Thermal Diffusivity
Calculate thermal diffusivity of materials using α = k / (ρ·cₚ). Free online physics calculator with material presets for copper, gold, silver, aluminum, water, air, and more. Get instant results with charts.
About This Calculator
The Thermal Diffusivity Calculator computes the thermal diffusivity (α) of any material using the formula α = k / (ρ × cₚ), where k is thermal conductivity, ρ is density, and cₚ is specific heat capacity. Thermal diffusivity measures how quickly heat spreads through a material — an essential property in thermodynamics, heat transfer analysis, and materials science.
This calculator is useful for engineers, physicists, students, and researchers working with heat transfer problems. Simply select a material from the preset list (copper, gold, silver, aluminum, water, air, wood, rubber, and more) to auto-fill its properties, or enter custom values for any material. The tool returns the thermal diffusivity in both m²/s and mm²/s, along with the volumetric heat capacity (ρ × cₚ) and a detailed breakdown of all input values.
Formula
Thermal diffusivity is defined as: α = k / (ρ × cₚ), where:
- α = Thermal diffusivity (m²/s)
- k = Thermal conductivity (W/m·K)
- ρ = Density (kg/m³)
- cₚ = Specific heat capacity (J/kg·K)
The product ρ × cₚ is known as the volumetric heat capacity (J/m³·K) — the heat required to raise the temperature of one cubic meter of material by one Kelvin.
Example Calculation
For water at 25°C: k = 0.607 W/m·K, ρ = 997 kg/m³, cₚ = 4186 J/kg·K. Volumetric heat capacity = 997 × 4186 = 4,173,442 J/m³·K. Thermal diffusivity α = 0.607 / 4,173,442 = 1.4558 × 10⁻⁷ m²/s = 0.1456 mm²/s.
Regional Notes
Worldwide: Thermal diffusivity is a fundamental material property independent of region. The SI unit m²/s is used internationally. In the US, thermal diffusivity is sometimes expressed in ft²/s (1 m²/s ≈ 10.7639 ft²/s). The Imperial system uses BTU/(hr·ft·°F) for thermal conductivity, lb/ft³ for density, and BTU/(lb·°F) for specific heat, resulting in diffusivity in ft²/hr.
Frequently Asked Questions
What is thermal diffusivity?
Thermal diffusivity (α) is a material property that measures the rate of heat transfer through a substance from one point to another. It quantifies how quickly heat penetrates a material and is defined as the ratio of thermal conductivity to volumetric heat capacity.
How do you calculate thermal diffusivity?
Thermal diffusivity is calculated using the formula α = k / (ρ × cₚ), where k is thermal conductivity in W/m·K, ρ is density in kg/m³, and cₚ is specific heat capacity in J/kg·K. The result is expressed in m²/s or mm²/s.
What is the thermal diffusivity of copper?
Copper has a thermal diffusivity of approximately 116 mm²/s at room temperature. This high value means copper conducts heat very rapidly, making it an excellent material for heat exchangers, radiators, and electrical components.
What is the difference between thermal diffusivity and thermal conductivity?
Thermal conductivity (k) measures how well a material conducts heat, while thermal diffusivity (α) measures how quickly heat spreads through a material. Diffusivity accounts for both conductivity and the material's heat storage capacity (density × specific heat). A material can have high conductivity but low diffusivity if it has high volumetric heat capacity.
What is the thermal diffusivity of water?
Water has a thermal diffusivity of approximately 0.145 mm²/s at 25°C. This low value indicates that heat spreads slowly through water compared to metals, which is why water is used as a coolant — it absorbs heat without rapidly conducting it away.
What units is thermal diffusivity measured in?
The SI unit of thermal diffusivity is square meters per second (m²/s). It is commonly expressed in mm²/s for most engineering applications. Other units include ft²/s (imperial) and cm²/s. One m²/s equals 10⁶ mm²/s.
What materials have high thermal diffusivity?
Metals typically have high thermal diffusivity. Gold has about 127 mm²/s, silver about 174 mm²/s, copper about 116 mm²/s, and aluminum about 97 mm²/s. Carbon-carbon composites can reach up to 216 mm²/s. These materials are used in heat sinks, thermal management, and high-performance engineering applications.
How is thermal diffusivity used in non-destructive testing?
Thermal diffusivity is used in thermographic damage detection, a non-destructive testing technique for composite structures. Flash lamps heat one side of a structure while an infrared camera monitors temperature changes on the other side. Anomalies in heat flow revealed by diffusivity calculations help detect hidden subsurface damage in aircraft and other critical components.