The heat transfer calculator above solves one mechanism at a time: conduction through a solid layer, convection from a surface into a moving fluid, or radiation exchanged between a surface and its surroundings. It deliberately does not add them together into a single figure, because the three are governed by different equations with different variables, and a page that blends them hides exactly the thing you need to see.
Arb Digital publishes free tools that name what they solved. The result panel always states which mode produced the number, and the supporting grid gives the heat flux per square metre, the rate in BTU per hour for anyone working in imperial units, the thermal resistance of the path, and the effective surface coefficient — which for radiation is a genuinely useful quantity most calculators never report.
What This Heat Transfer Calculator Does
In conduction mode it applies Fourier's law to a plane layer: the rate is the thermal conductivity times the area times the temperature difference, divided by the thickness. You give it the conductivity of the material, how thick the layer is, its area and the temperatures on each face.
In convection mode it applies Newton's law of cooling in its engineering form: the rate is the convection coefficient times the area times the difference between the surface and the bulk fluid. In radiation mode it applies the Stefan–Boltzmann law for a small object in large surroundings: emissivity times the Stefan–Boltzmann constant times area times the difference of the two absolute temperatures raised to the fourth power. Temperatures are converted to kelvin internally whichever scale you type in, which matters enormously for radiation and not at all for the other two.
What it does not do is series or parallel networks, transient warm-up, whole-building loads or fin efficiency. For a complete building envelope with several layers, windows and infiltration, the heat loss calculator handles the assembly and the insulation calculator deals with R-values. This page is the single-mechanism physics underneath both.
How to Use It
- Choose the mode first. Everything else on the panel depends on it, and the fields that do not apply are hidden so you cannot accidentally feed a conductivity into a radiation calculation.
- Use surface temperatures, not air temperatures. For conduction these are the two face temperatures of the layer. For convection and radiation the first box is the surface itself.
- Enter the area normal to the heat flow. For a wall that is the wall area; for a pipe it is the outer cylindrical surface, not the cross-section.
- Pick a conductivity from a datasheet where you can. The presets are typical room-temperature values, and real materials vary substantially with density and moisture.
- Read the effective coefficient. It puts all three modes on the same footing in W/m²·K, which is the only fair way to compare which mechanism is actually carrying the heat.
The Formulas: How Each Mode Is Calculated
Conduction through a plane layer is Q = k × A × (T₁ − T₂) ÷ L. The conductivity k is a genuine material property with units of watts per metre per kelvin. Work the defaults: a brick layer with k = 0.72, area 10 m², thickness 0.1 m and a 20 K difference gives Q = 0.72 × 10 × 20 ÷ 0.1 = 1,440 W. That is 144 W/m² of flux and 4,913 BTU/h.
Convection is Q = h × A × (Ts − T∞). It looks simpler and is far harder, because h is not a property of anything. It depends on the fluid, its velocity, the geometry, the orientation and even the temperature difference itself. Published values are correlations from experiment, which is why the field hint gives ranges rather than numbers.
Radiation between a surface and large surroundings is Q = ε × σ × A × (Ts4 − Tsurr4), with both temperatures in kelvin and σ the Stefan–Boltzmann constant, 5.670374419 × 10−8 W m−2 K−4. The three mechanisms and the assumptions behind each are set out in OpenStax University Physics, Mechanisms of Heat Transfer.
Why the Fourth Power Changes Everything
The single most important structural difference between the three modes is that conduction and convection are linear in temperature difference while radiation is not. Double the temperature difference across a wall and you double the conducted heat. Double it across a radiating surface and the answer depends entirely on where you started.
Work an example. A surface at 30 °C in 20 °C surroundings, emissivity 0.9, one square metre, radiates about 55 W. Raise it to 200 °C against the same surroundings and it radiates roughly 2,400 W — not eighteen times more, which the linear intuition suggests, but far more than that, because the fourth powers of 473 K and 293 K are what is being subtracted. At 600 °C the same surface is shedding over 30 kW.
The corollary is what surprises people in the other direction. Near room temperature, radiation is not negligible but it is quiet: the effective radiative coefficient for ordinary surfaces near 20 °C is about 5 to 6 W/m²·K, comparable to still-air natural convection. That is why the combined inside surface coefficient used in building physics is roughly 8 W/m²·K — convection and radiation contributing similar shares. It is also why a low-emissivity coating on a window works: it removes most of the radiative half of that pair without touching the convective half.
Thermal Resistance and Why Engineers Prefer It
Every mode can be rewritten as a resistance, defined as temperature difference divided by heat rate, with units of kelvin per watt. For conduction the resistance is L ÷ (k × A); for convection it is 1 ÷ (h × A). This is not decoration. Once each step is a resistance, a multi-layer wall becomes resistances in series that you simply add, exactly like electrical resistors, and parallel paths add as reciprocals.
