Heat Transfer Calculator

Background.

Heat leaks from warm to cold through every surface that separates them, and in steady conditions the leak rate depends on just three things. How easily heat passes through the barrier, how much barrier there is, and how big the temperature gap is across it. Engineers fold the first into a single number, the overall heat-transfer coefficient U, and the rate becomes Q̇ = U × A × ΔT.

The same equation sizes very different things. For a building, U is the U-value of a wall, roof or window, and the result is the heat a heating system must replace to hold the room temperature. For a heat exchanger, U describes the metal wall and the fluid films on either side, and the result is how much heat moves from the hot stream to the cold one. In both cases the answer comes out in watts, joules per second, so it converts directly into energy and cost: a steady 200 W running for a day is 4.8 kWh.

The proportionality is the useful part. Halve the U-value with better insulation and the loss halves. Double the area of glazing and the loss through it doubles. A cold night with twice the indoor-outdoor difference doubles the heating load. It also tells you where to look first: because each element contributes its own U × A, the weakest surfaces dominate. A window with several times the U-value of the wall around it can account for a large share of a room's loss while covering a small share of its area, and a few square metres of uninsulated ceiling can outweigh a well-insulated wall.

What the formula does not do is supply U or ΔT for you. U comes from adding up the thermal resistances of each layer and surface film, or from a manufacturer's rating. In a heat exchanger the temperature difference changes along the length of the unit, and the right value to use is the log-mean temperature difference, not the simple average. The equation also assumes conditions have settled; warming up a cold building or a thick wall takes extra energy that a steady rate leaves out.

What is heat transfer calculator?

The overall heat-transfer rate is the power, in watts, flowing through a surface that separates two regions at different temperatures, once conditions are steady. It is the product of the overall heat-transfer coefficient U, which combines conduction through the solid layers with convection (and often radiation) at each surface, the area A through which heat flows, and the temperature difference ΔT that drives the flow.

Two related quantities come up constantly. The product U × A, in watts per kelvin, is the heat-loss coefficient of an element or of a whole building: the power needed for every degree it is held warmer than its surroundings. The reciprocal of U, R = 1/U in m²·K/W, is the thermal resistance of one square metre, the figure insulation is usually sold by. Resistances in layers add, so R is the natural way to build up a wall, and U the natural way to work out a heat flow. For a sense of scale, well-insulated walls and roofs sit well below 1 W/(m²·K), a single pane of glass is close to 6, and liquid-to-liquid heat exchangers reach the hundreds or thousands, because metal walls and moving liquids pass heat far more readily than still air.

How to use this calculator.

1. 01Enter the overall heat-transfer coefficient U in W/(m²·K). For building elements this is the U-value from a product data sheet or energy assessment; for a heat exchanger, use the design or measured overall coefficient including any fouling allowance.
2. 02Enter the area in square metres through which the heat flows, for example the wall area net of windows, or the tube surface area on the side U is referred to.
3. 03Enter the driving temperature difference in kelvin. A difference of 20 °C is the same as 20 K, so you can use the gap between indoor and outdoor temperatures in Celsius directly. For a heat exchanger, enter the log-mean temperature difference.
4. 04When sizing a heater rather than estimating a typical day, use the design difference: your indoor set point minus the cold-weather outdoor design temperature that local building guidance publishes for your area, not an average winter temperature.
5. 05Read the heat-transfer rate in watts. Multiply by hours of operation and divide by 1,000 for kilowatt-hours.

The formula.

Q̇ = U × A × ΔT. Q̇ is the heat-transfer rate in watts. U, in W/(m²·K), is the reciprocal of the total thermal resistance of one square metre of the barrier: for a flat wall, 1/U = 1/h_in + Σ(L/k) + 1/h_out, where h are the surface coefficients and each layer of thickness L and conductivity k adds L/k. A, in m², is the area heat passes through, and ΔT, in K, is the temperature difference between the two sides. The product U × A, in W/K, is the heat lost per degree of difference.

The equation joins two older laws. Fourier's law of conduction gives the flow through a single solid layer as Q̇ = kAΔT/L, so a bare layer on its own has U = k/L: 0.2 m of insulation with k = 0.04 W/(m·K) gives 0.2 W/(m²·K) before the air films are counted. Newton's law of cooling gives the flow from a surface into the air or fluid beside it as h × A × ΔT. In steady state the same heat passes through every layer in turn, so the temperature drops across the layers add up to the whole ΔT and their resistances add like electrical resistors in series, which is where the 1/U sum comes from.

Two arrangements need care. Where heat has parallel routes, such as timber studs through insulation or a frame around a pane, the U × A values of the routes add instead of their resistances, so a small area of poor material carries a disproportionate share. Around a pipe or tube the area grows with radius, so U has to be quoted against a stated area, inside or outside; U × A comes out the same either way.

All three inputs enter linearly, so a 10% change in any one changes the result by 10%. In practice U and ΔT carry the most uncertainty, and U is not perfectly constant: surface coefficients in still air rise somewhat as the temperature difference grows. The equation assumes steady state and a single representative ΔT, entered as a positive difference; the result is the size of the flow from the warmer side to the cooler one.

A worked example.

Frequently asked questions.

References& sources.

1. [1]ASHRAE Handbook — Fundamentals, 2025 edition (BIBLIOGRAPHIC/PAYWALL), heat transfer.
2. [2]Incropera et al., Fundamentals of Heat and Mass Transfer, 8th ed. (PRINT).
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.
4. [4]NIST Special Publication 811, Guide for the Use of the International System of Units, 2008 edition.
5. [5]OpenStax, University Physics Volume 2, section 1.6, Mechanisms of Heat Transfer.