R-Value / U-Value (Series Wall)
Stack up to five layer R-values, get the assembly U-value plus heat flux — SI and US units side by side.
Your recent runs (stored only in your browser)
No calculations yet — results land here so you can compare runs.
The engineering
Thermal resistances in series add exactly like resistors in series: sum the layer R-values (air films, sheathing, insulation, drywall) and the assembly conductance U is the reciprocal of the total. Reach for this card when sizing envelope loads or checking whether a wall meets a code U-value — the code books speak U, the insulation bags speak R, and this card translates both ways.
The classic mistake is averaging U-values of layers instead of adding R-values — U-values never add in series. Also, don't forget the air films: ASHRAE gives roughly 0.12 m²·K/W (R-0.68 US) for a still interior surface and about 0.03 m²·K/W (R-0.17 US) for a 15-mph winter exterior. They're small, but on a single-pane window they're most of the resistance.
US R-values are ~5.68× the SI number for the same physical layer (1 hr·ft²·°F/Btu = 0.17611 m²·K/W). If a conversion looks off by a factor of six, that's the culprit.
Where this math comes from
The physics is Joseph Fourier's: his 1822 Théorie analytique de la chaleur established that steady heat flow through a slab is driven by temperature difference over resistance, which makes series layers add. But 'R-value' as a bench quantity is an American invention — Everett Shuman, a Penn State building researcher, pushed the reciprocal-of-conductance framing around 1945 precisely because bigger-is-better numbers were easier to sell to builders and insulation buyers than shrinking U-values.
ASHRAE (formed in its modern shape by the 1959 ASHAE–ASRE merger) baked tabulated layer resistances and surface-film coefficients into the Handbook of Fundamentals, making the series-sum method the standard envelope calculation. After a wave of exaggerated insulation advertising in the 1970s energy crunch, the FTC's 1979 R-value Rule made the number legally binding on the bag — one of the few thermal quantities with its own federal regulation.
- 1822Joseph FourierPublishes the conduction law that makes thermal resistances add in series.
- 1945Everett ShumanPopularizes the R-value — resistance instead of conductance — for rating insulation.
- 1959ASHRAEASHAE–ASRE merger; the Handbook of Fundamentals codifies layer R-values and film coefficients.
- 1979US Federal Trade CommissionR-value Rule (16 CFR 460) makes advertised R-values legally enforceable.
See the full timeline of the math behind every calculator →
Runs entirely in your browser — nothing you enter leaves this page. Your recent runs are stored only on your device.