The thermal resistance calculator above treats a wall, a board stack or a heat-sink path the way an electrical engineer treats a resistor network. Each layer contributes a resistance R = L/(kA), resistances in the same heat path add, resistances in parallel paths combine as conductances, and the whole assembly collapses to one number that a temperature difference divides into to give a heat flow. That analogy is not a teaching convenience. It is how multi-layer heat conduction is actually solved on paper before anyone opens a finite-element package. The series and parallel rules are the same ones OpenStax sets out for resistors in series and parallel.
Arb Digital builds free physics and engineering calculators that own one job properly, and this page owns the stack. It is deliberately different from its neighbours on this site: the heat transfer coefficient calculator returns a single convective resistance at one surface, the heat transfer calculator returns a heat rate for one layer in one mode, and the insulation calculator is a costing tool that converts a target R-value into bags and rolls to buy. None of them adds resistances up. This one does, in series and in parallel, and reports the result in every unit the trade uses.
What This Thermal Resistance Calculator Does
You give it an area, a temperature difference, up to two surface film coefficients and up to four conduction layers as thickness-and-conductivity pairs. It converts each entry to a resistance per unit area, sums them along the heat path, and reports four figures: total resistance in kelvin per watt, RSI in square-metre kelvin per watt, the same as an imperial R-value, and the U-value, which is the reciprocal of RSI. It then multiplies U by area and ΔT for the steady-state heat flow in watts.
It also does the part most calculators skip. Real assemblies are not uniform: a timber-framed wall has studs through the insulation, a block wall has mortar joints, a panel has fasteners. Those parallel paths are usually the dominant error in a hand calculation. Enter a bridging fraction and conductivity and the tool solves both paths, combines them by area-weighted conductance, and shows what the bridge cost you.
How to Use It
- Enter the area and the temperature difference. Area is measured normal to the heat flow. With surface films, ΔT is between the two bulk fluid temperatures; with both films at zero, between the two exposed surfaces.
- Set the film coefficients, or turn them off. These represent combined convection and radiation at each face. They belong to your geometry, orientation and air movement, not to the wall, and the tool takes them as inputs rather than assuming them.
- Fill in the layers from inside to outside. Thickness in millimetres, conductivity in watts per metre kelvin, zero thickness to disable a layer. Order does not change a series total but does change interface temperatures.
- Add the bridging path if the assembly has one. Enter the percentage of the face area occupied by the bridge and the bridge conductivity. The tool replaces layer 2 with the bridge over that fraction, which is the usual arrangement for studs, joists and mortar.
- Read the four figures together. Total resistance and heat flow depend on area; RSI, R-value and U-value do not, which is why labels use the second group.
The Formula: How Thermal Resistance Is Calculated
For steady one-dimensional conduction through a flat slab, Fourier's law integrates to Q = kAΔT/L. Rearranged into the resistance form that makes stacking possible, that is R = L/(kA), with Q = ΔT/R. The units are kelvin per watt, exactly analogous to ohms in the electrical case, with temperature difference playing the part of voltage and heat flow the part of current. The Georgia State University HyperPhysics page on heat transfer sets out the conduction relation in the same form.
A surface film adds a resistance of 1/(hA), where h is the surface heat transfer coefficient. Series resistances add: Rtotal = 1/(hiA) + ∑Lj/(kjA) + 1/(hoA). Because the area appears in every term, it factors out, which is why the trade works in resistance per unit area: RSI = 1/hi + ∑Lj/kj + 1/ho, and U = 1/RSI.
Parallel paths combine as conductances, not resistances. If a fraction f of the area follows a path of resistance Rb per unit area and the rest follows Ra, then U = (1 − f)/Ra + f/Rb. This is the area-weighted parallel-path method. It assumes no lateral heat spreading between the two paths, which makes it a lower bound on U for most real assemblies; the isothermal-planes method gives the upper bound, and published assembly figures usually sit between the two.