That analogy is why the resistance figure is in the result grid. If you are building up a wall by hand, run each layer through the calculator with the same area, note the resistance, and total them. The overall U-value of the assembly is then one divided by the total resistance times the area. Watch the two conventions though: R-value as sold on insulation is a per-unit-area resistance in m²·K/W, whereas the K/W figure here already includes the area. Multiply the K/W by the area to move between them.
The resistance view also shows immediately where the bottleneck is. In a typical insulated wall the insulation layer holds most of the resistance and the brick almost none, so improving the brick does nothing. In a heat exchanger with water on one side and air on the other, the air-side convection resistance dominates so completely that the metal wall between them is irrelevant — which is why air-side surfaces get finned and water-side ones do not.
The Coefficient h Is the Hard Part
Conductivity and emissivity are properties you can look up and trust to within a modest band. The convection coefficient is not. It varies by more than three orders of magnitude across ordinary situations, and getting it wrong by a factor of three is easy.
Two regimes matter. Natural convection, where the fluid moves only because warm fluid is buoyant, gives roughly 2 to 10 W/m²·K in air and depends on the orientation of the surface: a hot plate facing up convects far better than the same plate facing down, because the buoyant plume can leave. Forced convection, where a fan or pump drives the flow, gives 10 to several hundred in air and rises steeply with velocity.
Liquids are in another league. Water in forced flow runs from roughly 500 to 10,000 W/m²·K, and boiling or condensing water goes higher still, because a phase change moves latent heat rather than sensible heat. If you are choosing a value and cannot find a correlation for your geometry, bracket it: run the calculation at the low and high ends of a plausible range and see whether the conclusion changes. If it does, you need a real correlation rather than a guess.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using Celsius in the radiation formula — the fourth power only works in kelvin. Subtracting 20 from 100 in Celsius and raising the difference to the fourth power is not the same calculation and is wrong by orders of magnitude.
- Treating h as a material property — the convection coefficient depends on the flow, the geometry and the orientation. There is no single value for "air".
- Confusing R-value with thermal resistance — insulation R-value is per unit area in m²·K/W, while the resistance in K/W already includes the area. They differ by a factor of the area.
- Using air temperature as the surface temperature — a radiator's surface, a window pane and the room air are all at different temperatures, and the mode you are solving decides which one belongs in the box.
- Assuming radiation is negligible indoors — near room temperature it carries roughly the same share as natural convection, which is precisely why low-emissivity glazing works.
Related Free Tools From Arb Digital
Conductivity figures often arrive in the wrong units, and the thermal conductivity converter moves between W/m·K, BTU/h·ft·°F and the rest, while the heat flux converter does the same for W/m². For a whole building rather than one layer, use the heat loss calculator and the insulation calculator. Heating a mass rather than passing heat through a wall is the job of the specific heat calculator, and a phase change needs the latent heat calculator. Temperature scales are handled by the temperature converter, and the full free online tools hub lists everything Arb Digital publishes.
Frequently Asked Questions
Conduction moves heat through stationary matter by direct contact between molecules. Convection moves it by physically carrying warm fluid from one place to another. Radiation moves it as electromagnetic waves and needs no medium at all, which is how sunlight crosses empty space.
Whichever one you select, and it names the mode in the result label. It deliberately does not sum the three, because they take different inputs and combining them without stating the assumptions hides which mechanism is actually carrying the heat.
Because the Stefan-Boltzmann law depends on absolute temperature raised to the fourth power, and only an absolute scale has a true zero. Using Celsius gives an answer that is not merely offset but wrong by orders of magnitude.
Roughly 2 to 10 W per square metre per kelvin for still air, 10 to a few hundred for moving air, and 500 to 10,000 for flowing water. It is not a material property; it depends on the fluid, the velocity, the geometry and the orientation of the surface.
No. The effective radiative coefficient for an ordinary surface near 20 degrees Celsius is about 5 to 6 W per square metre per kelvin, comparable to natural convection in still air. That is why low-emissivity coatings on glazing make a measurable difference.
It is the fraction of the radiation a perfect black body would emit that this surface actually emits, between 0 and 1. Paint, plastic, brick, wood and skin are all close to 0.9. Polished metals are very low, often below 0.1.
Convert each layer to a thermal resistance, which is thickness divided by conductivity and area, then add the resistances in series exactly as you would electrical resistors. The total heat rate is the overall temperature difference divided by the total resistance.
This tool is provided for educational and preliminary engineering use. Real installations involve multi-layer paths, thermal bridging and transient behaviour that a single-mode steady-state calculation does not capture.
