Thermal Diffusivity Calculator — α = k / (ρ · Cₚ)
Enter a material's thermal conductivity, density, and specific heat capacity to compute its thermal diffusivity — a measure of how fast temperature changes propagate through it.
W/(m·K)
kg/m³
J/(kg·K)
s
α = k / (ρ · Cₚ) — higher means temperature changes spread faster
Formula
Thermal conductivity
Density
Specific heat capacity
Denominator
Thermal diffusivity
- 1
Volumetric heat capacity ρ × Cₚ
7,800 × 500 = 3,900,000Energy absorbed per unit volume per kelvin. - 2
α in m²/s
50 ÷ 3,900,000 = 0.00001282 - 3
α in mm²/s (× 10⁶)
0.00001282 × 1,000,000 = 12.8205
How does this calculator work?
Thermal diffusivity α = k/(ρ·Cₚ) combines conductivity and volumetric heat capacity to quantify how fast temperature waves travel through a material. Steel ≈ 12.8 mm²/s (fast), water ≈ 0.14 mm²/s (slow). The thermal penetration depth after time t is δ = 2√(α·t).
Formula
How this is calculated
Thermal diffusivity α (m²/s) measures how quickly a temperature disturbance at one surface of a material propagates through its bulk. It combines two competing effects: high thermal conductivity k promotes fast heat transport, while high volumetric heat capacity ρ·Cₚ means the material absorbs heat without changing temperature much, slowing propagation. The formula α = k/(ρ·Cₚ) is a material property — independent of geometry and boundary conditions — and is the key parameter in the transient heat-conduction equation ∂T/∂t = α·∇²T.
Materials with high diffusivity (metals) equilibrate quickly after a temperature change. Copper (α ≈ 112 mm²/s) reaches thermal equilibrium far faster than wood (α ≈ 0.08–0.13 mm²/s) or water (α ≈ 0.143 mm²/s), which is why a metal spoon in hot coffee heats up faster than a wooden one. Building materials like concrete (α ≈ 0.7–1.0 mm²/s) have intermediate diffusivity — they store heat well and release it slowly, which is useful for thermal mass in passive-solar design.
The thermal penetration depth δ = 2√(α·t) is a practical derived quantity: it approximates how far a sudden temperature change at one surface has significantly penetrated into a semi-infinite material after time t. For example, after 1 hour (3,600 s) in steel (α = 12.8 mm²/s), the penetration depth is about 430 mm; in concrete (α = 0.75 mm²/s) it is about 104 mm. This formula is an order-of-magnitude estimate for semi-infinite geometry — actual penetration in finite-thickness slabs requires the full analytical or numerical solution.
Frequently asked questions
Thermal conductivity k (W/m·K) measures steady-state heat flow through a material at a given temperature gradient — useful for calculating heat losses through walls and pipes. Thermal diffusivity α (m²/s) measures how fast a temperature change propagates in transient conditions. A material can have high k but low α if it has a very high heat capacity (e.g. water: k = 0.6 W/m·K but α = 0.14 mm²/s). For steady-state calculations use k; for time-dependent problems use α.
Approximate values in mm²/s: still air ≈ 19, water ≈ 0.14, wood ≈ 0.10–0.13, concrete ≈ 0.7–1.0, glass ≈ 0.34, brick ≈ 0.5, ice ≈ 1.0, aluminium ≈ 97, copper ≈ 112, steel ≈ 12–14, silver ≈ 166. Higher diffusivity means faster thermal equilibration.
The penetration depth δ = 2√(α·t) is the approximate distance into a material at which the temperature has changed significantly after a step change applied at the surface. It is useful for estimating: how deep frost penetrates soil overnight, how fast a metal casting cools, or whether a thermal disturbance has reached the interior of a wall after a given time. It grows with the square root of elapsed time.
Also known as
TG we-Calculate Editorial Team. (2026). Thermal Diffusivity Calculator — α = k / (ρ · Cₚ) [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/thermal-diffusivity-calculator
TG we-Calculate Editorial Team. "Thermal Diffusivity Calculator — α = k / (ρ · Cₚ)." TG we-Calculate. 2026. https://we-calculate.com/calculator/thermal-diffusivity-calculator.
TG we-Calculate Editorial Team, "Thermal Diffusivity Calculator — α = k / (ρ · Cₚ)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/thermal-diffusivity-calculator
@misc{wecalculate_thermal_diffusivity_calculator, title = {Thermal Diffusivity Calculator — α = k / (ρ · Cₚ)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/thermal-diffusivity-calculator}}, year = {2026}, note = {TG we-Calculate} }
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