Heat Loss Calculator: Conduction, Convection and Radiation Explained

Point a thermal camera at a house on a winter night and the building stops being a shape and becomes a leak. The windows blaze. The walls glow a dull orange, brighter at the corners and above the radiators. The roof, if the loft has been insulated, is nearly black — the same colour as the sky behind it. Every joule the boiler put into that house is on its way out, and the camera is showing you the exits. There are three of them, and they are different enough that each needs its own remedy: heat crawls through the walls by conduction, rides the air out through the gaps by convection, and leaves the warm brickwork as the infrared radiation the camera was built to see.

There are three things on this page to push on until those three exits stop being vocabulary and start being furniture. A fingertip you can press onto a block of steel or oak, with a thermometer buried in the block that refuses to move. A wall you build one layer at a time while the temperature profile through it visibly re-shapes. And a mug of coffee you can turn into a vacuum flask one design feature at a time, watching which leak floods back when you take a feature away. One idea sits under all of it, the same one the ideal gas law rests on: temperature is a measure of how fast molecules are moving, and heat is that motion being passed along.

What Are Conduction, Convection and Radiation? (Heat Transfer Explained)

Heat is energy on the move because of a temperature difference. It goes from hotter to colder — never the other way without something paying for it — and the three mechanisms differ in what carries it. In conduction the energy is handed from molecule to neighbouring molecule while the molecules stay put. In convection the hot material itself gets up and goes. In radiation nothing material moves at all; the energy travels as electromagnetic waves, which is why it works across empty space.

What is conduction? Heat passed molecule to molecule

Hold one end of a metal spoon in a pot of soup and the handle warms. Nothing flowed up the spoon. The atoms at the hot end vibrate harder, jostle their neighbours into vibrating harder, and the disturbance walks up the handle like a rumour through a crowd. In a metal there is a second carrier: the free electrons that make it an electrical conductor also ferry thermal energy, and they are far quicker at it than lattice vibrations alone, which is why the best electrical conductors are the best thermal conductors too.

How well a material conducts is its thermal conductivity, $k$, in watts per metre per kelvin. The spread is enormous. Aluminium sits at 237 W/m·K, steel at 45, brick at 0.77, oak at 0.17 and expanded polystyrene at 0.035 — nearly seven thousand times worse than aluminium. Foam is a poor conductor for the same reason a duvet is: it is mostly trapped air, and still air is among the worst conductors there is. Conduction needs matter, and it prefers matter that is dense and stiff. In a vacuum there is nothing to conduct through.

Everyday examples: the spoon; a cold floor tile under a bare foot; a pan bottom heating the water above it; the fabric of a house wall; an ice cube melting faster in your hand than on the counter.

What is convection? Hot fluid that moves itself

Warm a pocket of air or water and it expands. Expanded fluid is less dense, so the cooler, denser fluid around it sinks underneath and shoves it upward — Archimedes' principle, applied to a parcel of fluid instead of a boat. The parcel carries its heat with it. That is natural convection: the fluid is both the medium and the delivery van. Blow the fluid along with a fan or a pump and it is forced convection, the same transfer with the motion supplied from outside.

Convection needs two things. It needs a fluid — a gas or a liquid, something whose molecules are free to travel — and it needs gravity, or something standing in for it, to make "less dense" mean "rises". In orbit a candle burns as a small blue sphere, because there is no up for the hot combustion products to go.

Everyday examples: a radiator warming a whole room from one wall; a kettle rolling as it comes to the boil; a sea breeze on a hot afternoon; cumulus clouds; the shimmer above a hot road; the draught under a door.

What is radiation? Heat as electromagnetic waves

Everything warmer than absolute zero radiates. At room temperature the radiation is infrared, invisible to you and blindingly bright to a thermal camera. At the temperature of a toaster element some of it edges into visible red; at the surface of the Sun it peaks in the visible, which is not a coincidence — your eyes evolved to see what the Sun sends. Radiation needs no matter in between. It is how the Sun's heat reaches Earth across the vacuum between them, and it is the one route a vacuum flask cannot block with a vacuum.

Everyday examples: sunlight on your face; the warmth of a campfire, felt on the side of you that faces it and not the other; frost forming on a clear, calm night as the ground radiates its heat away to the sky; a foil blanket that keeps a marathon runner warm by reflecting their own radiation back at them.

The three rarely turn up alone. A radiator conducts heat from the water inside to its outer skin, convects most of it into the room air and radiates the rest, and the room loses all of it through the walls by the same three routes in a different order. The rest of this page takes them one at a time, with one thing to touch for each.

Why Does Metal Feel Colder Than Wood?

It isn't. Leave a steel ruler and a wooden one on the same desk overnight and by morning they are at exactly the same temperature; a thermometer pressed to each will say so. Your hand disagrees because your hand is not measuring the ruler. It is measuring the skin of your own fingertip, and what sets that skin's temperature is how fast the thing you are touching can drain heat out of it.

