Calculate k, Heat Flow, Area, Thickness or ΔT | Fourier's Law of Conduction
Result
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📝 Step-by-step solution
Select what to calculate and enter values
💡 k in W/(m·K) | Q in Watts (W) | A in m² | L in meters (m) | ΔT in Kelvin (K) or °C
📖 What is Thermal Conductivity?
Thermal conductivity (k) is a material property that measures how well a material conducts heat.
It is defined as the amount of heat (in Watts) that passes through a 1 m² area of material that is 1 m thick
when the temperature difference across the material is 1 Kelvin.
Materials with high k (metals like copper, aluminum) are excellent conductors, while
materials with low k (wood, foam, air) are good insulators.
🧮 Fourier's Law Formula
Q = k × A × ΔT / L
Rearranged: k = Q × L / (A × ΔT) A = Q × L / (k × ΔT) L = k × A × ΔT / Q ΔT = Q × L / (k × A)
Where:
Q = Heat flow rate (W)
k = Thermal conductivity (W/(m·K))
A = Cross-sectional area (m²)
ΔT = Temperature difference (K or °C)
L = Material thickness (m)
📝 Worked Example
Example: Heat Loss Through a Glass Window
Given: Glass window 1 m² area, 5 mm thick (L = 0.005 m),
thermal conductivity k = 0.8 W/(m·K), temperature difference ΔT = 20°C
Formula: Q = k × A × ΔT / L Calculation: Q = 0.8 × 1 × 20 / 0.005 = 3200 W Result: Heat loss through the window is 3200 W (3.2 kW).
📊 Common Thermal Conductivity Values
Material
k (W/(m·K))
Type
Silver
429
Metal
Copper
401
Metal
Aluminum
237
Metal
Steel (carbon)
~50
Metal
Stainless Steel
~16
Metal
Glass
~1.0
Insulator
Water
0.6
Fluid
Brick
~0.7
Building
Wood (oak)
~0.17
Insulator
Fiberglass
0.04
Insulator
Air
0.026
Gas
Vacuum Panel
0.005
Insulator
💡 Real-World Applications
Building insulation — choosing materials with low k to reduce energy costs.
Heat sinks — using high-k metals to dissipate heat from electronics.
Thermal barriers — aerospace and automotive heat shielding.
Cooking — cast iron (high k) vs ceramic (low k) cookware performance.
HVAC design — estimating heat loss/gain through walls and windows.
⚠️ Limitations & Assumptions
📌 Important Notes
Assumes steady-state heat conduction (no time variation).
Assumes uniform material with constant k (k varies with temperature).
Does not account for convection or radiation losses.
Assumes 1D heat conduction — real objects may have multi-dimensional flow.
Does not include thermal contact resistance at interfaces.
Results are theoretical estimates — real-world values may vary.
📚 Sources & References
Authoritative Sources
Incropera & DeWitt — Fundamentals of Heat and Mass Transfer
NIST — Thermophysical Properties of Matter
ASHRAE Handbook — Fundamentals
CRC Handbook of Chemistry and Physics
Engineering Toolbox — Thermal Conductivity of Common Materials
❓ Frequently Asked Questions
What is the SI unit of thermal conductivity?
The SI unit is Watt per meter-Kelvin (W/(m·K)). It represents how many watts of heat
pass through a 1-meter-thick material with 1 m² area per 1 Kelvin temperature difference.
Why is thermal conductivity important?
It determines how quickly heat flows through materials. Engineers use it to design insulation,
heat sinks, thermal barriers, and HVAC systems efficiently.
Does thermal conductivity change with temperature?
Yes. For most metals, k decreases slightly as temperature increases. For gases, k increases with temperature.
For building materials, the change is often small but should be considered in precision work.
What is the difference between conductivity and resistivity?
Thermal conductivity (k) measures how well a material conducts heat.
Thermal resistivity (R) is its reciprocal (R = 1/k) — a measure of how well it resists heat flow.
What is the difference between thermal conductivity and thermal resistance?
Thermal conductivity (k) is a material property (intrinsic).
Thermal resistance (R) depends on both material and geometry: R = L / k.
A thick piece of the same material has higher thermal resistance.
This Thermal Conductivity Calculator is provided for informational and educational purposes only.
Results are based on Fourier's law under steady-state, 1D, uniform-material assumptions.
Real-world heat transfer is more complex and may involve convection, radiation, contact resistance,
and temperature-dependent material properties. Always verify critical engineering calculations
with appropriate software or a qualified engineer.