Thermal Diffusivity Converter
Convert thermal diffusivity between m²/s, cm²/s, mm²/s, ft²/s, ft²/h, and more with step-by-step solutions.
Thermal Diffusivity Converter
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Formula: alpha = k / (rho x cp) | converted = value x (fromFactor / toFactor)
Worked example — 9.7 x 10^-5 m²/s = 0.97 cm²/s
Formula
alpha = k / (rho x cp) | converted = value x (fromFactor / toFactor)
Thermal diffusivity (alpha) equals thermal conductivity divided by density times specific heat capacity. Unit conversion multiplies the value by the ratio of the source unit factor to the target unit factor, both relative to the SI base unit m²/s.
Worked Examples
Example 1: Aluminum Diffusivity Conversion
Problem:Convert aluminum thermal diffusivity of 9.7 x 10^-5 m²/s to cm²/s.
Solution:9.7e-5 m²/s x (1 / 1e-4) = 0.97 cm²/s
Result:9.7 x 10^-5 m²/s = 0.97 cm²/s
Example 2: Imperial to SI Conversion
Problem:Convert 1.0 ft²/h to m²/s.
Solution:1.0 ft²/h = 1.0 x 0.092903 / 3600 = 2.5806e-5 m²/s
Result:1.0 ft²/h = 2.5806 x 10^-5 m²/s
Frequently Asked Questions
What is thermal diffusivity?
Thermal diffusivity is a material property that measures how quickly heat spreads through a substance. It is defined as the ratio of thermal conductivity to the product of density and specific heat capacity, expressed as alpha = k / (rho * cp). The SI unit is meters squared per second (m²/s). Materials with high thermal diffusivity, like metals, heat up and cool down faster than materials with low thermal diffusivity, like wood or rubber.
How is thermal diffusivity different from thermal conductivity?
Thermal conductivity (k) measures a material's ability to conduct heat in steady state, while thermal diffusivity (alpha) describes how quickly temperature changes propagate through a material in transient conditions. A material can have high conductivity but low diffusivity if it has a high volumetric heat capacity. Thermal diffusivity accounts for both the ability to conduct heat and the amount of energy needed to change temperature.
What are typical thermal diffusivity values for common materials?
Copper has a thermal diffusivity of about 1.11 x 10^-4 m²/s, aluminum is about 9.7 x 10^-5 m²/s, steel is around 1.5 x 10^-5 m²/s, and water is approximately 1.43 x 10^-7 m²/s. Insulators like wood have very low values around 1.5 x 10^-7 m²/s. These values help engineers predict how fast heat will diffuse through different materials in applications like casting and heat treatment.
Why do engineers need to convert thermal diffusivity units?
Engineers working across international teams or with legacy data often encounter thermal diffusivity in different unit systems. American engineering references may use ft²/s or ft²/h, while scientific literature uses m²/s or cm²/s. Consistent units are critical in heat transfer calculations such as the Fourier number (Fo = alpha * t / L²), where mismatched units lead to incorrect results in thermal analysis and simulation.
Why does thermal diffusivity carry units of area per unit time?
It falls straight out of alpha = k/(rho*cp). Conductivity is W/(m*K), density is kg/m^3 and specific heat is J/(kg*K); dividing leaves J per second over J per metre, which reduces to m^2/s. That is the same dimensional group as mass diffusivity and kinematic viscosity, and it is why diffusivity behaves like a spreading rate for area rather than a rate of heat flow.
How does the Fourier number use thermal diffusivity?
The Fourier number is Fo = alpha*t/L^2, a dimensionless comparison of how far heat has diffused against the size of the body. Values well below one mean the interior has barely responded and only a surface layer has changed temperature; values near or above one mean the object is approaching a uniform temperature. Rearranged, it says the thermal penetration depth grows roughly as the square root of alpha times time.
When does thermal diffusivity let me use a lumped-capacitance model?
The test is the Biot number, Bi = h*L/k, comparing surface convection resistance with internal conduction resistance. Below about 0.1 the interior stays nearly uniform and the body can be treated as a single temperature that decays exponentially. Above that, internal gradients matter and you need a transient conduction solution in which diffusivity, through the Fourier number, sets the timescale.
How does thermal diffusivity differ from mass diffusivity?
Both are expressed in m^2/s and both describe spreading, but thermal diffusivity moves energy while mass diffusivity moves species through concentration gradients. Their ratio is the Lewis number, Le = alpha/D, which tells you whether a heat front or a concentration front leads in a coupled process such as drying, combustion or evaporative cooling. Because the units match, mislabelled data is easy to mix up.
How is thermal diffusivity measured in a laboratory?
The dominant technique is the laser flash method: a thin disc of known thickness L is pulsed on one face and an infrared detector records the temperature rise on the opposite face. Diffusivity follows from the half-rise time as alpha = 0.1388*L^2/t_half. Because the method returns alpha directly, conductivity is usually back-calculated as k = alpha*rho*cp using separately measured density and specific heat.
Why do ft^2/h figures look so much bigger than the same value in m^2/s?
Because the unit itself is far smaller: 1 ft^2/h equals 0.092903 m^2 divided by 3600 s, or about 2.58 x 10^-5 m^2/s. The numeric value therefore rises by roughly 38,750 times when you convert m^2/s to ft^2/h. That is why American heat transfer tables show water near 0.0055 ft^2/h while SI tables show 1.43 x 10^-7 m^2/s for the same material.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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