Thermodynamics

Thermal Resistance Calculator

Calculate total thermal resistance from temperature drop and heat flow, or solve plane-wall conduction resistance from thickness, conductivity, and area.

Formula R = ΔT / Q̇Reviewed Aug 14, 2026

Thermal resistance tells you how strongly a component or wall opposes heat flow. This calculator covers two common engineering uses: the general heat-flow definition R = ΔT / Q̇, and steady one-dimensional conduction through a plane wall, R = L / (kA). Use the first mode when you know a temperature drop and a heat-transfer rate; use the second when you want resistance directly from wall thickness, thermal conductivity, and area.

Calculation Bench

Calculation Mode

Solve for

01Temperature Difference

ΔT · Magnitude of the temperature drop driving heat transfer across the element or wall.

02Heat Transfer Rate

Q̇ · Rate of heat flow through the system.

Heat-flow mode uses the overall definition R = ΔT / Q̇. Enter positive magnitudes for the temperature drop and heat-transfer rate.

Solution

Enter the required values to calculate thermal resistance in heat flow mode.

R = ΔT / Q̇

Formula Sheet

R = \dfrac{\Delta T}{\dot{Q}}

\Delta T = \dot{Q} R

\dot{Q} = \dfrac{\Delta T}{R}

R = \dfrac{L}{kA}

L = R k A

k = \dfrac{L}{RA}

A = \dfrac{L}{Rk}

RThermal Resistance
ΔTTemperature Difference
Q̇Heat Transfer Rate
LWall Thickness
kThermal Conductivity
AArea

Variables & Units

Symbol	Variable	Description	Common Units
R	Thermal Resistance	Overall thermal resistance magnitude between two temperature nodes.	K/W, °C/W, °F·h/Btu
ΔT	Temperature Difference	Magnitude of the temperature drop driving heat transfer across the element or wall.	K, °C, °F
Q̇	Heat Transfer Rate	Rate of heat flow through the system.	W, kW, MW, Btu/h
L	Wall Thickness	Thickness of the plane layer measured along the one-dimensional heat-flow direction.	mm, cm, m, km, in, ft
k	Thermal Conductivity	Material property describing how readily the wall conducts heat.	W/(m·K), kW/(m·K), Btu/(h·ft·°F)
A	Area	Cross-sectional area normal to the direction of heat flow.	mm², cm², m², in², ft²

How to Use This Calculator

01Choose the calculation mode first. Use Heat Flow when you want the overall thermal resistance relation R = ΔT / Q̇. Use Plane Wall when you want steady one-dimensional conduction through a flat layer.
02Choose which variable to solve for. The calculator then shows only the inputs needed for that equation form.
03Enter positive magnitudes for temperature difference, heat transfer rate, resistance, thickness, conductivity, and area. This page works with thermal-resistance magnitudes, not signed heat-flow direction.
04Select Calculate to see the result, the active formula, and a substitution line with coherent units.

How the Formula Works

The general thermal-resistance definition mirrors Ohm's law: heat-transfer rate is analogous to electrical current, temperature difference is analogous to voltage difference, and thermal resistance is analogous to electrical resistance. In that form, Q̇ = ΔT / R, so for a fixed heat-transfer rate, larger resistance produces a larger temperature drop.

For steady one-dimensional conduction through a plane wall of uniform thickness, Fourier's law can be rearranged into a resistance form: R = L / (kA). Resistance increases when the wall gets thicker, when the cross-sectional area gets smaller, or when the material conductivity k decreases. High-conductivity materials such as metals therefore create much less thermal resistance than insulation materials at the same thickness and area.

Worked Example 01

Thermal resistance from temperature rise and heat flow

Known

Temperature Difference (ΔT): 40 K
Heat Transfer Rate (Q̇): 80 W

Formula

R = ΔT / Q̇

Substitution

R = 40 / 80

Result

R = 0.5 K/W

If 80 W of heat produces a 40 K temperature rise across a thermal path, the overall thermal resistance is 0.5 K/W.

Worked Example 02

Temperature difference from resistance and heat flow

Known

Thermal Resistance (R): 0.25 K/W
Heat Transfer Rate (Q̇): 120 W

Formula

ΔT = Q̇ R

Substitution

ΔT = 120 × 0.25

Result

ΔT = 30 K

A thermal path with 0.25 K/W carrying 120 W develops a 30 K temperature drop.

Worked Example 03

Plane-wall resistance from thickness, conductivity, and area

Known

Wall Thickness (L): 0.1 m
Thermal Conductivity (k): 0.04 W/(m·K)
Area (A): 10 m²

Formula

R = L / (k A)

Substitution

R = 0.1 / (0.04 × 10)

Result

R = 0.25 K/W

A 100 mm insulation layer with conductivity 0.04 W/(m·K) across 10 m² gives a total conduction resistance of 0.25 K/W.

Worked Example 04

Required plane-wall thickness

Known

Thermal Resistance (R): 0.5 K/W
Thermal Conductivity (k): 0.04 W/(m·K)
Area (A): 10 m²

Formula

L = R k A

Substitution

L = 0.5 × 0.04 × 10

Result

L = 0.2 m

To reach 0.5 K/W across 10 m² with a material conductivity of 0.04 W/(m·K), the wall must be 0.2 m thick.

Applications

01Estimating thermal bottlenecks from a known temperature rise and dissipated power
02Checking insulation-layer resistance in a steady plane-wall approximation
03Back-solving required wall thickness, conductivity, or area during thermal screening studies

Assumptions

01Heat-flow mode uses the lumped thermal-resistance relation R = ΔT / Q̇.
02Plane-wall mode assumes steady, one-dimensional conduction through a uniform flat layer with constant thermal conductivity.
03The page works with positive magnitudes only and does not track heat-flow direction signs.

Where This Model Stops

01Does not model cylindrical or spherical conduction, convection resistances, contact resistance, radiation exchange, or multi-layer series/parallel networks.
02Plane-wall mode assumes no internal heat generation and neglects edge effects or multidimensional heat spreading.
03This page returns total thermal resistance in K/W, not area-normalized building-insulation R-value or thermal insulance in m²·K/W.

References

[1]
16.4 Thermal Resistance Circuits
MIT Unified Thermodynamics and Propulsion Notes
States the resistance-circuit analogy and gives the plane-wall conduction form R = L/(kA).
[2]
NIST Guide to the SI, Appendix B.8
National Institute of Standards and Technology
Provides official conversion factors for thermal conductivity and BTU-based heat-rate units.
[3]
NIST Guide to the SI, Appendix B.9
National Institute of Standards and Technology
Provides official conversion factors for thermal resistance units such as °F·h/Btu to K/W.

Frequently Asked Questions

What is the difference between thermal resistance and building R-value?

This calculator returns total thermal resistance in K/W. Building-insulation R-value is usually area-normalized resistance, expressed like m²·K/W or h·ft²·°F/Btu, so it is not the same quantity unless area is handled separately.

When should I use Heat Flow mode instead of Plane Wall mode?

Use Heat Flow mode when you already know the temperature drop and heat-transfer rate for the whole path. Use Plane Wall mode when you want conduction resistance directly from thickness, conductivity, and area of a flat uniform layer.

Why does wall area reduce thermal resistance?

Because conduction resistance is inversely proportional to area in R = L/(kA). A larger area gives heat more cross-section to flow through, so the same material and thickness oppose heat less strongly.

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