Steel drains heat fast. Touch it and a warm front races into the metal while your fingertip's surface crashes to within a degree of the block's temperature and stays there. Oak can barely take heat away at all, so your fingertip stays close to its own 34 °C and the wood feels close to neutral. The block never changed temperature in either case — a thermometer twenty millimetres inside it would not flinch — and the simulation below has exactly such a thermometer, so you can watch it not flinch.

What decides the contact temperature is a property called thermal effusivity, $e = \sqrt{k\rho c}$ — conductivity, density and specific heat capacity rolled into one number that measures how readily a material's surface exchanges heat with whatever touches it. Press two bodies together and the interface settles, at once, at a weighted average of their temperatures, weighted by effusivity:

$T_c = \frac{e_s T_s + e_m T_m}{e_s + e_m}$

Skin has an effusivity of about 1 176 W·s½/m²·K. Steel's is 13 156, eleven times higher, so the average is pulled almost all the way to the steel's temperature: $T_c = 21.1$ °C. Oak's is 523, less than half of skin's, so the average stays on skin's side at 29.7 °C. Expanded polystyrene, at 37, barely registers: 33.6 °C. Inside each body the disturbance then spreads by diffusion, $T(x,t) = T_0 + (T_c - T_0)\,\mathrm{erfc}\!\left(x/(2\sqrt{\alpha t})\right)$ with $\alpha = k/\rho c$, and it has reached a depth of roughly $2\sqrt{\alpha t}$ — 6.8 mm into steel after one second, 0.65 mm into oak. The probe at 20 mm stays put because the front has not got there yet, and by the time it has, the fingertip has long since given up.

How Much Heat Escapes Through a Wall? Fourier's Law and U-Values Explained

A wall is conduction's home fixture. It is flat, it is thick in one direction only, and once the heating has been on for a few hours the temperature at every depth inside it has stopped changing — a steady state, with heat entering the room-side face at exactly the rate it leaves the outside face. That makes it the one heat-transfer problem you can solve in full with arithmetic.

What is Fourier's law of conduction?

Heat flows downhill in temperature, and the steeper the hill the faster it flows. Fourier's law puts that in numbers for a slab of thickness $d$ and area $A$ with a temperature difference $\Delta T$ across it:

$\frac{Q}{t} = \frac{k A\,\Delta T}{d}$

Double the temperature difference and you double the flow. Double the area and you double it again. Double the thickness and you halve it, because the same drop is spread over twice the distance and the gradient is half as steep. And $k$ multiplies the whole thing, which is why the choice of material matters more than any amount of extra thickness — 25 mm of foam beats 115 mm of extra brick, as you are about to see.

Try it on a square metre of solid 215 mm brick with 15 K across it: $0.77 \times 1 \times 15 / 0.215 = 53.7$ W. That is too pessimistic for a real wall, and the reason is instructive. The brick is not the only thing between the room air and the outside air. There is a thin film of nearly still air clinging to each face, and each film is a resistance in its own right.

How do you calculate a U-value?

Rearrange Fourier's law and the slab looks like a resistor. Its thermal resistance is $R = d/k$, in m²·K/W, and the heat flow per square metre is $q = \Delta T / R$ — Ohm's law with temperature as the voltage. Layers in series add their resistances, exactly as series resistors do, and the two surface films get standard values: $R_{si} = 0.13$ on the inside, where the air is still, and $R_{se} = 0.04$ on the outside, where wind keeps the film thin. The U-value is the reciprocal of the total:

$U = \frac{1}{R_{si} + \sum d_i/k_i + R_{se}}, \qquad \frac{Q}{t} = U A\,\Delta T$

For the solid brick wall with 12.5 mm of plasterboard on the inside: the brick contributes $0.215/0.77 = 0.279$, the plasterboard $0.0125/0.25 = 0.050$, and with the films the total is $0.13 + 0.279 + 0.050 + 0.04 = 0.499$ m²·K/W. So $U = 2.00$ W/m²·K, and with 15 K across it the wall passes $q = 2.00 \times 15 = 30$ W through every square metre. Not 54: the films took nearly half.

The U-value tells you the total. The resistances tell you something better — where the temperature goes. The same $q$ flows through every layer, so each layer's share of the 15 K drop is $q R_i$: 3.9 K across the inside film, 8.4 K across the brick, 1.5 K across the plasterboard, 1.2 K across the outside film. The room-side face of that wall sits at $20 - 3.9 = 16.1$ °C. Four degrees below the air in the room, before the wall has even started. Hold on to that number.

What U-value does a house need?

