Economic insulation thickness
Insulation is a capital cost that buys a running saving, so the right thickness is where the marginal cost of another millimetre equals the marginal energy it saves — not the thickest that will fit. There is also a curiosity: below the critical radius (k/h) adding insulation increases heat loss, because the extra surface area outweighs the extra resistance.
| Thickness | Heat loss | Energy | Capital | Total |
|---|---|---|---|---|
| 0 mm | 408.4 W/m | $196 | $0 | $196 |
| 25 mm | 71.2 W/m | $34 | $0 | $34 |
| 50 mm | 44.6 W/m | $21 | $1 | $22 |
| 75 mm | 34.5 W/m | $17 | $1 | $18 |
| 100 mm | 29.0 W/m | $14 | $2 | $16 |
| 125 mm | 25.6 W/m | $12 | $3 | $15 |
| 150 mm | 23.2 W/m | $11 | $4 | $15 |
| 175 mm | 21.5 W/m | $10 | $5 | $15 |
| 200 mm | 20.1 W/m | $10 | $6 | $15 |
| 225 mm | 19.0 W/m | $9 | $7 | $16 |
| 250 mm | 18.1 W/m | $9 | $8 | $17 |
| 275 mm | 17.3 W/m | $8 | $10 | $18 |
| 300 mm | 16.7 W/m | $8 | $12 | $20 |
The economic thickness is 150 mm, where 11 of annual energy cost meets 4 of annualised insulation cost. Beyond that the saving per millimetre falls below its price.
q = ΔT / (ln(r₂/r₁)/2πk + 1/2πr₂h) · Per metre of pipe.
rc = k/h · Below it, insulation increases loss.
energy + capital × CRF · The curve to minimise.
i(1+i)ⁿ / ((1+i)ⁿ − 1) · Capital recovery factor.
A clear path from inputs to results.
Insulation is a capital cost that buys a running saving, so the right thickness is where the marginal cost of another millimetre equals the marginal energy it saves — not the thickest that will fit.
How to use
- Enter the pipe diameter and the insulation conductivity.
- Set the fluid and ambient temperatures and the surface film coefficient.
- Add the installed cost, energy price, hours and life.
- Read the economic thickness and the cost curve.
The formula
Reference: Cylindrical conduction with a surface film coefficient, ASTM C680 and ISO 12241 practice.
Worked example
A 100 mm pipe at 150 °C
- 100 mm outside diameter, k = 0.04 W/m·K.
- 150 °C fluid, 20 °C ambient, h = 10 W/m²·K.
- Insulation $300/m³, energy $0.08/kWh, 6,000 hours, 15 years at 6%.
- 1
Bare, the pipe loses 408 W/m — the only resistance is the surface film.
- 2
At 50 mm of insulation the loss falls to 45 W/m.
- 3
The energy cost falls from $196 a year to $21, while the annualised insulation cost rises from zero to $7.
- 4
At 150 mm the total is lowest: $11 of energy plus $4 of capital.
- 5
Beyond that the capital rises faster than the energy falls, so the curve turns up.
150 mm economic · 23 W/m · $15 a year total.
Interpreting the result
The critical radius is the counter-intuitive part: below k/h, adding insulation increases heat loss because the extra surface area outweighs the extra resistance. It only happens on small pipes with poor surface coefficients, but on a 10 mm instrument line it is real.
Assumptions & limitations
- Steady-state, one-dimensional radial conduction.
- A constant surface film coefficient combining convection and radiation.
- Insulation cost proportional to volume.
- No labour that scales with surface area rather than volume.
Frequently asked questions
Why is there an optimum at all?
Because energy cost falls with thickness while capital cost rises. The minimum of the sum is the economic thickness, and it moves with the energy price rather than with the pipe.
Does doubling the energy price double the thickness?
Roughly, yes — the optimum scales close to linearly with the square root of the price ratio, so a doubling buys about 40% more thickness.
What about the surface temperature?
It matters for personnel protection: 60 °C is the usual limit for a touchable surface, which can require more thickness than the economic calculation does.
What is the critical radius?
k/h. Below it, the insulation adds more surface area than resistance and the heat loss goes up. For mineral wool on a small pipe it can be 30 mm or more.
Should I just insulate as much as possible?
No. Beyond the economic thickness the extra capital never repays, and on a retrofit the labour often dominates the material anyway.
Methodology last reviewed 2026-10-22. Results are informational and not financial or engineering advice — see our disclaimer.