Thermal Conductivity Calculator

Compute thermal conductivity (k) or heat transfer rate (Q) using Fourier's law. Real‑time unit conversion and material database. Verified for engineering accuracy.

Q = heat transfer rate (W), k = thermal conductivity (W/(m·K)), A = cross‑sectional area (m²), ΔT = temperature difference (K or °C), L = thickness (m).

Result: 400.0 W/(m·K)
Heat flow Q vs ΔT (fixed k, A, L)
Current ΔT
Common materials at room temperature (W/(m·K)): Copper 400, Aluminum 237, Steel ~50, Water 0.6, Air 0.026, Polyurethane foam 0.03. Click badges above to set k.

Understanding Thermal Conductivity

Fourier's Law of Heat Conduction

The rate of heat conduction through a material is proportional to the temperature gradient and the area perpendicular to the heat flow. For one‑dimensional steady conduction:

Q = -k · A · (dT/dx) → Q = k · A · (ΔT / L)

where k is the thermal conductivity (W/(m·K)), a material property indicating how easily heat passes through. The negative sign indicates heat flows from hot to cold.

Microscopic Origin: Electrons and Phonons

In solids, heat is conducted by two main carriers:

  • Electrons: Dominant in metals. Free electrons transfer kinetic energy efficiently. High electrical conductivity usually correlates with high thermal conductivity (Wiedemann‑Franz law).
  • Phonons: Lattice vibrations. Dominant in non‑metals (e.g., ceramics, polymers). Imperfections and grain boundaries scatter phonons, reducing k.

Gases conduct heat via molecular collisions; their k is low and increases with temperature.

Temperature Dependence

  • Metals: k decreases with temperature (electron scattering increases).
  • Non‑metals: k generally increases with temperature (phonon activity increases).
  • Gases: k increases with temperature (higher molecular speed).
  • Insulators: k often peaks then declines at high T.
Example: Copper k drops from ~400 W/(m·K) at 300 K to ~380 at 500 K.

Measurement Methods

  • Steady‑state methods: Guarded hot plate, heat flow meter – direct application of Fourier's law.
  • Transient methods: Laser flash analysis, hot‑wire method – measure thermal diffusivity and compute k = α·ρ·cp.

Thermal Resistance and Composite Walls

For a slab, thermal resistance R = L / (k·A) (K/W). For multiple layers in series, total R = Σ Ri, and Q = ΔT / Rtotal. This concept is essential in building insulation and heat exchanger design.

Engineering Applications

Heat sinks (electronics)
High‑k materials (Cu, Al) rapidly spread heat; fins increase surface area.
Building insulation
Low‑k materials (fiberglass, foam) trap air to reduce heat loss.
Cryogenics
Multi‑layer insulation (MLI) uses radiation shields and low‑k spacers.
Heat exchangers
Tube materials chosen for high k (metals) to maximize heat transfer.

Thermal Conductivity of Common Materials (at 20°C)

Material k (W/(m·K)) Material k (W/(m·K))
Silver 429 Stainless steel (304) 15
Copper 400 Ice (0°C) 2.2
Gold 318 Glass (soda‑lime) 1.0
Aluminum 237 Brick 0.6–1.0
Brass 109 Water 0.6
Iron 80 Wood (oak) 0.15
Steel (mild) 50–60 Air (still) 0.026

Values are approximate; actual conductivity depends on purity, temperature, and moisture.

Frequently Asked Questions

Thermal conductivity (k) measures how well a material conducts heat. Thermal diffusivity (α = k/(ρ·cp)) measures how quickly heat spreads through a material, combining conductivity, density, and specific heat. High α means rapid temperature change.

This calculator handles single‑layer conduction. For composite walls, you would need to combine thermal resistances (R = L/(kA)) in series and then use ΔT total to find Q. The concept is analogous to electrical resistors.

Air has very low thermal conductivity (~0.026 W/(m·K)) because gas molecules are far apart, limiting energy transfer through collisions. Trapped air (e.g., in foam) provides excellent insulation, provided convection is suppressed.

Kelvin (K) and degrees Celsius (°C) are interchangeable for differences because a change of 1 K equals a change of 1 °C. The calculator treats them the same.

The values are typical at room temperature. Actual conductivity depends on purity, alloy, temperature, and moisture. For critical engineering, refer to material datasheets or standards (e.g., ASTM C518).

Negative ΔT simply indicates the direction of heat flow (from hot to cold). The calculator uses the magnitude; ensure you interpret sign according to your convention (e.g., positive ΔT = hot side minus cold side).