Heat Transfer Calculator

What the heat transfer calculator does

Heat moves from hot to cold in three distinct ways, and this calculator handles all of them. Choose conduction, convection, or radiation and enter the relevant quantities, and it returns the heat transferred or the rate at which it flows. A basic mode also covers the energy to heat a mass through a temperature change.

Below is how the three mechanisms differ, the equation each one uses, and two worked examples.

How to use it

1. Choose the mechanism: basic heating, conduction, convection, or radiation.
2. Enter the values that mode asks for, such as conductivity and thickness for conduction, or area and emissivity for radiation.
3. Press Calculate for the result, or Reset to clear it.

The three ways heat travels

Heat always flows from warmer to cooler, but it gets there by three different routes, and which one dominates depends on the situation. Conduction passes heat through direct contact, convection carries it in a moving fluid, and radiation sends it across space as electromagnetic waves. Most real situations involve a mix, but it helps to understand each on its own.

A hot drink shows all three at once. Heat conducts up the metal spoon, convects through the swirling liquid and the air above it, and radiates from the warm surface. This calculator treats each mechanism separately, with its own inputs and its own physical law, so you can work out whichever one your problem calls for.

Conduction

Conduction is heat passing through a material by direct contact, as the jostling of fast-moving warm atoms is handed along to their slower neighbours. It is how a metal handle grows hot on a pan, and how heat leaks through a wall or a window. The rule that governs it is Fourier's law, and over a span of time it gives the heat Q from the thermal conductivity k, the area A, the temperature difference across the material, the time t, and the material's thickness L:

Q = k × A × ΔT × t ÷ L

Heat flows faster through a better conductor, a larger area, and a steeper temperature difference, and more slowly through a thicker barrier. The thermal conductivity k is the material's own property: metals conduct well and have high values, while insulators like foam or air conduct poorly. This is the whole logic of insulation, choosing low-conductivity materials and making them thick to slow the heat creeping through.

Convection

Convection is heat carried away by a moving fluid, a liquid or a gas, as it flows past a surface. Warm air rising from a radiator, the breeze that cools you on a hot day, the water circulating in a heating system: all are convection. The heat transfer rate follows Newton's law of cooling, written from the convective coefficient h, the surface area A, and the temperature difference between the surface and the fluid:

Q = h × A × ΔT

The convective coefficient h bundles up how effectively the moving fluid carries heat away, which depends on the fluid and how fast it moves. A stronger draught or a more vigorous flow gives a higher coefficient and faster cooling, which is exactly why blowing on hot food cools it, and why a fan makes a warm room feel cooler. This mode gives a rate, the heat carried away each second, rather than a total.

Radiation

Radiation is heat sent out as electromagnetic waves, needing no material in between, which is how the Sun's warmth crosses the vacuum of space to reach us, and how you feel the heat of a fire across a room. Its rate is set by the Stefan-Boltzmann law, from the surface area A, the emissivity, the Stefan-Boltzmann constant, and crucially the fourth powers of the absolute temperatures of the object and its surroundings:

Q = σ × emissivity × A × ( T₄⁴ − T₃⁴ )

The standout feature is that the temperatures enter as fourth powers, which makes radiation rise explosively with temperature. Double the absolute temperature and the radiated power leaps by a factor of sixteen. This is why a poker glows and pours out heat once it is hot enough, while a warm object near room temperature radiates only gently. The emissivity, a number between zero and one, says how good a radiator the surface is, with a perfect black emitter at one and a shiny reflective surface much lower. The calculator works in absolute temperature internally, so radiation is computed correctly even though you enter Celsius.

The basic heating mode

Alongside the three mechanisms, the calculator offers a basic mode that simply finds the energy to change a mass's temperature, using the central heat equation, the heat being the mass times the specific heat times the temperature change. This is the same relationship behind the specific heat and calorimetry tools, and it answers the question of how much energy a heating job needs, rather than how the heat travels to get there.

It rounds out the tool nicely: the three transfer modes tell you how heat moves between things, while the basic mode tells you how much heat a given warming actually takes. Together they cover both sides of a heating problem, the flow and the total.

Units and precision

The calculator works in SI units: areas in square metres, conductivity in watts per metre per kelvin, the convective coefficient in watts per square metre per kelvin, and temperatures in degrees Celsius, which it converts to absolute temperature where the physics requires it. The conduction and basic modes include a span and return a total heat in joules, while convection and radiation return a rate in watts, the heat flowing each second. Results carry several decimal places.

Two worked examples

Conduction. Heat passing through a 4-millimetre glass pane of area 1 square metre, with a conductivity of 0.8 watts per metre per kelvin, a 20-degree difference across it, over 10 seconds: Q = kAΔTt/L = (0.8 × 1 × 20 × 10) ÷ 0.004 = 40,000 joules, or 40 kilojoules.

Radiation. A surface of area 1 square metre and emissivity 0.9 at 100 degrees Celsius (373 kelvin), surrounded by walls at 20 degrees Celsius (293 kelvin), radiates a net Q = σ × 0.9 × 1 × (293⁴ − 373⁴) ≈ −613 watts. The negative sign shows the hot surface is losing heat, shedding about 613 watts to its cooler surroundings.

Questions people ask

What are the three types of heat transfer?

Conduction, through direct contact in a material; convection, carried by a moving fluid; and radiation, sent across space as electromagnetic waves. This calculator handles all three separately.

Which type of heat transfer works through a vacuum?

Radiation. It travels as electromagnetic waves and needs no material in between, which is how the Sun's heat reaches Earth across empty space.

Why does radiation depend so strongly on temperature?

Because the Stefan-Boltzmann law uses the fourth power of absolute temperature. Doubling the absolute temperature multiplies the radiated power by sixteen, so hot objects radiate vastly more than warm ones.

Why do some modes give joules and others watts?

Conduction and basic heating include a time span, so they give a total heat in joules. Convection and radiation give the rate of heat flow, measured in watts, the heat transferred per second.

References

A quick note on where the physics comes from. The three mechanisms of heat transfer, with Fourier's law for conduction, Newton's law of cooling for convection, and the Stefan-Boltzmann law for radiation, are standard thermodynamics, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. The SI units follow the US National Institute of Standards and Technology. The HyperPhysics link is worth a quick click to confirm it lands where you expect.

1. OpenStax, University Physics Volume 2, Section 1.6, Mechanisms of Heat Transfer. https://openstax.org/books/university-physics-volume-2/pages/1-6-mechanisms-of-heat-transfer
2. HyperPhysics, Heat Transfer. http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heatra.html
3. National Institute of Standards and Technology (NIST), Special Publication 811, Guide for the Use of the International System of Units (SI). https://www.nist.gov/pml/special-publication-811