How to use the R-value and U-value converter
Enter a positive number in either the R-value field or the U-value field, leaving the other one blank. Editing one field clears the other so there is only one authoritative input. Select Convert to calculate the reciprocal. The result uses imperial units by default; select the SI option to add RSI in m²·K/W and metric U-value in W/(m²·K). Reset clears the inputs, result, scale, and shareable query parameter.
The temperature difference, ΔT, does not change the R-to-U conversion. It is used only for the heat-flux estimate. Enter the difference between the warm and cold sides of the surface, not either temperature by itself. For example, 70 °F indoors and 20 °F outdoors gives ΔT = 50 °F. The resulting heat flux is expressed per square foot, so finding total conductive heat transfer requires multiplying that figure by the relevant surface area.
Formulas for reciprocal thermal resistance and heat flow
For a uniform layer or a single complete path under steady-state conditions, thermal transmittance is the reciprocal of thermal resistance:
Formula: U = 1 / R R = 1 / U
Layers arranged in series are crossed one after another, so their R-values add. U-values should not be added or averaged for those layers:
Formula: R_total = R_1 + R_2 + ⋯ + R_n U_assembly = 1 / (∑ i = 1 n R_i)
Once U and the temperature difference are known, steady-state heat flux is:
Formula: q = U × Δ T
The calculator converts imperial R-value to metric RSI with the standard unit factor:
Formula: R_SI = 0.1761 × R_IP
Worked example: comparing a U-0.28 window with R-3.2
Suppose one replacement window is rated U-0.28 and another is described as R-3.2. Converting the first product gives ≈ 3.57. Because R-3.57 is greater than R-3.2, the U-0.28 window has the lower conductive heat transfer. The difference is modest, and a purchase decision should also consider air leakage, solar heat gain, installation quality, and climate.
For an opaque example, R-13 corresponds to U ≈ 0.0769. With ΔT = 50 °F, its idealized heat flux is about 3.85 Btu/(h·ft²). A 100 ft² uniform surface would therefore conduct roughly 385 Btu/h under those steady conditions. A framed wall cannot be treated as a uniform R-13 layer because the studs provide a second, more conductive route.
Thermal bridging and the parallel-path wall formula
A wood-framed wall has at least two parallel paths. One crosses the insulation-filled cavities; the other crosses studs, plates, headers, and other framing. The framing factor is the fraction of wall area assigned to the stud path. Each path has its own total resistance, and the path U-values are weighted by area:
Formula: U_assembly = f_frame / R_stud + (1 − f_frame) / R_cavity R_effective = 1 / U_assembly
Consider a 2×6 wall with R-20.4 cavity insulation, R-0.45 gypsum, R-0.55 sheathing, R-0.61 siding, and interior and exterior air films totaling R-0.85. The cavity path is about R-22.9. Replacing the cavity insulation with 5.5 inches of softwood at R-1.25 per inch gives a stud path near R-9.3. At a 25% framing factor, the result is approximately U-0.060, or effective R-16.7. That is substantially weaker than the batt label suggests.
Continuous exterior insulation raises both path resistances. Adding R-6 continuous insulation to the example produces paths near R-28.9 and R-15.3, reducing the weighted U-factor to about U-0.042. This is why code descriptions such as “R-20 + R-5 continuous insulation” distinguish cavity insulation from material that covers framing.
Common insulation values and result interpretation
Material performance depends on product density, temperature, aging, moisture, and testing method, so design documents should use the manufacturer’s tested value. The ranges below are useful for checking whether an input is plausible.
