Thermal Resistance Calculator

Thermal resistance indicates how much a material impedes heat flow. The higher the thermal resistance, the slower the rate of heat transfer. This explains why a wall with fiberglass insulation maintains room temperature and why a CPU cooler can dissipate hundreds of watts of heat without damaging the chip.

This calculator computes the thermal resistance from thickness, conductivity and area of a flat layer. It also supports reverse calculation: if one of the four fields is left empty, it will be computed. Also by activating "heat flow" mode you can compute how much heat in watts flows through a given layer for a given temperature difference.

What is thermal resistance?

The thermal resistance is similar to the electrical resistance in a circuit. While in the circuit the voltage drives the flow of electricity through a resistor, in the case of wall construction the temperature difference drives the heat flow through a material.

A thick layer of fiberglass has a high thermal resistance and allows very little heat to pass through. A thin sheet of aluminum has almost no thermal resistance so the heat flows through it with virtually no hindrance. The unit in the SI system is Kelvin per watt (K/W), which indicates the temperature difference in Kelvins required to conduct one watt of power through this layer.

Formula for thermal resistance.

For heat transfer through a uniform plate in the direction of its length, thermal resistance is the value calculated by dividing thickness by the product of thermal conductivity and area.

Here L is the thickness in the direction of heat flow, k is the thermal conductivity of the material and A is the cross-sectional area through which the heat flows. The greater the layer thickness, the higher the thermal resistance, while a higher thermal conductivity of the material as well as a larger surface lead to lower thermal resistance.

As this equation contains four variables it can be rearranged to calculate any missing variable. Leave a field blank and the calculator will solve for that value.

Example calculation:

Suppose there is a polystyrene insulation board with a thickness of 5 cm covering a wall with an area of 4 square meters. The thermal conductivity of the polystyrene is about 0.035 W/(m·K). The thermal resistance can be calculated as follows:

If the temperature of the inner surface is 20 °C and that of the outer surface is 0 °C, then there is a temperature difference of 20 K. The heat flow is the value obtained by dividing the temperature difference by the thermal resistance.

This is the only power required to compensate for heat loss through this slab of insulation. If the thickness is doubled, the loss is halved and if a material with twice the thermal conductivity is used, the loss doubles.

Thermal resistance and heat flow - Ohm's law of thermodynamics

If there is thermal resistance present, the heat flow follows a formula similar to Ohm's law. The temperature difference drives the heat flow through the thermal resistance.

This analogy is so accurate that engineers create thermal schematics. In multi-layer wall constructions the heat resistances are connected in series while for parallel heat transfer paths the heat resistances are connected in parallel.

The Difference Between Thermal Resistance and R-Value

Building codes use the R-value, which is the thermal resistance per unit area and has units of m2.K/W or hr.ft2.F/BTU. The thermal resistance mentioned here is an absolute thermal resistance for a given surface area and has units of K/W.

To calculate the R-value, multiply the result by the area. To recover the absolute thermal resistance, divide the R-value by the area. The U-value, or heat transfer coefficient, is the inverse of the R-value in SI units. When calculating heat losses, you multiply the U-value by the area and temperature difference. By activating the R-value layer, these three values can be shown simultaneously.

Units for thermal resistance:

Kelvin per Watt is the SI unit. As a temperature difference of one Kelvin is equal to a temperature difference of one degree Celsius, the numerical values for K/W and C/W are identical. The US units use hours-degree Fahrenheit per BTU and have larger numerical values.

Thermal conductivity of typical materials:

The thermal conductivity k determines whether a material is a conductor or an insulator, and its values can span five orders of magnitude. Representative values at room temperature are given below; actual values vary with temperature and water content.

Other shapes: cylinders and spheres.

This calculator is designed for flat models and assumes that the area remains constant along the path of heat flow. For pipes and tanks, the area increases outwardly so logarithms are used for hollow cylinders and differences in reciprocals for hollow spheres when calculating thermal resistance.

where r1 and r2 are the inner and outer radii respectively and L is the length of the cylinder. For thin curved layers on small diameter pipes there is a critical adiabatic radius, r_cr = k/h. If the actual radius is below this radius adding an insulation layer can actually increase heat loss since the increase in surface area exceeds the newly added thermal resistance.

Convection and radiation

Pure conduction is only part of the picture. When a surface comes into contact with air or a liquid, there is another heat transfer resistance due to convection R = 1 / (h A), where h is the convective heat transfer coefficient. Radiation provides yet another path for heat flow.

In actual wall structures, which are surrounded by air on both sides, these surface resistances are in series with the conduction layer so that the total heat transfer resistance is their sum. Calculate each individual heat transfer resistance and add them together like resistors in an electrical circuit.

Applications for calculating heat transfer resistance.

In buildings the R-values of walls, roofs and windows determine how hard HVAC (heating, ventilation, air conditioning) systems have to work to maintain a comfortable indoor climate. Electronics designers select heat sinks and fans based on the temperature difference between components and their environment; incorrect choices can cause chips to slow down or be damaged.

Calculating the insulation of pipes prevents them from freezing in winter or condensing water in summer. The same mathematical relationships can also be used to determine the size of heat exchangers, insulate furnace walls, or keep cryogenic tanks at low temperatures.

How to use this calculator:

Enter thickness, thermal conductivity and area. Use the appropriate unit for each parameter and check resulting thermal resistance. Leave empty fields if you want to calculate other values. Enter desired thermal resistance and two other values and the calculator will give you the third value.

Turn on Heat Flow to show the power flowing through a layer in watts. Turn on R-Value Layer to show values relevant for building codes and turn on Material Layer to compare results with copper, glass or foam.

Assumptions and limitations.

The central calculation assumes that the heat flows one-dimensionally and stably through conduction in a homogeneous plate, with the surface being perpendicular to the direction of heat flow. The calculations neglect end effects, thermal bridges, the thermal contact resistance between layers, as well as changes in thermal conductivity depending on temperature.

In addition to this, only heat conduction is modelled. Convection at the surface, radiation and curved shapes each have their own independent relationships that must be added to this heat conduction term.