Worked example, matching the defaults on the page. Films give 1/8 = 0.125 and 1/25 = 0.04. Layers give 0.0125/0.25 = 0.05, 0.100/0.04 = 2.5 and 0.009/0.13 = 0.069231. The main path is therefore 2.784231 m²·K/W. The bridge replaces the 2.5 term with 0.100/0.13 = 0.769231, giving 1.053462 on the bridged path. With f = 0.12, U = 0.88/2.784231 + 0.12/1.053462 = 0.316068 + 0.113916 = 0.429984 W/m²·K. RSI is 1/0.429984 = 2.3257 m²·K/W, the imperial R-value is 2.3257 × 5.678263 = 13.21, the total resistance over 10 m² is 0.23257 K/W, and the heat flow is 0.429984 × 10 × 20 = 86.0 W. Those figures were computed independently before the code was written and match it to the digit.
Thermal Bridging Is Usually the Biggest Number You Ignored
Run the defaults, then set the bridging fraction to zero. The pure series stack gives RSI 2.784 and U 0.359. Put the studs back at 12 per cent and U rises to 0.430 — a 20 per cent increase in heat loss from a detail that occupies an eighth of the wall. That is the whole reason the parallel path is on this page. A designer who calculates the clear-field build-up and stops there will consistently under-predict heat loss, and the error grows as the insulation gets better, because a good insulation layer makes the bridge relatively more conductive, not less.
The effect is worse with metal. Swap the bridge conductivity from timber to light-gauge steel and the bridged path collapses to almost nothing, so the parallel conductance term dominates the assembly at a few per cent coverage. That is why steel framing uses thermal breaks, and why one unbroken steel fixing can cost more heat than a square metre of the panel around it.
One honest limitation: the area-weighted method treats the two paths as thermally isolated. Real bridges spread heat sideways, so the true answer sits between this number and the isothermal-planes number, and an awkward junction needs a two- or three-dimensional numerical model instead.
RSI, R-Value and U-Value: The Same Physics in Three Labels
Three numbers describe the same property, and mixing them up is the commonest reading error in this field. RSI is resistance per unit area in SI, m²·K/W. The imperial R-value is the same quantity in ft²·°F·h/BTU, and the factor is 5.678263: RSI 2.0 is about R-11.4, and a North American "R-19" product is around RSI 3.35.
U-value goes the other way: it is thermal transmittance, 1/RSI, in W/m²·K, and it is the number that building regulations in most of the world specify because it multiplies straight into a heat-loss total. Low U is good; high R is good. A U-value of 0.30 W/m²·K corresponds to RSI 3.33 and imperial R-19. Whenever a figure looks implausible, check which of the three you are holding before you check the physics.
One further trap: a declared label R-value is a product figure measured under standard conditions. It excludes surface films, fasteners and framing, and assumes nominal uncompressed thickness. The assembly number this page builds is always lower than the sum of the labels, and that gap is not an error in either figure.
The Same Arithmetic Runs an Electronics Heat Sink
Nothing here is specific to buildings. A power semiconductor's datasheet gives a junction-to-case resistance in kelvin per watt, the interface material adds a case-to-sink resistance, and the sink adds a sink-to-ambient resistance. Those add in series, and the junction temperature rise above ambient is the dissipation multiplied by the sum. The second preset button shows the same arithmetic on that scale.
The electronics case exposes two things the building case hides. Contact resistance at every interface is real and often dominant, because two nominally flat metal surfaces touch only at asperities; interface material exists to fill gaps, not to beat metal. And spreading resistance matters — a small die on a large sink does not use the whole sink. If you are working in that direction, the thermal conductivity calculator and the thermal diffusivity calculator cover the properties themselves, and diffusivity, not conductivity, governs how fast a transient settles.
Interface Temperatures Tell You Where the Dew Point Sits
Once you have the layer resistances, every interface temperature follows for free: each layer drops a share of ΔT in proportion to its share of the total resistance. A layer holding 40 per cent of the resistance drops 40 per cent of the temperature difference, which is why the bar breakdown reports the drop across each element.
That distribution decides where water condenses. Move an insulation layer from the outside of a wall to the inside, and the total resistance does not change at all, but the structural layer behind it now runs cold instead of warm, and the plane where the air reaches its dew point moves with it. Series resistance arithmetic cannot tell you whether that plane is a problem — that needs vapour resistance, air-tightness and the actual indoor humidity — but it tells you exactly where to look. Our dew point calculator gives the temperature at which the moisture in the air will start to condense, and comparing it to the interface temperature is the standard first check.