In Ireland the building regulations (Technical Guidance Document L, 2019 edition, for new dwellings) set maximum U-values of 0.18 W/m²·K for walls, 0.16 for roofs, 0.18 for floors and 1.4 for windows and doors. Against those, the walls people actually live behind are sobering:

Two things stand out. The plain double-glazed window is worse than the wall limit by a wide margin, which is why windows dominate the thermal image of a house whose walls have been done. And the gap between a 1970s wall and the current standard is not closed by more block — it is closed by a few centimetres of a material that traps air. The physics of the 1970s cavity wall is the physics of the modern one; the modern one just has the cavity filled with something that stops the air moving.

Why do cold walls get damp?

Air at 20 °C and 70% relative humidity — ordinary Irish indoor air in winter, with cooking, showers and breathing all adding water — has a dew point of 14.4 °C. Any surface colder than that pulls water out of the air. On the solid brick wall the inside face was 16.1 °C with 5 °C outside; drop the outside to −3 °C and the flow rises to 46 W/m², the inside film spends 6 K of it, and the face falls to 14.0 °C. Below the dew point. The wall sweats, the wallpaper lifts, and mould gets its foothold in the coldest corner, where two cold faces meet.

The cure is not more heating, or not only that. Dry the air — ventilate, so the dew point falls (at 60% humidity it is 12.0 °C) — or warm the surface, which is what insulation does. With 100 mm of wool on the outside, the inside face of the same wall sat at 19.35 °C with 5 °C outside, and with −10 °C outside it is still 18.7 °C, four degrees clear of the dew point. The heat that used to be spent in the room-side film is spent in the wool instead, and the face stays warm and dry.

How Does Convection Move Heat? (Why Hot Air Rises)

Hot air does not rise because heat "goes up". It rises because it is pushed. Warm a parcel of air and it expands; it now weighs less than the same volume of the cooler air around it, and that cooler air, being denser, slides underneath and lifts it — the same buoyancy that floats a boat, acting on a bubble of gas instead of a hull. Take away gravity and the effect vanishes. Take away the density difference and it vanishes too, which is why a sealed room at one even temperature is perfectly still.

A radiator is misnamed. Most of what it does is convection: it warms the air touching it, that air rises up the wall and across the ceiling, cools against the far wall and the window, sinks, and creeps back across the floor to be warmed again. The loop is why the floor under a window is the coldest place in a room, and why a radiator goes under the window in the first place — it warms the cold air where it lands and breaks the draught before it reaches your ankles. A kettle boils the same way, one rolling loop from the element to the surface. A sea breeze is the same loop the size of a coastline: land heats faster than sea by day, the air over it rises, and cooler sea air pours in underneath.

Water plays a trick on this. Almost every fluid gets denser as it cools, all the way down. Water gets denser as it cools until just above freezing, then expands again, so a lake in autumn convects until the whole column is a few degrees above zero and then stops — the coldest water floats. That reversal is why lakes freeze from the top down, and why anything living under the ice is in water that is, by lake standards, warm.

Convection is also why the gap in a double-glazed window is about 16 mm and not wider. Make it narrower and conduction across the thin air layer takes over. Make it much wider and the air in the gap starts to circulate — up the warm pane, across, down the cold one — and the window becomes a radiator working for the outside. The wall builder above gives a sealed cavity a fixed resistance of 0.18 m²·K/W for the same reason: a trapped air layer is a good insulator only while the air stays trapped.

How Does Radiation Carry Heat Through a Vacuum?

Every surface radiates, and how much depends ferociously on its temperature. The Stefan–Boltzmann law gives the power leaving a surface of area $A$ and emissivity $\varepsilon$:

$P = \varepsilon \sigma A T^4$

with $\sigma = 5.67 \times 10^{-8}$ W/m²·K⁴ and $T$ in kelvin — it has to be kelvin, because a fourth power only means something when the zero is a real zero. The exponent is the whole story. Double the absolute temperature and the radiated power goes up sixteen times. A person's skin at 306 K radiates 868 W from its 1.8 m², but receives 730 W back from the walls of a 293 K room, and it is the 138 W difference that is lost. Net radiation is always an exchange:

$P_{net} = \varepsilon \sigma A \left(T^4 - T_{surroundings}^4\right)$

Emissivity, $\varepsilon$, is a number between 0 and 1 that says how good the surface is at radiating compared with a perfect black body. Matt, rough, dark or painted surfaces sit near 0.9 — and so, in the infrared, does human skin whatever its colour, and so does water. Polished metal sits near 0.1, and a silvered mirror surface as low as 0.03. The same number governs absorption: a surface that radiates poorly also absorbs poorly, which is why the silvering in a flask does double duty and why a foil blanket works in both directions.

The Sun is the loudest example. At the top of Earth's atmosphere, sunlight arrives at about 1 361 W on every square metre held face-on to it — the solar constant — having crossed the vacuum in between with nothing to carry it but the waves themselves.

Why is Earth's average temperature what it is?

