135 (275) | 195 (383) |
| 4 km (13,123 ft) | 95 (203) | 115 (239) | 135 (275) | 175 (347) | 255 (491) |
| 5 km (16,404 ft) | 115 (239) | 140 (284) | 165 (329) | 215 (419) | 315 (599) |
| 6 km (19,685 ft) | 135 (275) | 165 (329) | 195 (383) | 255 (491) | 375 (707) |
Thermal Conductivity of Rocks and Heat Flow at 25 °C/km
Conductivity ranges from Engineering ToolBox (room temperature, no pressure stated); measured values vary with porosity, water content and temperature. Heat flow q = k × 25 °C/km at the middle of each range.
| Rock | k (W/m·K) | q at 25 °C/km | Gradient for 65 mW/m² |
|---|---|---|---|
| Granite | 1.7–4 | 71 mW/m² | 22.8 °C/km |
| Marble | 2.08–2.94 | 63 mW/m² | 25.9 °C/km |
| Slate | 2.01 | 50 mW/m² | 32.3 °C/km |
| Sandstone | 1.7 | 43 mW/m² | 38.2 °C/km |
| Basalt | 1.67 | 42 mW/m² | 38.9 °C/km |
| Limestone | 1.26–1.33 | 32 mW/m² | 50.2 °C/km |
| Sand, saturated | 2–4 | 75 mW/m² | 21.7 °C/km |
| Clay, saturated | 0.6–2.5 | 39 mW/m² | 41.9 °C/km |
| Coal | 0.2 | 5 mW/m² | 325 °C/km |
Mean surface heat flow: about 65 mW/m² over continental crust and 101 mW/m² over oceanic crust, 87 mW/m² globally (Pollack, Hurter & Johnson, 1993, Reviews of Geophysics).
Quick answer
The geothermal gradient is the temperature rise per unit depth: gradient = ΔT / Δz = (T_deep − T_shallow) / (z_deep − z_shallow). In continental crust it is typically about 25–30 °C per km near the surface. Temperature at depth is T = T_surface + gradient × depth, and the conductive heat flow is q = k × gradient, where k is the rock's thermal conductivity in W/m·K.
Examples
| Inputs | Result |
|---|---|
| 15 °C at surface, 105 °C at 3 km | Gradient = 90 / 3 = 30 °C/km (1.65 °F/100 ft) |
| 15 °C surface, 30 °C/km, 4 km deep | T = 15 + 30 × 4 = 135 °C (275 °F) |
| Granite k = 3.0 W/m·K, 25 °C/km | q = 3.0 × 0.025 = 0.075 W/m² = 75 mW/m² |
| Mean continental heat flow 65 mW/m², k = 2.5 | Gradient = 65 / 2.5 = 26 °C/km |
Choose what to solve for, enter your values, then check the heat-flow card below the result.
Summary
The Geothermal Gradient Calculator finds the rate at which temperature rises with depth — the geothermal gradient ΔT/Δz — from two temperature readings, and uses the linear geotherm T = T_surface + gradient × depth to give the temperature at any depth, the depth to a target temperature, or the implied surface temperature. Results are shown in °C/km, °F/mi and °F per 100 ft. A heat-flow card applies Fourier's law, q = k × gradient, with conductivities for common rocks so you can compare your site with average continental (65 mW/m²) and oceanic (101 mW/m²) heat flow.
How it works
- Choose what to solve for: temperature at depth, depth to a target temperature, gradient, or surface temperature.
- Gradient mode uses two readings: an upper temperature at an upper depth (0 for the surface) and a deeper temperature at a lower depth, so gradient = ΔT ÷ Δz. Use it with surface and bottom-hole temperatures or with two points from a temperature log.
- The other modes apply the linear geotherm T = T_surface + gradient × depth and rearrange it.
- Every result is shown in °C/km, °F/mi and °F/100 ft, the unit common in oil and gas well logs.
- The heat-flow card multiplies the gradient by the thermal conductivity k of the rock (Fourier's law, q = k × dT/dz) and compares the result with average continental and oceanic heat flow.
Use cases
- Work out the gradient from a bottom-hole temperature and the mean surface temperature.
- Estimate the temperature at a planned well or borehole depth.
- Find how deep you must drill to reach a target temperature, such as 150 °C.
- Convert a gradient between °C/km, °F/mi and °F per 100 ft.
- Estimate conductive heat flow from a gradient and the rock type, or the gradient implied by a known heat flow.
- Teach the linear geotherm and Fourier's law in earth science classes.