Calculate thermal resistance in K/W for a slab, pipe wall or sphere from thickness and conductivity, plus slab R-value, heat flow, or k from an R-value.

Steady one-dimensional conduction. This is component resistance in K/W, not an area-normalized building R-value.

Additional series resistance
Blank means zero. Add only resistances on the same heat-flow path.

Thermal Resistance Formula

For steady, one-dimensional heat conduction, use the plane-slab relation below for a flat layer. The calculator also supports radial hollow-cylinder resistance ln(rₒ/rᵢ)/(2πkL) and hollow-sphere resistance (rₒ−rᵢ)/(4πkrᵢrₒ). The cylinder model excludes end losses; conductivity is treated as constant.

R = (X) / (A × k)
  • R = thermal resistance of the layer
  • X = thickness measured in the direction of heat flow
  • A = cross-sectional area perpendicular to heat flow
  • k = thermal conductivity of the material

A higher thermal resistance means the layer opposes heat flow more strongly. A lower thermal resistance means heat passes through the layer more easily.

Rearranged Forms

This calculator solves total resistance, steady heat flow, or required plane-slab thickness. For thickness, subtract the added series resistance from the target total before using k and area. The area and conductivity rearrangements below are algebraic references; their R refers to the conduction layer alone. The conductivity-from-R-value mode uses the area-based R-value, k = X/R.

X = (Rₜₒₜₐₗ - Radded) × A × k
A = (X) / (R × k)
k = (X) / (R × A)

How Thermal Resistance Relates to Heat Flow

Use the temperature difference across the complete series path to find heat rate. Define ΔT as side 1 minus side 2, or inner minus outer for a radial shell. Positive heat rate is in that direction; negative heat rate reverses it. Zero ΔT gives zero steady heat rate.

dotQ = (Δ T) / (Rₜₒₜₐₗ)

This means:

  • Increasing thickness increases thermal resistance.
  • Increasing area decreases thermal resistance.
  • Increasing thermal conductivity decreases thermal resistance.

Input Guide

Input Meaning Common Units Effect on Resistance
Thickness of Material The distance heat travels through the layer m, cm, mm, in, ft More thickness increases resistance
Cross-Sectional Area The area normal to the heat-flow path m², in², ft² More area decreases resistance
Thermal Conductivity How readily the material conducts heat W/(m·K), BTU/(hr·ft·°F) Higher conductivity decreases resistance
Thermal Resistance Total opposition to heat flow for the entered layer and area K/W, hr·°F/BTU Higher values indicate less heat transfer

How to Use the Calculator

  1. Choose resistance, heat flow, slab thickness or conductivity from an R-value, then enter the visible required fields. Select slab, cylinder or sphere geometry where applicable.
  2. Use the material thickness in the same direction the heat is traveling.
  3. Enter the cross-sectional area that the heat passes through, not the full outside surface area unless they are the same.
  4. Select the correct unit set for each field.
  5. Select Calculate. Resistance includes any added series/contact term; heat flow uses that total. Required thickness applies only to a slab, and its target total resistance must be strictly greater than the added resistance.

Example

A panel is 0.05 m thick, has an area of 2 m², and has a thermal conductivity of 0.04 W/(m·K), with no additional series/contact resistance.

R = (0.05) / (2 × 0.04) = 0.625 K / W

If the temperature difference across the panel is 10 K, the heat-transfer rate is:

dotQ = (10) / (0.625) = 16 W

So under those conditions, about 16 watts of heat flow through the panel.

Multiple Layers

Many real systems contain more than one thermal resistance. When heat passes through layers one after another, the resistances add directly.

Rₜₒₜₐₗ = R₁ + R₂ + … + Rₙ

If heat can split into separate parallel paths, the combined resistance is found by adding reciprocals.

(1) / (Rₜₒₜₐₗ) = (1) / (R₁) + (1) / (R₂) + … + (1) / (Rₙ)

When This Calculation Is Useful

Thermal resistance is commonly used when comparing insulation materials, wall sections, pipe insulation, oven panels, machine housings, electronic assemblies, heat shields, and any design where controlling heat flow matters.

Important Assumptions

  • The slab equation applies to a flat layer; use the appropriate radial equation for a hollow cylinder or sphere. All models assume steady one-dimensional conduction.
  • The material is treated as uniform through the section.
  • The geometry equations do not automatically include convection, contact resistance, radiation or internal heat generation. An additional nonnegative series/contact resistance may be supplied explicitly in K/W; blank means zero. It must refer to the same component path, not an area-normalized building R-value.
  • Thermal conductivity can vary with temperature, moisture content, density, and material composition.

Common Mistakes

  • Using the wrong area for the heat-flow path.
  • Entering thickness that is not aligned with heat flow.
  • Mixing metric and imperial units without converting them.
  • Using a single-layer equation for a multilayer assembly.
  • Assuming the conductivity value is constant when operating temperature changes significantly.