How this instrument works
Thermal resistance answers the builder's question head-on: how hard does this layer make it for heat to cross? Divide thickness by conductivity and out comes R, quoted in square metre kelvin per watt. Conductivity k belongs to a material — mineral wool 0.04, polyisocyanurate 0.022, softwood 0.13, brick near 0.8, glass 1.0, mild steel 50, copper 400 W/m·K. Thickness is yours to choose. Brick 100 mm deep manages R = 0.125; identical depth in wool reaches 2.5, twenty times better, because wool is mostly trapped air and air conducts badly.
Joseph Fourier published the conduction law underneath all of this in 1822, and its shape is deliberately electrical in feel: heat flux plays current, temperature difference plays voltage, R plays resistance. Layers stacked across a wall add like series resistors, which is why this arithmetic stays so pleasant. Turning that into a shop-floor label came much later — Everett Shuman, running Penn State's building research programme during the 1940s, is credited with putting a single R number on insulation so buyers could compare products instead of guessing. Two scales inherited that idea and still trip people up: an American bag reads R-13 or R-30 in ft²·°F·hr/BTU, while European and Australian datasheets quote RSI in m²·K/W. One imperial unit equals 0.1761 metric, so divide by 5.678 to land in this sheet's units.
R = d ⁄ k describes steady one-dimensional conduction through a uniform slab, and every word there is a restriction. Nothing models timber studs or steel fixings puncturing an insulated bay and short-circuiting it; a 90 mm stud every 600 mm can strip a fifth off real wall performance, and that bridging is the gulf between the designer's sum and the thermographer's photograph. Nothing models moisture either — soaked fibrous insulation conducts far closer to water than to air, so a modest leak can gut R. Conductivity drifts with temperature, climbing a few percent per ten kelvin in foams, which is why manufacturers quote k at a stated mean temperature, often 10 °C. Big air cavities break the model outright, since air circulates and ferries heat by convection rather than merely conducting it.
- Put your layer depth into Material thickness — millimetres, centimetres or metres, so a 100 mm batt goes in as 100 mm with no arithmetic first.
- Type the material property into Thermal conductivity (W/m·K): mineral wool 0.04, EPS 0.036, PIR 0.022, softwood 0.13, brick 0.8, dense concrete 1.4.
- Read Thermal resistance (m²·K/W). That is one layer's R-value at that depth, nothing else included.
- Repeat for every layer in your build-up and total them, then add surface films of roughly 0.13 inside and 0.04 outside for a wall.
- Take the reciprocal of that total whenever a specification asks for U-value instead.
Worked example — 100 mm of mineral wool
A standard 100 mm mineral wool batt drops between ceiling joists. Material thickness = 0.1 m, Thermal conductivity (W/m·K) = 0.04. Divide straight through: R = 0.1 ⁄ 0.04 = 2.5 m²·K/W, precisely what that product's packaging claims.
Read 2.5 as a heat bill. Hold 20 K across that batt — 20 °C indoors against a freezing night — and flux is q = 20 ⁄ 2.5 = 8 W/m². Over a 100 m² ceiling, 800 W walks out, about a small fan heater left running permanently. Carry an identical batt to an American supplier and its label says R-14, since 2.5 × 5.678 = 14.2 in imperial units: same wool, same behaviour, different arithmetic printed on a bag.
Questions
Is this the same R-value printed on insulation packaging?
Yes, so long as both sit in matching units. This sheet returns RSI in m²·K/W, standard across Europe, Australia and Canadian metric labelling. American packaging uses ft²·°F·hr/BTU, a unit 5.678 times smaller, so an R-13 batt is RSI 2.29 and an R-30 loft blanket is RSI 5.28. Neither figure insulates better than another; a bigger number on a bag simply means a smaller unit sits behind it.
Why is my answer in m²·K/W rather than K/W?
Because this is resistance per unit area, which is what building specifications compare. Absolute resistance of a real object is d ⁄ (k·A), measured in K/W, and it shrinks as the panel grows. Dividing area out yields a figure describing a material build-up rather than one particular wall, so a 2.5 rating holds whether that wall covers 4 m² or 400. Multiply back by area only when you want a specific component's resistance, as heat sink datasheets do.
Can I add the R-values of every layer together?
For layers stacked one behind another, yes — heat crosses each in turn, so resistances add exactly as series resistors do. A build-up of 100 mm wool at 2.5, 12.5 mm plasterboard at 0.06 and 100 mm brick at 0.125 totals 2.69, and standards then add surface films near 0.13 inside plus 0.04 outside. Addition breaks down where materials sit side by side rather than in sequence: studs bypassing insulation form a parallel path, needing area-weighted treatment instead of a sum.
What separates R-value from U-value?
They are reciprocals. R measures resistance in m²·K/W and grows as the build-up improves; U measures transmittance in W/m²·K and shrinks. A wall totalling R = 5 has U = 0.2, meaning 0.2 watts cross each square metre per kelvin of difference. European regulations set limits on U, American codes prefer R, and one division moves between them. Invert a complete build-up only, surface films included — never a single layer on its own.
Does doubling insulation depth halve heat loss?
It halves that layer's contribution, not the wall's. R scales linearly with d, so 200 mm of wool gives 5 instead of 2.5, but loss follows an assembly's whole total including plasterboard, cladding and surface films. Going from R = 2.69 to R = 5.19 cuts flux by 48 percent; a third batt above that adds just 17 points more. Every extra millimetre buys less than one before it, which is why insulation depth gets settled by economics rather than by physics.
Why does a finished wall underperform its calculated R?
Three reasons usually, none of them present in this formula. Framing bridges insulation, and timber-framed construction at 15 percent framing fraction typically forfeits 10 to 20 percent of rated resistance. Air travels where it should not, through edge gaps or convection loops inside a loosely filled cavity, ferrying heat past insulation instead of through it. Moisture raises k sharply, since water conducts about 0.6 W/m·K against still air's 0.026. Careful sealing plus a continuous outboard layer closes most of that gap.