Thermal Diffusivity Calculator
Enter thermal conductivity, density and specific heat to compute thermal diffusivity α=k/(ρ·c_p). Water k=0.6, ρ=1000, c_p=4182 → α≈1.435e-7 m²/s; copper ≈1.1e-4 (≈800× faster).
Input Data
Results
At a glance:Thermal diffusivity (symbol α) quantifies how fast a temperature change (a thermal signal) propagates through a material. It is defined as α=k/(ρ·c_p), where α is thermal diffusivity (m²/s), k thermal conductivity (W/(m·K)), ρ density (kg/m³) and c_p specific heat at constant pressure (J/(kg·K)). Term by term: the numerator k is the material's ability to conduct heat; the denominator ρ·c_p is the volumetric heat capacity (storage ability). The diffusivity is the ratio: a large α means the material 'conducts fast and stores little', so a temperature change spreads quickly and uniformly (e.g. metals); a small α means 'stores much and conducts slowly', so the change propagates slowly (insulation, soil, wood). It differs from thermal conductivity — conductivity only says how much heat flows in steady state, while diffusivity says how fast a temperature change travels in transient state. Example: at 20°C, water k=0.6, ρ=1000, c_p=4182 → α=0.6/(1000×4182)≈1.435e-7 m²/s. Copper α≈1.1e-4 m²/s, about 800× water, so metal feels 'cool fast' and equalises temperature extremely quickly. Thermal diffusivity is central to transient conduction: a thermal signal penetrates to depth δ≈√(α·t) in time t, explaining why daily/seasonal soil temperature swings affect only the shallow layer while deep underground stays constant. Uses: (1) transient conduction and penetration-depth estimation; (2) soil temperature vs depth and season (agriculture, ground-source heat pumps); (3) food cooling/heating time prediction; (4) dimensionless Fourier number Fo=α·t/L². Notes: (1) take all three properties at the same temperature and moisture (soil moisture matters greatly); (2) use c_p at constant pressure (J/(kg·K)); (3) keep SI units — α is typically 10⁻⁷ (non-metals) to 10⁻⁴ (metals); (4) this formula is for homogeneous materials; composites/porous media need effective properties.
Formula
Thermal diffusivity: α = k / (ρ·c_p)
k conductivity, ρ density, c_p specific heat; α in m²/s
Penetration depth: δ ≈ √(α·t); Fourier number: Fo = α·t/L²
$$\alpha = \frac{k}{\rho\,c_p}$$How to Use
- Enter thermal conductivity k (water 0.6, soil 0.5–2).
- Enter density ρ (water 1000) and specific heat c_p (water 4182).
- The tool computes α=k/(ρ·c_p) in m²/s.
Case Studies
Penetration depth of daily soil temperature swing
Hong Kong farmland surface soil has large day-night swings; dry soil α≈4.46e-7 m²/s.
One day t=86400 s: δ≈√(α·t)=√(4.46e-7×86400)≈0.196 m.
The daily swing mainly affects a ~0.2 m shallow layer; deeper stays nearly constant — useful for seeding and root protection.
Metal vs water equalisation speed
Copper α≈1.16e-4, water α≈1.435e-7 — about 800× apart.
Equalisation time ∝ L²/α, so copper is ~800× faster than water at the same scale.
This is why metal heat sinks spread heat instantly while water/soil change temperature slowly.
Content review: Calculatorism Editorial Team. Results are for reference only; please refer to the relevant authorities for the official figures.