Heat Conduction Calculator
Heat flow through a solid layer by Fourier's law, with the thermal resistance and what it costs over a day and a year.
Results
What this tool does
Conduction is heat travelling through material by being handed from one molecule to the next, and it obeys a relationship as simple as Ohm's law: the flow is the temperature difference divided by the resistance. The resistance is thickness divided by conductivity — thicker is better, and a poorer conductor is better still. Put in the material's conductivity, the area, the thickness and the temperature difference, and this page gives the watts crossing it, the resistance and R-value of the layer, and what continuous loss adds up to in energy.
Formula
Fourier's law: Q = k × A × ΔT ÷ L · thermal resistance: R = L ÷ (k A)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
k | Thermal conductivity | W/(m·K) |
a | Area | m² |
dt | Temperature difference | K |
l | Thickness | m |
h | Hours per day | h |
Q | Heat crossing it | W |
QA | Heat flux | W/m² |
R | Thermal resistance | K/W |
RV | R-value of this layer | m²·K/W |
U | U-value of this layer alone | W/(m²·K) |
E | Energy over that many hours | kWh |
EY | Energy over a year at that rate | kWh |
GR | Temperature gradient | K/m |
Worked example
- Thermal conductivity0.04 W/(m·K)
- Area10 m²
- Temperature difference20 K
- Thickness0.1 m
- Hours per day24 h
- Heat crossing it80.0000 W
- Heat flux8.0000 W/m²
- Thermal resistance0.250000 K/W
- R-value of this layer2.500000 m²·K/W
- U-value of this layer alone0.400000 W/(m²·K)
- Energy over that many hours1.9200 kWh
- Energy over a year at that rate700.80 kWh
- Temperature gradient200.0000 K/m
Limitations
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.
Frequently asked questions
How does this differ from the U-value calculator?
This one is the bare physics: one material, one thickness, one temperature difference, and Fourier's law with nothing added. The U-value calculator is the building version, which also includes the thin films of still air clinging to each face of the wall — the surface resistances — because those are part of how a wall performs in a real room and are specified in building standards. Use this page for a single layer of anything; use the U-value page when you are sizing insulation to meet a regulation.
Why does doubling the thickness only halve the loss?
Because conduction is inversely proportional to thickness, and inverse relationships give diminishing returns. Going from no insulation to fifty millimetres might cut the loss by eighty per cent; going from fifty to a hundred cuts what is left by half again, which is a much smaller number of watts. Every further layer costs the same and saves less. That is the whole reason insulation specifications stop where they do rather than continuing forever.