EngineeringFormulaThermodynamics
Thermal Conductivity Calculator
Back-solve material thermal conductivity from heat-flow data, or use a known k-value to estimate heat rate, heat flux, and thermal resistance.
Thermal conductivity, k, is the material property that tells you how easily heat conducts through a substance. Search intent for this calculator is usually practical: users either have a lab or field measurement and need k = Q̇L/(AΔT), or they know the material and want to estimate the heat flow through a simple slab. This page focuses on that material-property workflow, with common material presets, nearest-material comparison, heat flux, and resistance context alongside the headline k-value.
Q̇ · Measured steady heat flow through the sample.
A · Cross-sectional area perpendicular to heat flow.
ΔT · Use a temperature difference, not absolute temperature.
L · Material thickness in the heat-flow direction.
Steady flat-layer conduction only. For multi-layer walls, surface films, and code-style U-values, use the U-Value Calculator instead.
Solution
Enter heat-flow data or pick a material conductivity to calculate thermal conductivity context.
k = Q̇ L / (A ΔT)
Formula Sheet
- kThermal Conductivity
- Q̇Heat Transfer Rate
- QHeat Energy
- tTime
- AArea
- ΔTTemperature Difference
- LThickness
Common Thermal Conductivity Values
| Material | Typical k | Use |
|---|---|---|
| Dry air | 0.026 W/(m·K) | Still air near room temperature |
| Rigid foam insulation | 0.03 W/(m·K) | Typical closed-cell insulation range |
| Mineral wool | 0.04 W/(m·K) | Common building insulation |
| Softwood | 0.12 W/(m·K) | Across-grain building lumber estimate |
| Water | 0.6 W/(m·K) | Liquid water near room temperature |
| Brick | 0.72 W/(m·K) | Approximate masonry value |
| Glass | 1 W/(m·K) | Soda-lime glass approximation |
| Concrete | 1.4 W/(m·K) | Normal-weight concrete approximation |
| Carbon steel | 50 W/(m·K) | Room-temperature engineering estimate |
| Aluminum | 237 W/(m·K) | Common pure aluminum reference |
| Copper | 401 W/(m·K) | High-conductivity metal reference |
Variables & Units
| Symbol | Variable | Description | Common Units |
|---|---|---|---|
| k | Thermal Conductivity | Material property describing heat conduction ability. | W/(m·K), Btu/(h·ft·°F) |
| Q̇ | Heat Transfer Rate | Steady heat-flow rate through the sample or slab. | W, kW, Btu/h |
| Q | Heat Energy | Total heat transferred over the measurement interval. | J, kJ, Btu |
| t | Time | Measurement interval for heat energy. | s, min, h |
| A | Area | Area normal to heat flow. | m², ft², in² |
| ΔT | Temperature Difference | Temperature drop across the material thickness. | K, °C, °F |
| L | Thickness | Conduction path length through the material. | mm, cm, m, in |
How to Use This Calculator
- 01Use Measured Rate when you already know heat-transfer rate in watts. Enter area, temperature difference, and thickness to solve for material conductivity.
- 02Use Energy Over Time when your experiment reports heat energy over a time interval. The calculator first converts Q/t into watts, then solves k.
- 03Use Known Material when you already know k or choose a material preset. The calculator estimates heat-transfer rate, heat flux, and thermal resistance for the slab.
- 04Use a temperature difference, not absolute hot-side/cold-side temperatures. A 20 °C temperature difference equals a 20 K temperature difference.
- 05Compare the result with the material table. If a measured k-value is far from any expected material, recheck thickness, area, heat-rate, contact losses, and units.
How the Formula Works
For steady one-dimensional conduction through a flat slab, Fourier's law reduces to Q̇ = kAΔT/L. Rearranging gives k = Q̇L/(AΔT).
If heat energy Q is measured over time t, the heat-transfer rate is Q̇ = Q/t before applying the conductivity formula.
The calculator also reports heat flux q'' = Q̇/A = kΔT/L, area-normalized resistance R' = L/k, and total resistance R = L/(kA). These extra outputs help users act on the result instead of seeing only a bare k-value.
Worked Example 01
Back-solve insulation conductivity from measured heat rate
Known
- Heat transfer rate: 80 W
- Thickness: 0.10 m
- Area: 10 m²
- Temperature difference: 20 K
Formula
k = Q̇ L / (A ΔT)
Substitution
k = 80 × 0.10 / (10 × 20)
Result
k = 0.04 W/(m·K)
That value is in the insulation range and close to mineral wool or similar building insulation.
Worked Example 02
Find k from heat energy over time
Known
- Heat energy: 30,000 J
- Time: 10 s
- Thickness: 0.02 m
- Area: 1 m²
- Temperature difference: 30 K
Formula
k = Q L / (t A ΔT)
Substitution
Q̇ = 30000/10 = 3000 W; k = 3000 × 0.02 / (1 × 30)
Result
k = 2 W/(m·K)
The energy measurement is first converted into watts before applying Fourier's law.
Worked Example 03
Copper heat flow through a small bar
Known
- Thermal conductivity: 401 W/(m·K)
- Area: 4 cm²
- Temperature difference: 80 K
- Thickness: 0.20 m
Formula
Q̇ = k A ΔT / L
Substitution
Q̇ = 401 × 0.0004 × 80 / 0.20
Result
Q̇ = 64.16 W
Copper conducts heat strongly even through a relatively small cross-section.
Applications
- 01Back-solving k from a guarded-hot-plate style measurement
- 02Comparing an unknown material result against common insulation, masonry, liquid, and metal values
- 03Estimating slab heat rate and heat flux from a known material k-value
- 04Checking whether a material behaves more like an insulator, masonry, or conductor
Assumptions
- 01Steady one-dimensional conduction through a uniform flat material layer.
- 02Thermal conductivity is constant across the temperature range.
- 03Heat flow is perpendicular to the entered area.
- 04Temperature difference is entered as a positive magnitude.
Where This Model Stops
- 01Does not include convection films, radiation, contact resistance, moisture, thermal bridges, anisotropic materials, or temperature-dependent property curves.
- 02Measured conductivity can be badly skewed by heat loss around sample edges or poor sensor contact.
- 03Use the U-Value Calculator for multi-layer assemblies and the Heat Conduction Calculator for general solve-any-variable Fourier-law work.
References
- [1]Thermal Conductivity - Online Converter
Engineering ToolBox
Reference for thermal conductivity units and common material-property framing.
- [2]
- [3]Thermal Conductivity Calculator
CalculatorLib
Reference for energy-over-time measurement workflow and resistance output.
Frequently Asked Questions
How is this different from the Heat Conduction Calculator?
Heat Conduction Calculator is the broad Fourier-law solver for heat rate, heat flux, area, thickness, and temperature difference. This page is focused on thermal conductivity as a material property, with material presets, nearest-material comparison, and resistance context.
Is thermal conductivity the same as R-value?
No. Thermal conductivity k measures how easily a material conducts heat. Area-normalized resistance is R' = L/k, so thicker layers and lower k-values create higher insulation resistance.
Can I use degrees Celsius for ΔT?
Yes, if it is a temperature difference. A 20 °C difference equals a 20 K difference. Do not enter absolute surface temperatures in this field.
Why does measured k not match the material table?
Common causes are heat leakage around the sample, wrong area or thickness units, transient rather than steady heat flow, moisture, contact resistance, or a material whose k changes with temperature.