Thermal Expansion Converter
Convert a coefficient of linear thermal expansion between 1/°C, 1/K, µm/m·°C, and in/in·°F. Enter a value and select the From unit and To unit. Note: the current calculator gives incorrect results for some unit pairs.
Convert Thermal Expansion Coefficients Between Units
Thermal Expansion Formula
Where:
- \(\alpha_{\mathrm{from}}\) — the entered coefficient of linear thermal expansion.
- \(\alpha_{\mathrm{to}}\) — the coefficient expressed in the selected destination unit.
- \(s\) — the value of one selected unit expressed in 1/°C: \(s=1\) for 1/°C or 1/K, \(s=10^{-6}\) for µm/m·°C, and \(s=1.8\) for in/in·°F.
This formula converts the coefficient without changing the physical expansion it describes. The current calculator does not apply these factors correctly for every unit pair; see the limitation below.
Thermal Expansion – Calculation Example
Example: convert the default value of 1 per degree Celsius to micrometers per meter per degree Celsius.
\[1\,\mathrm{°C}^{-1}\times\frac{1}{10^{-6}}=1{,}000{,}000\,\mu\mathrm{m}/(\mathrm{m}\cdot\mathrm{°C})\]
Result: the correct conversion is 1,000,000 µm/m·°C. With these default selections, the current calculator instead displays 0.000001; that displayed value is incorrect.
How to use the calculator
- Enter a nonnegative number in Expansion coefficient value. Use a coefficient of linear expansion, not a measured change in length.
- Choose the value’s existing unit in From unit.
- Choose the unit you want in To unit.
- Read Converted Thermal Expansion Coefficient. Before using a result involving µm/m·°C or in/in·°F, check it against the conversion relationships below: the current calculator can display an incorrect value.
What the thermal expansion coefficient means
The coefficient of linear thermal expansion describes the fractional change in a material’s length for a temperature change. A coefficient of 12 µm/m·°C means that, for approximately every 1°C rise, a freely expanding one-meter length becomes about 12 micrometers longer. The same coefficient can be written as \(12\times10^{-6}\,\mathrm{°C}^{-1}\) or \(12\times10^{-6}\,\mathrm{K}^{-1}\).
Degrees Celsius and kelvins have equal-sized temperature intervals: a change of 1°C is a change of 1 K. Their coefficient values are therefore identical, even though the two temperature scales have different zero points. A temperature change of 1°F equals 5/9°C, so the numerical coefficient per °F is 5/9 of the coefficient per °C. The inch-per-inch part is a ratio of lengths and contributes no extra conversion factor.
Engineers use these coefficients to estimate changes in dimensions when temperatures vary, such as the movement of a bridge joint or the fit between two components. The coefficient alone does not give a length change: you also need the original length and temperature change. Other thermal properties answer different questions. For example, thermal conductivity concerns how readily a material conducts heat, while specific heat concerns the energy needed to change its temperature.
Conversion checks and limitations
Important: the calculator’s current conversion factors are reversed for µm/m·°C and are also incorrect for in/in·°F. Its displayed result is reliable for conversion between 1/°C and 1/K, or when the From unit and To unit are identical, but results involving different units outside those cases should not be used without an independent check. The worked example shows the discrepancy using the default selections.
- \(1\,\mathrm{°C}^{-1}=1\,\mathrm{K}^{-1}=1{,}000{,}000\,\mu\mathrm{m}/(\mathrm{m}\cdot\mathrm{°C})\).
- \(1\,\mathrm{°C}^{-1}=\frac{5}{9}\,\mathrm{in}/(\mathrm{in}\cdot\mathrm{°F})\), approximately 0.555556 in/in·°F.
- For a known coefficient \(\alpha\), a small, freely occurring length change can be estimated with \(\Delta L\approx\alpha L_0\Delta T\). Use compatible temperature units for \(\alpha\) and \(\Delta T\).
Linear coefficients can depend on temperature, material composition, and direction within the material. The length-change estimate assumes a roughly constant coefficient over the temperature range; it does not calculate stress when expansion is restrained. If heating or cooling of the material is also relevant, the heat transfer converter addresses a different quantity and does not replace a thermal expansion calculation.
Frequently Asked Questions
How do I convert µm/m·°C to in/in·°F by hand?
Multiply the value by \(10^{-6}\), then by \(5/9\). For example, \(12\,\mu\mathrm{m}/(\mathrm{m}\cdot\mathrm{°C})\) becomes \(12\times10^{-6}\times5/9\approx6.67\times10^{-6}\,\mathrm{in}/(\mathrm{in}\cdot\mathrm{°F})\). The length ratio needs no meter-to-inch conversion: both the numerator and denominator change together. Check conversions involving these units independently because this calculator can display an incorrect result.
What is a typical coefficient of linear thermal expansion?
It depends strongly on the material. Near room temperature, carbon steel is often around 11–13 µm/m·°C, aluminum around 22–24 µm/m·°C, and borosilicate glass around 3–4 µm/m·°C. These are rough comparisons, not design specifications. Alloys, heat treatment, temperature range, and measurement direction can change the value; use data for the exact material when tolerances matter.
Can a thermal expansion coefficient be negative or zero?
Yes. A negative coefficient means a material contracts along the measured direction as its temperature rises over the stated range. Some engineered materials and particular crystal directions show this behavior. A coefficient near zero indicates little length change over that range. This calculator’s input accepts only nonnegative values, so it cannot represent a negative coefficient.
Is a linear expansion coefficient the same as a volumetric expansion coefficient?
No. A linear coefficient describes fractional change in one length; a volumetric coefficient describes fractional change in volume. For a freely expanding, isotropic solid with small expansion, the volumetric coefficient is approximately three times the linear coefficient: \(\beta\approx3\alpha\). That shortcut may not apply to anisotropic materials or to large temperature changes. Do not convert between the two by changing units alone.
Why do published expansion coefficients for the same material differ?
A published coefficient may be measured at one temperature or averaged across a specified temperature interval. Material grade, composition, processing, and measurement direction can also differ. Check the source’s temperature range and whether its value is a linear or volumetric coefficient before comparing figures. For a wide temperature range, a single room-temperature value may give a poor length-change estimate.
How do I estimate the change in a gap between two different materials?
Estimate each part’s length change separately using its own coefficient, starting length, and temperature change. Then compare the movements in the direction that affects the gap. For two equal-length parts heated equally, the difference in expansion is approximately \((\alpha_1-\alpha_2)L_0\Delta T\). The actual clearance also depends on how the parts are mounted and where each length is measured.
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