Four steady-state tools: slab conduction, wall U-value, convection, radiation
Heat moves three ways, and honest calculations keep them separate, which is this page’s structure. Conduction: Fourier’s law through a single slab. Wall build-up: layers in series with surface resistances, giving the total R-value, the U-value and the heat loss at your area and temperature difference. Convection: Newton’s cooling law with your surface coefficient. Radiation: the Stefan-Boltzmann exchange between a surface and its surroundings, emissivity included. Everything is steady-state: temperatures are fixed boundary conditions, and the transient and phase-change cases the model cannot cover are named in the limitations rather than approximated in secret.
Disclaimer: This calculator gives estimates for general information only. It is not financial, medical or other professional advice. Building heat-loss and thermal design for regulated work belongs with the governing codes and a qualified engineer.
What these tools do
Conduction prices a temperature difference across a material: heat flow proportional to conductivity, area and the difference, inversely to thickness (Fourier’s law), which is why insulation works by thickness and why its k-value is so small. The wall tool stacks layers as resistances in series (each layer’s R is thickness over k), adds the standard inside and outside surface resistances, and inverts the sum into the U-value the building trade specifies. Convection prices a surface against a moving fluid through the coefficient h, the honest fudge factor that packages fluid mechanics into one number you supply. Radiation prices the electromagnetic exchange every surface constantly makes with its surroundings, quartic in absolute temperature, which is why it dominates at high temperatures and hides at low ones.
How to use them
- k values come from the material’s datasheet. Typical published figures: brick about 0.77, concrete 1.4, mineral wool 0.04, expanded polystyrene 0.035, softwood 0.13, steel 50, copper 400 W/m·K. Moisture raises the conductivity of porous materials substantially, the classic reason old insulation underperforms its label.
- Layer order does not matter for the total. Series resistances add in any order; order matters for where condensation forms inside the wall, a separate analysis this page does not pretend to do.
- h is the softest number in building physics. It swings with air speed, orientation and surface roughness; run the convection tool at the ends of its plausible range and treat the truth as bracketed, not pinpointed.
- Radiation needs absolute temperature. The tool converts your Celsius inputs to kelvin internally; entering kelvin figures as if Celsius is the classic error here, and the inputs are labelled so it cannot happen quietly.
The formulas
- Conduction: Q = k × A × ΔT / thickness. Layer resistance: R = thickness / k. Wall: U = 1 / (0.13 + ΣR + 0.04); Q = U × A × ΔT.
- Convection: Q = h × A × ΔT. Radiation: Q = ε × σ × A × (T_hot⁴ – T_cold⁴), σ = 5.67 × 10⁻⁸ W/m²K⁴, temperatures in kelvin.
Worked examples
The insulated wall. 100 mm brick (k 0.77), 50 mm mineral wool (k 0.04), 12 mm plaster (k 0.5), with the standard surface films: layer resistances 0.13, 1.25 and 0.02, total R 1.57 m²K/W, U-value 0.64 W/m²K, and at 10 m² with 20 degrees across it, a heat loss of 127.08 W. The insulation layer owns 80 percent of the resistance on 30 percent of the thickness, the whole economics of the wall in one row of the results.
The same wall’s grandmother. A single 220 mm brick leaf alone (the conduction tool): Q = 0.77 × 10 × 20 / 0.22 = 700.00 W. Five and a half times the insulated wall’s loss, which is the retrofit argument stated in watts instead of adjectives.
Two surfaces. A panel at h = 10 over 2 m² and 15 degrees convects 300.00 W. A square metre at 100°C with emissivity 0.9 facing 20°C surroundings radiates 611.69 W net: at stove temperatures radiation is not a correction term, it is the main event, and the quartic law is why.
Reading your results
Read the wall’s layer rows as a budget: the biggest R owns the performance, and money spent thickening any other layer buys almost nothing until the leader is addressed. Read U-values comparatively (lower is better, and modern codes for walls in cold climates live near 0.3 and below, which the example wall at 0.64 does not reach). Read convection and radiation figures as the two halves of most real surface losses: at room temperatures they are comparable in size, which is why radiators, confusingly named, do a good deal of both.
Limitations
- Steady-state only. Warm-up, cool-down, thermal mass and intermittent heating are transient problems; nothing here predicts a temperature over time.
- Phase change is out of scope. Boiling, condensation and melting carry latent heat under specific conditions the brief for this page requires be modelled properly or not at all; they are not at all.
- One-dimensional flow. Corners, studs, fixings and edges bridge heat around the layers (thermal bridging); real wall assessments add those paths separately.
- Radiation assumes a small surface facing large surroundings. Two surfaces exchanging with each other at comparable size need view-factor geometry beyond this tool.
Frequently asked questions
R-value and U-value: which do I use?
They are reciprocals describing the same wall from opposite directions: R totals the resistance (bigger is better, and layers add), U states the conductance the heating calculation consumes (smaller is better, Q = U × A × ΔT). North American practice quotes R (in imperial units there, roughly 5.68 times the metric R), European practice quotes U. This page prints both from the same layer stack so a figure from either tradition can be checked against the other.
Why does radiation explode at high temperatures?
Because it follows the fourth power of absolute temperature: doubling kelvin multiplies radiated power sixteenfold. At room temperature the term is a few hundred watts per square metre of exchange, comparable to convection; at furnace temperatures it dwarfs everything, which is why high-temperature engineering is mostly radiation management and why the Stefan-Boltzmann tool earns its place beside the other two.
Is my wall’s U-value the whole heat-loss story?
No: it prices transmission through that wall’s flat area only. A room’s loss adds every surface at its own U, plus ventilation and infiltration losses that often rival the fabric total, plus the bridging paths the limitations name. The wall figure is the standard building block (and the regulated one), and whole-building heat loss is assembled from blocks like it, which is the honest way the Electricity Cost and heating calculations elsewhere build upward.
Why did doubling insulation not halve the loss?
Because the insulation is one resistance among several: the films, the brick and the plaster keep their shares, so doubling the wool’s R from 1.25 to 2.50 moves the example’s total from 1.57 to 2.82 and the U from 0.64 to 0.35, a large gain but not a halving of the whole. The layer budget in the results shows this arithmetic before money is spent on it, which is the wall tool’s main practical use.
Related calculators
Method: Fourier conduction, series-resistance wall model with standard surface films, Newton convection and Stefan-Boltzmann radiation, all steady-state with assumptions stated. Last reviewed: 14 October 2026.