Thermal Resistance
Calculate thermal resistance of plates, cylinders, and spheres. Free online heat transfer calculator with material database, interactive charts, and critical radius of insulation analysis for physics and engineering.
About This Calculator
The Thermal Resistance Calculator computes the thermal resistance of common engineering shapes — plates, hollow cylinders, and hollow spheres — using Fourier's law of heat conduction. This tool is essential for engineers, physics students, and anyone working with heat transfer, insulation design, or thermal management. By selecting a material from the built-in database (including diamond, copper, aluminum, glass, wood, and insulators) and entering the geometric dimensions, you instantly get the thermal resistance in K/W.
Thermal resistance R is defined as the ratio of temperature difference ΔT to heat flow Q: R = ΔT / Q. For a plate, the formula is R = t / (k × A), where t is thickness, k is thermal conductivity, and A is cross-sectional area. For a hollow cylinder, R = ln(r₂/r₁) / (2πLk), and for a hollow sphere, R = (r₂ − r₁) / (4πr₁r₂k). For hollow geometries, the calculator also determines the critical radius of insulation — the outer radius at which heat flow is maximized — when a convective heat transfer coefficient is provided.
Regional Notes
Thermal resistance is a universal physics concept with the same SI units (K/W) worldwide. This calculator uses SI units exclusively — meters, W/m·K, and W/m²·K. The material database includes common materials used globally, and the formulas apply equally in all regions.
Applications
Thermal resistance calculations are used in building insulation design (walls, windows), cryogenic storage tank design (e.g., SpaceX Starship's liquid oxygen and hydrogen tanks), electronic component cooling, HVAC system analysis, heat exchanger design, and industrial pipe insulation. Understanding thermal resistance helps engineers select the right materials and thicknesses to minimize heat loss or gain.
Frequently Asked Questions
What is thermal resistance?
Thermal resistance is the ability of an object to resist the flow of heat. It is defined as the ratio of the temperature difference across the object to the heat flow rate, measured in K/W. A higher thermal resistance means better insulation.
How is thermal resistance calculated for a plate?
For a plate, thermal resistance R = t / (k × A), where t is the plate thickness in meters, k is the thermal conductivity of the material in W/m·K, and A is the cross-sectional area in m².
How is thermal resistance calculated for a hollow cylinder?
For a hollow cylinder, thermal resistance R = ln(r₂/r₁) / (2πLk), where r₁ and r₂ are the inner and outer radii, L is the cylinder length, and k is the thermal conductivity.
How is thermal resistance calculated for a hollow sphere?
For a hollow sphere, thermal resistance R = (r₂ − r₁) / (4πr₁r₂k), where r₁ and r₂ are the inner and outer radii, and k is the thermal conductivity of the material.
What is critical radius of insulation?
Critical radius of insulation is the outer radius at which heat flow through a hollow cylinder or sphere is maximum. For a cylinder it equals k/h and for a sphere it equals 2k/h, where k is thermal conductivity and h is the convective heat transfer coefficient.
What is the difference between thermal conductivity and thermal resistance?
Thermal conductivity is a material property that measures how well a material conducts heat, independent of shape. Thermal resistance depends on both the material (conductivity) and the geometry (thickness, area, shape) of the object.
Which materials have high thermal resistance?
Materials with low thermal conductivity have high thermal resistance. These include air (0.024 W/m·K), urethane foam (0.022 W/m·K), glass fibre (0.04 W/m·K), soft rubber (0.13 W/m·K), and wood (0.17 W/m·K). These are commonly used as insulators.
Do I need to use SI units for this calculator?
Yes, the calculator uses SI units: meters for length and radius, m² for area, W/m·K for thermal conductivity, and W/m²·K for heat transfer coefficient. The result is in K/W.