Where This Page Stops
This is a steady-state, one-dimensional model assuming constant conductivity and no heat storage. All three assumptions are routinely violated: insulation conductivity rises with mean temperature, moisture can multiply a material's conductivity several times over, and junctions are two- and three-dimensional. MIT's Intermediate Heat and Mass Transfer course materials set out where the one-dimensional treatment stops being adequate.
Radiation is not modelled separately. It is folded into whatever surface film coefficient you enter, and inside a reflective cavity that treatment is poor. If your assembly has an air cavity, enter a cavity resistance from a published source as a layer rather than deriving one from the conductivity of air, which gives a wildly optimistic answer.
Arb Digital builds technical calculators and reference pages for engineering and manufacturing sites — the kind that earn links because the maths is correct and the assumptions are stated.
Browse the free tools Talk to Arb DigitalCommon Mistakes to Avoid
- Adding parallel resistances directly. Two paths in parallel do not give a resistance equal to the sum, or to the average. Convert to conductance, area-weight, then invert.
- Mixing RSI and imperial R-value. The factor is 5.678263 and it is easy to lose. An assembly that "should be R-20" and comes out at 3.5 is almost always an RSI number being read on an imperial scale.
- Using the label R-value as the assembly R-value. Product figures exclude surface films, framing, fasteners and installation compression. The assembly is always worse.
- Ignoring the bridge because it looks small. A few per cent of area at a hundred times the conductivity dominates the answer, and the better the insulation, the worse the bridge gets in relative terms.
- Treating an air gap as a conduction layer. Cavity resistance depends on emissivity, width, orientation and heat-flow direction, and computing it from the conductivity of air overstates it badly.
Related Free Tools From Arb Digital
For a single-mode heat rate rather than a stack, use the heat transfer calculator; for the convective surface coefficient that feeds the film terms here, the heat transfer coefficient calculator; and if you are buying material rather than analysing it, the insulation calculator converts a target R-value into quantities. On the material side, the thermal conductivity calculator and thermal conductivity converter handle k and its unit systems, the thermal diffusivity calculator covers transient response, and the thermal expansion calculator covers what the temperature gradient does to dimensions. Browse the full free online tools hub for the rest.
Frequently Asked Questions
It is the ratio of the temperature difference across a heat path to the heat flow through it, measured in kelvin per watt. For conduction through a flat slab it equals thickness divided by the product of conductivity and area, and it behaves exactly like electrical resistance: series values add, parallel values combine as conductances.
Resistances along the same heat path add directly. Resistances on separate parallel paths do not: convert each path to a conductance, weight each conductance by the fraction of the area it occupies, add those, and invert the total to get the effective resistance.
They are the same quantity in different units. RSI is square-metre kelvin per watt; the imperial R-value is square-foot degree-Fahrenheit hours per BTU. Multiply RSI by 5.678263 to get the imperial R-value, so RSI 2.0 is about R-11.4.
U-value is the reciprocal of the resistance per unit area, so U equals one divided by RSI, in watts per square metre kelvin. A low U-value and a high R-value describe the same well-insulated assembly.
Because label figures are product values measured in isolation. The assembly total is reduced by framing and fastener bridging, by installation compression, and by the fact that declared values assume a standard mean temperature that your assembly may not run at.
Often a great deal. With the defaults on this page, adding a timber bridge over twelve per cent of the area raises the U-value by about twenty per cent. The effect grows as the insulation improves and becomes severe with metal bridges, which is why thermal breaks exist.
No. It is a steady-state model with no thermal mass, so it describes the condition reached after temperatures have settled. Transient behaviour is governed by thermal diffusivity and heat capacity rather than by resistance alone.
Yes. Junction-to-case, interface and sink-to-ambient resistances are in series and add in kelvin per watt exactly as wall layers do. Be aware that contact resistance and heat spreading from a small source are real effects that a one-dimensional slab model does not capture.
This tool is provided for education and engineering estimation only. It evaluates a one-dimensional steady-state resistance network from figures you enter and does not select materials, verify a build-up or demonstrate compliance with any building or product standard. Conductivity values must come from declared manufacturer data or measurement, and any assembly that has to meet a regulation or carry a performance claim should be assessed by a qualified building services or thermal engineer.
