Heat Loss / Gain Results
Bare Pipe Heat Loss
—
BTU/hr
Insulated Heat Loss
—
BTU/hr
Insulated Loss per ft
—
BTU/hr per ft
Energy Cost & Condensation Analysis
| Insulation Thickness | Heat Loss (BTU/hr) | % Reduction | Est. Annual Cost |
|---|
Cylindrical heat loss: q = |Tf − Ta| / (R_ins + R_out), where R_ins = ln(r2/r1)/(2πkL) and R_out = 1/(h·2πr2·L). r1 = pipe OD/2, r2 = r1 + insulation thickness (ft). Bare pipe: R_out only at pipe surface. h = 1.5 BTU/hr·ft²·°F (still air). Critical radius r_crit = k/h; for very small pipes with thin insulation, q may increase until r2 > r_crit (this is physically correct, not a calculation error). Dew point from Magnus formula. Annual cost assumes 8,760 hr/yr.
About This Calculator
This calculator estimates heat loss (or heat gain on cold lines) for bare and insulated pipe using the cylindrical conduction resistance of the insulation in series with the outer air film. Enter the pipe size, insulation type and thickness, fluid and ambient temperatures, and length; the tool returns bare and insulated heat rates in BTU/hr, the percent reduction, and the loss per foot.
A thickness comparison table shows diminishing returns as insulation is added, and an annual energy-cost estimate folds in plant efficiency and energy rate. For chilled or cold-water lines below the surrounding air temperature, a Magnus-formula dew-point check flags condensation risk so you can specify a vapor barrier.
Formula & Method
| Heat rate | q = |Tf − Ta| ÷ (Rins + Rout) |
| Insulation R | Rins = ln(r₂ ÷ r₁) ÷ (2π · k · L) |
| Film R | Rout = 1 ÷ (h · 2π · r₂ · L) |
| Critical radius | rcrit = k ÷ h |
This is the steady-state cylindrical conduction model from standard heat-transfer practice and ASHRAE Fundamentals. r₁ is the pipe outer radius, r₂ = r₁ + insulation thickness (ft), k is the insulation thermal conductivity, and h ≈ 1.5 BTU/hr·ft²·°F is the still-air outer-film coefficient. The bare-pipe case uses only the outer film at the pipe surface. Below the critical radius rcrit = k ÷ h, thin insulation can slightly raise heat transfer — correct physics, not an error. Dew point uses the Magnus formula; annual cost assumes 8,760 hr/yr at 3,412 BTU per kWh.
Frequently Asked Questions
How is pipe insulation heat loss calculated?
Heat loss is found from the cylindrical (radial) conduction resistance of the insulation in series with the outer air-film resistance. The heat rate q equals the temperature difference between fluid and ambient divided by the sum of those resistances. The insulation resistance grows with the natural log of the outer-to-inner radius ratio, so each added inch of thickness returns less benefit than the last.
What thermal conductivity (k) should I use?
Thermal conductivity k is a property of the insulation, in BTU-inch per hour per square foot per degree Fahrenheit. This tool uses about 0.27 for fiberglass and elastomeric, 0.30 for mineral wool, 0.33 for foam glass, and 0.16 for cellular glass. Lower k means less heat loss for the same thickness. Real k rises with temperature, so manufacturer data at the mean operating temperature is more exact.
What is the critical radius of insulation?
The critical radius equals k divided by the outer film coefficient h. On very small pipes with thin insulation, adding insulation can slightly increase heat loss until the outer radius exceeds the critical radius, because the growing surface area outpaces the added resistance. This is correct physics, not a calculation error. Insulate beyond the critical radius for net savings.
Why does the tool check for condensation on cold pipes?
When the fluid is colder than the surrounding air, the pipe or insulation surface can fall below the dew point and sweat. The calculator finds the dew point from ambient temperature and relative humidity using the Magnus formula and warns when the fluid temperature is below it. Cold-pipe insulation needs a continuous vapor barrier to keep moisture from reaching the cold surface.
Results are design estimates for preliminary sizing. Verify final designs against applicable codes and standards — engineering judgment and a licensed professional engineer’s review are required.