Approximate thermal resistance of common materials
| Material | Typical R per inch | Approximate reciprocal U |
|---|
| Fiberglass batt | R-3.2 to R-3.8 | U-0.31 to U-0.26 |
| Expanded polystyrene | R-4.0 | U-0.25 |
| Extruded polystyrene | R-5.0 | U-0.20 |
| Closed-cell spray foam | R-6.0 to R-6.5 | U-0.17 to U-0.15 |
| Softwood framing | About R-1.25 | About U-0.80 |
Reciprocal performance has diminishing returns. Increasing R-10 to R-20 cuts ideal conductive heat flow in half, from U-0.10 to U-0.05. Increasing R-40 to R-50 changes U from 0.025 to 0.020, a smaller absolute reduction. That does not make high insulation levels useless, but it does mean that air sealing, window performance, equipment efficiency, and moisture durability should be considered alongside added R-value.
Climate, installation, and retrofit guidance for R-values
Climate-zone requirements differ because heating, cooling, condensation, and solar conditions vary. Codes may specify cavity R-value, continuous insulation, or a maximum whole-assembly U-factor. Always check the locally adopted code rather than treating a general climate table as an approval. A target may also differ for walls, roofs, floors, windows, and doors.
In retrofits, seal uncontrolled air paths before assuming that more insulation will solve every comfort problem. Gaps around penetrations, rim joists, attic bypasses, and poorly installed windows can carry heat and moisture around insulation. Batts should fill cavities without gaps or compression. Foam products need compatible flashing and fire protection, while assemblies in cold or humid climates require a moisture-control strategy appropriate to their drying direction.
International R-value and U-value units
Imperial R-value uses ft²·°F·h/Btu, while metric thermal resistance, often called RSI, uses m²·K/W. Multiply imperial R by 0.1761 to obtain RSI. Thus R-19 is about RSI 3.35. Metric U-value uses W/(m²·K); an imperial U-factor is multiplied by about 5.678 to obtain that value. The reciprocal relationship remains valid only when R and U use matching unit systems.
Limitations and assumptions of this R/U conversion
The basic converter assumes steady-state, one-dimensional conduction through a uniform layer or a path whose total R-value is already known. It does not independently model air leakage, solar gain, thermal mass, radiant barriers, changing outdoor temperatures, moisture transport, fasteners, balconies, steel framing, or three-dimensional junctions. The heat-flux result is a rate per unit area, not an annual energy prediction.
The Assembly Builder is educational rather than a permit-ready simulation. It uses simplified material values, two idealized parallel paths, fixed air films, and a framing factor. Complex projects should use tested product data and an accepted whole-building or whole-assembly method such as ASHRAE procedures or ISO 6946. Confirm compliance with the authority having jurisdiction and seek professional advice where condensation, fire safety, or structural details are significant.
Sources: The reciprocal, series-layer, air-film, and parallel-path methods are described in the ASHRAE Handbook—Fundamentals and ISO 6946. Material testing is addressed by ASTM C518. See also the U.S. Department of Energy’s insulation guidance, the 2021 IECC residential provisions, and NIST unit guidance.
R-value and U-value questions people ask
Is U-value always 1 divided by R-value?
Yes for one uniform layer or one complete thermal path expressed in matching units. It is not enough to invert the cavity insulation label and call that a framed wall’s U-factor. The wall has parallel framing and cavity paths, so their U-values must be weighted by area.
Can R-values from different layers be added?
Yes, when heat crosses those layers in series. Add drywall, insulation, sheathing, continuous insulation, and applicable surface films as resistances, then invert the total. Do not add their U-values.
Why do windows usually list U-factor?
A window rating represents the conductance of glass, gas spaces, spacers, and frame as a complete product. Lower U-factor means less conductive heat transfer. U-0.30 is equivalent to about R-3.33.
Why can cavity insulation stop producing large whole-wall gains?
Studs remain a lower-resistance path regardless of how much insulation fills the adjacent bay. Once that path dominates the weighted result, continuous insulation is more effective because it also covers the framing.
Does a higher R-value guarantee lower energy bills?
No. It reduces ideal conductive heat flow through the treated area, but actual savings also depend on climate, air leakage, windows, equipment, controls, utility prices, workmanship, and the amount of surface upgraded.