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physics

Thermal Conductivity Calculator

Calculate the rate of heat transfer through a material using Fourier's law Q/t = kA(ΔT)/d. Determine heat flow through walls, insulation, and other barriers for building science and engineering.

Reviewed by Christopher FloiedUpdated

This free online thermal conductivity calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Thermal Conductivity Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

The Thermal Conductivity Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

Formula Reference

Thermal Conductivity Calculator Formula

See calculator inputs for the governing equation

Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.

When to Use This Calculator

  • Use the Thermal Conductivity Calculator when you need accurate results quickly without the risk of manual computation errors or unit conversion mistakes.
  • Use it to verify calculations made by hand or in spreadsheets — an independent check can catch errors before they lead to costly decisions.
  • Use it to explore how changing input parameters affects the output — a quick way to develop intuition and identify the most influential variables.
  • Use it when collaborating with others to ensure everyone is working from the same numbers and applying the same assumptions.

About This Calculator

The Thermal Conductivity Calculator is a free, browser-based calculation tool for engineers, students, and technical professionals. Calculate the rate of heat transfer through a material using Fourier's law Q/t = kA(ΔT)/d. Determine heat flow through walls, insulation, and other barriers for building science and engineering. It implements standard formulas and supports both metric (SI) and imperial unit systems with automatic unit conversion. All calculations are performed instantly in your browser with no data sent to a server. Use this calculator as a quick reference and sanity-check tool during design, analysis, and learning. Always verify results against primary engineering references and applicable standards for any safety-critical application.

About Thermal Conductivity Calculator

The Thermal Conductivity Calculator applies Fourier's law to determine the rate of heat transfer through a solid material. Heat flows from hot to cold regions at a rate proportional to the temperature difference and cross-sectional area, and inversely proportional to the material thickness. The proportionality constant k (thermal conductivity) characterizes how well a material conducts heat. Copper (385 W/m·K) is an excellent conductor; fiberglass insulation (0.04 W/m·K) resists heat flow. This calculation is fundamental to building insulation design, heat sink engineering, and industrial process control.

The Math Behind It

Fourier's law of heat conduction states that heat flux (power per unit area) is proportional to the negative temperature gradient: q = −k(dT/dx). For a flat slab with uniform cross-section: Q̇ = kAΔT/d. **Thermal conductivity values** (W/m·K): - Diamond: 2000 (best natural conductor) - Copper: 385 - Aluminum: 237 - Steel: 50 - Glass: 1.0 - Concrete: 0.8 - Wood: 0.12 - Fiberglass: 0.04 - Polyurethane foam: 0.025 - Aerogel: 0.013 - Vacuum: 0 (no conduction) **Thermal resistance (R-value)**: R = d/k (m²·K/W). Higher R means better insulation. R-values add for layers in series: R_total = R₁ + R₂ + R₃. **U-value**: U = 1/R_total (W/m²·K). Overall heat transfer coefficient including conduction, convection, and radiation. Used in building energy codes. **Three modes of heat transfer**: 1. **Conduction**: Through solid materials (Fourier's law) 2. **Convection**: Through fluids (air, water) carrying heat 3. **Radiation**: Electromagnetic waves (Stefan-Boltzmann law) **Why metals conduct heat well**: Free electrons carry thermal energy rapidly through the metal lattice. This is why good electrical conductors are also good thermal conductors (Wiedemann-Franz law). **Building applications**: Wall assemblies combine multiple layers with different k values. Calculating total R-value determines energy efficiency and required insulation thickness to meet building codes.

Formula Reference

Fourier's Law

Q̇ = kAΔT/d

Variables: k = thermal conductivity (W/m·K), A = area, ΔT = temperature difference, d = thickness

Worked Examples

Example 1: Insulated Wall

k = 0.04 W/m·K (fiberglass), A = 10 m², ΔT = 20 K, d = 0.1 m

Step 1:Q̇ = 0.04 × 10 × 20 / 0.1
Step 2:= 8 / 0.1 = 80 W

80 W heat loss through the insulated wall.

Example 2: Copper Heat Sink

k = 385 W/m·K, A = 0.001 m², ΔT = 30 K, d = 0.01 m

Step 1:Q̇ = 385 × 0.001 × 30 / 0.01
Step 2:= 11.55 / 0.01 = 1155 W

1155 W conducted through the copper — highly effective.

Common Mistakes & Tips

  • !Confusing thermal conductivity (W/m·K) with thermal conductance (W/K) — conductivity is a material property; conductance depends on geometry.
  • !Forgetting to convert thickness to meters when other values are in SI units.
  • !Assuming heat transfer is only by conduction — in practice, convection and radiation often contribute significantly.

Related Concepts

Frequently Asked Questions

Why does metal feel cold while wood feels warm?

Metal has high thermal conductivity (50-400 W/m·K) and quickly draws heat from your skin. Wood has low conductivity (0.12 W/m·K) and does not draw heat quickly. Both are at room temperature — the sensation of cold is about heat transfer rate, not temperature.

What is R-value in insulation?

R-value = thickness/conductivity (d/k) in m²·K/W (or ft²·°F·h/BTU in US units). Higher R-value means better insulation. US building codes typically require R-13 to R-60 depending on climate zone and building component.

Why is aerogel such a good insulator?

Aerogel is 99.8% air trapped in a nanoporous silica structure. Air itself has very low thermal conductivity (0.025 W/m·K), and the tiny pores suppress convection. Aerogel achieves k = 0.013 W/m·K, approaching vacuum insulation.