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Signed Conduction Heat Flux & Temperature Gradient

Solve one-dimensional heat flux, conductivity, temperature difference or thickness with temperature-interval units.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

With k = 2 W/(m·K), ΔT = 10 K and Δx = 0.5 m, signed heat flux is −40 W/m².

q = −k ΔT / Δx

Worked example

Enter these known values and leave the other values blank.

Thermal conductivity constant (λ)
2 W/(m·K)
Temperature difference (ΔT)
10 °C
Distance (Δx)
.5 m
Heat flux (q)
-40 W/m²

Assumptions and limitations

  • Heat flux is signed per unit area. The negative sign indicates flow opposite the increasing-temperature direction. Multiply flux by area separately for heat transfer rate.
  • Assumes steady, one-dimensional conduction through a uniform material with constant nonnegative conductivity and positive thickness.
  • Temperature difference uses interval conversions: a change of 18°F equals 10 K, without a 32-degree offset. BTU choices use the International Table definition.

Common questions

What should I check before using this result?

Heat flux is signed per unit area. The negative sign indicates flow opposite the increasing-temperature direction. Multiply flux by area separately for heat transfer rate.

References

Bookify uses the exact International Table BTU for heat-flux units and interval temperature conversions. BTU-based thermal units use the International Table BTU and exact mass, time, length and temperature-interval definitions.

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