Earth catches sunlight over a disc of area $\pi R^2$ but radiates from its whole surface, $4\pi R^2$, so the average power absorbed per square metre of surface is a quarter of the solar constant, less the 30% that clouds, ice and deserts reflect straight back:

$\frac{S(1 - a)}{4} = \frac{1361 \times 0.7}{4} = 238 \text{ W/m}^2$

In the long run Earth must radiate that much back, or it would warm until it did. Setting $\sigma T^4 = 238$ gives $T = 255$ K, about −18 °C. The real average surface temperature is around 288 K, 15 °C. The 33 K gap is the greenhouse effect: the atmosphere is nearly transparent to the incoming visible light but absorbs much of the outgoing infrared and re-radiates part of it downward, so the surface has to run warmer than 255 K to push 238 W/m² out through the top. The 255 K is what a thermal camera in orbit sees; the 288 K is what you live in.

How Does a Vacuum Flask Keep Coffee Hot?

James Dewar built the first one in 1892, at the Royal Institution in London, and it had nothing to do with coffee. He needed to keep liquefied gases cold for long enough to study them, and a glass vessel inside another glass vessel with the air pumped out of the gap did it. He never patented it. The design was commercialised as the Thermos, and it is unchanged today because it was right the first time: three exits, and a separate door on each.

Ask why a flask works and most people say "the vacuum". The vacuum handles conduction and convection through the wall — there is nothing in the gap to jostle and nothing to circulate — and it is powerless against radiation, which crosses it as easily as sunlight crosses space. That is the job of the silvering on the glass. And neither touches the biggest leak of all, which is the top. An open cup of hot coffee loses more heat through its open top — most of that as evaporation — than by every other route combined, and the door on that one is the stopper.

The lid comes first because evaporation is not like the other losses. Conduction, convection and radiation all move heat by making molecules elsewhere move faster. Evaporation moves heat by removing the fastest molecules. Every gram of water that leaves the surface as vapour takes roughly 2.3 kJ with it — the latent heat of vaporisation — and it takes it from the molecules left behind, which is why a cup of coffee with a skin of steam over it cools so much faster than the same cup under a saucer. Trap the vapour and the trick stops working. The same vapour, pinned under a droplet on a pan far above boiling, becomes the insulating layer that lets the droplet skate for minutes instead of flashing away.

There is a second lesson in the flask, and it is the one the Carnot engine post turns on. Every watt leaving the drink is heat crossing a finite temperature gap — 80 °C to 20 °C — and heat that flows across a finite gap is irreversible: it could in principle have been made to do work on the way, and now it never will. A Carnot engine avoids that loss by running infinitely slowly. A flask cannot stop the flow, only slow it, and its whole design is an attempt to make an unavoidable 60 K gap leak as slowly as an engineer can arrange.

How Is Heat Transfer Examined in the Leaving Cert?

Heat transfer sits in Strand 2.1 of the Physics specification (first examined in 2027), and it was on the old syllabus too, so the question shapes are well worn. You will be asked to define the three mechanisms and give an example of each — the definitions in the first section are written to be quoted. You will be asked to explain, in terms of those mechanisms, why a vacuum flask has a vacuum, a silvered surface and a stopper, or why a metal handle feels colder than a wooden one, or why a hot-water tank is lagged. And you will be asked to calculate: the rate of heat loss through a window or a wall from $Q/t = UA\,\Delta T$, or the U-value from a measured loss, or — less often — the conductivity from $Q/t = kA\,\Delta T/d$. Watch the units. U is in W/m²·K, k is in W/m·K, and thicknesses arrive in millimetres and want converting to metres before they go anywhere near a formula.

The 2027 Physics in Practice investigation brief is domestic sustainability in energy usage and losses, due on 11 December 2026, and a heat-loss investigation is a natural fit. Measure something the formulas on this page predict. A cooling curve is the classic: the same volume of hot water in an open cup, a lidded cup and an insulated cup, temperature read every minute alongside the room temperature, then plotted as temperature above room against time. If the loss is proportional to that temperature difference — mostly convection — a plot of $\ln(T - T_{room})$ against time is a straight line, with a slope equal to the loss rate per degree of difference divided by the water's heat capacity. If your points bend away from the line at the hot end, that bend is real: it is the evaporation and radiation terms, which do not scale in simple proportion to the temperature difference, and saying so in the report is worth more than pretending they are not there. For a wall or a window the equivalent is heat loss against temperature difference, whose slope is $UA$.

The same content, at much the same depth, appears in GCSE Physics (thermal conductivity, insulation, the flask), at A-Level (Fourier's law with $\Delta T/d$ as a gradient, and Stefan–Boltzmann in the astrophysics option) and in the AP Physics 2 thermodynamics unit. The worked examples below are the four question shapes that cover most of it.

Worked Examples for Physics Exams