Heat Conduction CalculatorCalculator
Calculate steady-state conductive heat transfer rate (Q/t), heat flux, thermal resistance (R-value), and U-factor using Fourier's Law.
Conduction Wall Parameters
Thermal Transmission Results
Heat Conduction Calculator - Fourier's Law & Thermal R-Value: Free Heat Conduction Calculator. Calculate Fourier conductive heat transfer (Q/t = kAΔT/d), heat flux (W/m²), thermal resistance R-value, and U-value.
How to Use the Heat Conduction Calculator
Input Thermal Conductivity (k)
Enter material conductivity in W/(m·K) (e.g., 0.04 for fiberglass, 385 for copper).
Specify Surface Area & Thickness
Enter cross-sectional heat transfer area (m²) and barrier thickness (meters).
Set Boundary Temperatures
Specify hot-side temperature T_hot and cold-side temperature T_cold in Celsius.
Evaluate Heat Loss & R-Value
Inspect heat conduction in Watts, BTU/hr, heat flux (W/m²), and insulation R-value.
Engineering Mechanics & Physics Guide
Heat conduction is the transfer of internal thermal energy by microscopic collisions of particles and movement of electrons within a body. Formulated by French mathematician and physicist Jean-Baptiste Joseph Fourier in 1822, Fourier's Law of Heat Conduction states that the time rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area through which the heat flows.
For one-dimensional steady-state heat conduction across a plane wall of thickness d and surface area A, Fourier's equation takes the algebraic form: Q/t = (k · A · ΔT) / d, where k is the thermal conductivity of the material in Watts per meter-Kelvin (W/m·K), and ΔT = T_hot - T_cold is the temperature differential across the barrier.
Thermal Resistance (commonly designated as R-value in building envelope architecture) quantifies a material's ability to resist conductive heat flow: R = d / k (in metric RSI units of m²·K/W). In the United States, commercial insulation is rated in imperial R-values (hr·ft²·°F/BTU), where R_US ≈ 5.678 × RSI. The U-factor (thermal transmittance) is simply the reciprocal of the total R-value: U = 1 / R.
Materials exhibit vast differences in thermal conductivity spanning five orders of magnitude. Excellent thermal conductors (like pure copper at k = 385 W/m·K and aluminum at k = 205 W/m·K) are engineered into microchip heat sinks and boiler tubing. High-performance insulators (such as fiberglass at k = 0.04 W/m·K and silica aerogel at k = 0.015 W/m·K) trap stagnant air to virtually arrest conductive heat loss.
Key Analytical Advantages
Building Envelope Sizing
Determines insulation R-values and heating/cooling loads for residential buildings.
Electronics Thermal Management
Sizes copper and aluminum heat spreaders for microprocessors and power electronics.
Fourier's Law Precision
Calculates heat flux q (W/m²) and total thermal wattage Q/t across plane walls.
Dual R-Value Standards
Simultaneously displays international metric RSI and US customary R-values.
Real-Time Energy Audit
Converts thermal heat losses into daily electrical kWh cost equivalents.
Confidential Process Engineering
Proprietary HVAC and semiconductor thermal models remain 100% private.
Frequently Asked Questions
Thermal resistance (R-value) is directly proportional to thickness d and inversely proportional to thermal conductivity k: R = d / k. Doubling thickness doubles R-value; using a material with half the conductivity doubles R-value.
Metric RSI is measured in m²·K/W. US customary R-value is measured in hr·ft²·°F/BTU. To convert metric RSI to US R-value, multiply by approximately 5.678 (e.g., RSI 3.52 ≈ R-20).
Heat flux (q = (Q/t) / A) is the rate of heat energy transfer per unit cross-sectional area, measured in Watts per square meter (W/m²) or BTU/(hr·ft²).
Silica aerogel consists of 95% to 99% air trapped inside nanometer-sized pores. The pores are smaller than the mean free path of air molecules, preventing air molecules from colliding and transferring heat.
No. Conduction requires physical matter (atoms or free electrons) to transfer kinetic vibrational energy. In a pure vacuum, conduction is zero, and heat can only transfer via electromagnetic radiation.