Temperature Gradient Converter

What the temperature gradient converter does

The temperature gradient converter changes a rate of temperature change with distance from one unit to another. Enter a value, choose the unit it is in and the unit you want, and press Calculate. It handles °C/m, °C/km, K/m, °F/ft and °F/m, the combinations that appear in meteorology, geology, building physics and heat-transfer work.

How the conversion works

Every input is first converted to °C per metre, then to the target unit. Two facts make it simple. A change of 1 K is exactly a change of 1 °C, so K/m and °C/m are identical. A change of 1 °F is 5/9 of a °C, and a foot is 0.3048 m, so 1 °F/ft = (5/9) ÷ 0.3048 = 1.8227 °C/m.

Worked examples

Why the temperature offset does not matter

Converting a temperature needs the 32-degree offset: 20 °C is 68 °F. Converting a temperature difference or gradient does not, because the offset cancels: a change of 10 °C is a change of 18 °F, and the converter uses only the 9/5 scale factor. Entering a gradient into an ordinary temperature converter is a common error that adds a spurious 32 °F.

Where gradients are used

• Meteorology. The environmental lapse rate determines atmospheric stability. When air cools with height faster than the moist adiabatic rate (about 5 °C/km), it is unstable and thunderstorms can form.
• Geothermal energy and drilling. A gradient of 25 to 30 °C/km means a 3 km well reaches 90 to 100 °C above surface temperature; volcanic regions can exceed 100 °C/km.
• Heat conduction. Fourier’s law gives heat flux q = −k × (dT/dx). The gradient is the driving force; multiply by thermal conductivity to get watts per square metre. The Fourier heat transfer calculator does this directly.
• Building physics. Steep gradients across thin layers, such as a single-glazed window, mean high heat loss and condensation risk on the cold face.
• Materials. Thermal gradients cause differential expansion and stress; glass and ceramics crack when the gradient exceeds what their thermal shock resistance allows.

Common mistakes

• Adding 32 when converting to Fahrenheit. Gradients are differences; only the 1.8 factor applies.
• Mixing km and m. 6.5 °C/km is 0.0065 °C/m, a factor of a thousand.
• Confusing °F/ft with °F per 1,000 ft. Aviation quotes lapse rates per thousand feet; multiply °F/ft by 1,000.
• Treating a gradient as a temperature. The units look similar but describe a slope, not a level.

Related tools

The temperature converter handles absolute temperatures with the proper offsets. The thermal conductivity converter and heat flux converter cover the other quantities in Fourier’s law, and the pressure unit converter is useful alongside lapse rates in atmospheric calculations.

External references

• Wikipedia: Lapse rate
• Wikipedia: Geothermal gradient

Frequently asked questions

Is K/m the same as °C/m?

Yes. A kelvin and a degree Celsius are the same size; only their zero points differ, and zero points cancel in a gradient.

How do I convert °C/km to °F per 1,000 ft?

Multiply by 0.5486. The standard 6.5 °C/km lapse rate is 3.57 °F per 1,000 ft.

What is a typical temperature gradient in a house wall?

With 20 °C inside and 0 °C outside across a 300 mm wall, the average gradient is 67 °C/m, but most of the drop occurs across the insulation layer, where the local gradient can exceed 130 °C/m.

Can the gradient be negative?

Yes. Sign indicates direction. A temperature inversion in the atmosphere has a positive gradient with height instead of the usual negative one.

Does the converter handle °R (Rankine)?

Not as a separate unit, but Rankine degrees are the same size as Fahrenheit degrees, so °R/ft equals °F/ft.