How to use this calculator

Choose a plane wall (a slab, a building wall, a panel) or a cylindrical wall (a pipe or the insulation around it). Enter the thermal conductivity, the dimensions and the temperature difference between the two surfaces. The chart shows how the temperature drops through the wall: a straight line for a plane wall, a logarithmic curve for a cylinder.

Formulas

Fourier's law, plane wallQ = k A ΔTt R = tk A q″ = QA

Cylindrical wall of length LQ = 2π k L ΔTln(r_o/r_i) R = ln(r_o/r_i)2π k L

Temperature profileT(x) linear for a plane wall; T(r) − T_oT_i − T_o = ln(r_o/r)ln(r_o/r_i) for a cylinder

Thermal resistances add in series like electrical resistors, so a wall with several layers has Q = ΔT_total / ΣR.

Worked example

200 mm brick wall, 10 m², 20 °C difference (the default)

R = 0.20 / (0.72 × 10) = 0.0278 K/W.
Q = 20 / 0.0278 = 720 W, and q″ = 720 / 10 = 72 W/m².
The R-value per unit area is t/k = 0.20 / 0.72 = 0.278 m²·K/W, or about R-1.6 in US units.

For a pipe: 50 mm of fiberglass (k = 0.04 W/m·K) around a 60 mm pipe, 10 m long, with a 100 °C difference loses Q = 2π × 0.04 × 10 × 100 / ln(80/30) = 256 W.

Typical thermal conductivities near room temperature

Material	k (W/m·K)	k (BTU/h·ft·°F)
Copper	401	232
Aluminum 6061	167	96.5
Carbon steel	≈ 50	≈ 29
Stainless steel 304	14.9	8.6
Concrete	1.4	0.81
Common brick	0.72	0.42
Softwood (pine)	0.12	0.069
Fiberglass batt insulation	0.04	0.023

Assumptions and limits

Steady state: temperatures are not changing with time.
One-dimensional heat flow with constant thermal conductivity and no internal heat generation.
Surface temperatures are known. If you only know the air temperatures, add convection resistances 1/(hA) on each side.
Conductivity varies with temperature, moisture and density, so treat the material values as typical, not exact.

Frequently asked questions

What is the difference between R and the R-value?

R in K/W is the resistance of the whole wall. The building R-value is the resistance of one unit of area, t/k, in m²·K/W or ft²·°F·h/BTU. Divide the R-value by the area to get R.

Why does the cylinder profile curve?

Heat spreads over a larger area as it moves outward, so less temperature drop is needed per unit thickness near the outside. That is why the curve flattens toward the outer surface.

Can adding insulation increase heat loss?

For small wires and tubes, yes, up to the critical radius r_c = k/h, because the larger outer surface sheds more heat by convection. For most pipes the outer radius is already past this point.

For education and preliminary checks only. Have a qualified engineer verify any design before it is built.