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Thermal Resistance

R = L/(kA) for plates. Cylinder: R = ln(r₂/r₁)/(2πLk). Sphere: R = (r₂-r₁)/(4πr₁r₂k). Series: R_total = R₁+R₂. Parallel: 1/R_total = 1/R₁+1/R₂.

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R = L/(kA) for plane wall Cylinder: R = ln(r₂/r₁)/(2πLk) Series: R_total = ΣRᵢ Critical radius r_cr = k/h

Key quantities
R = L/(kA)
Plate
Key relation
R = ln(r₂/r₁)/(2πLk)
Cylinder
Key relation
R_total = R₁+R₂
Series
Key relation
r_cr = k/h
Critical r
Key relation

Ready to run the numbers?

Why: Thermal resistance governs heat loss in walls, pipes, and insulation. R-value = L/k for building materials.

How: Plate: R = L/(kA). Cylinder: R = ln(r₂/r₁)/(2πLk). Q = ΔT/R. Critical radius r_cr = k/h for cylinders.

R = L/(kA) for plane wallCylinder: R = ln(r₂/r₁)/(2πLk)
Sources:ASHRAE HandbookNIST

Run the calculator when you are ready.

Calculate Thermal ResistancePlate, cylinder, or sphere

🏠 Wall Insulation R-Value

Calculate thermal resistance of insulated wall

💻 Heat Sink

Thermal resistance of aluminum heat sink

🏗️ Multi-Layer Wall

Composite wall with multiple insulation layers

🔧 Pipe Insulation

Thermal resistance of insulated pipe

⚡ Electronic Thermal Management

Thermal resistance network for electronic cooling

Thermal Resistance Inputs

W/(m·K)
Thickness must be a positive number
Thickness must be a positive number

For educational and informational purposes only. Verify with a qualified professional.

🔬 Physics Facts

🌡️

R = L/(kA) thermal resistance

— Heat Transfer

📐

Cylinder R = ln(r₂/r₁)/(2πLk)

— Conduction

📊

Series resistances add

— Heat Transfer

🔥

Critical radius r_cr = k/h for insulation

— Heat Transfer

What is Thermal Resistance?

Thermal resistance (R) measures opposition to heat flow. For a plate: R = L/(k·A). Higher R means better insulation. R-value (m²·K/W) is thermal resistance per unit area, commonly used in building codes.

How To Use This Calculator

  1. Select shape: Plate, Cylinder, or Sphere
  2. Enter dimensions (thickness, area, radii) and material
  3. Set hot and cold temperatures
  4. Click Calculate for thermal resistance and heat transfer rate

📐 Key Formulas

  • Plate: R = L/(k·A)
  • Cylinder: R = ln(r₂/r₁)/(2πLk)
  • Sphere: R = (r₂-r₁)/(4πr₁r₂k)
  • Heat flux: Q = ΔT/R

❓ FAQ

What is critical radius of insulation?

For cylinders/spheres, adding insulation can initially increase heat loss if the radius is below critical. r_cr = k/h (cylinder) or 2k/h (sphere).

⚠️ Disclaimer: Thermal conductivity varies with temperature. Use manufacturer data for design. Verify building code R-value requirements.

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