Calculators
Thermal Expansion Calculator
Solve linear thermal expansion with ΔL = αL₀ΔT.
Estimate one-dimensional thermal expansion or contraction with ΔL = αL₀ΔT. Solve length change, linear expansion coefficient, or temperature change.
Calculated result
1.2 mm
Final length: 2.0012 m
ΔL = αL₀ΔT
Positive ΔT predicts expansion and negative ΔT contraction for materials with a positive coefficient. The linear model assumes a constant coefficient over the temperature range and unconstrained, approximately uniform material behavior.
About This Tool
Temperature changes can make solids expand or contract. For many engineering and classroom estimates over moderate temperature ranges, linear expansion is modeled as ΔL = αL₀ΔT, where L₀ is initial length, α is the material's linear expansion coefficient, and ΔT is temperature change. This calculator solves the direct formula or rearranges it for α or ΔT while handling common length and temperature-difference units.
How To Use It
- Choose whether to solve length change, expansion coefficient, or temperature change.
- Enter the known initial length and the other required values with their units.
- Use a positive temperature change for heating and a negative value for cooling. Celsius and kelvin differences have the same numeric size; Fahrenheit differences are scaled by 5/9.
- Use a coefficient appropriate to the material and temperature range. Published coefficients are often approximate and temperature-dependent.
Examples
Steel-like example
For L₀ = 2 m, α = 12 µm/(m·°C), and ΔT = 50 °C, ΔL = 1.2 mm and the final length is 2.0012 m.
Cooling contraction
With the same 2 m length and coefficient but ΔT = −50 °C, ΔL = −1.2 mm, indicating contraction.
Fahrenheit temperature difference
A 90 °F temperature increase equals a 50 °C difference, so it produces the same expansion as +50 °C.
Solve the coefficient
If a 1 m sample lengthens 1.2 mm across 100 °C, α = 12 µm/(m·°C).
Useful Notes
Linear expansion formula
The common first-order model is ΔL = αL₀ΔT. Final length is L = L₀ + ΔL. The coefficient α has reciprocal-temperature units and describes fractional length change per degree.
Temperature differences are not absolute temperatures
For ΔT, a change of 1 °C equals a change of 1 K. A change of 1 °F equals 5/9 °C. Absolute-temperature offsets such as 32 or 273.15 are not used when converting a temperature difference.
Expansion coefficients vary
A material's coefficient can depend on composition, crystal direction, treatment, and temperature. Reference-table values are usually approximations for a stated range, so precision beyond the source data may be misleading.
Constraints can create thermal stress
The equation predicts free dimensional change. If a component is prevented from expanding or contracting, forces and thermal stresses can develop instead. This calculator does not model those stresses.
Linear versus area and volume expansion
This page models one-dimensional length change. Area and volume expansion use different relationships and may require additional assumptions about isotropic material behavior.
FAQ
What does a negative length change mean?
It means contraction relative to the initial length. For a material with positive α, cooling gives negative ΔT and therefore negative ΔL.
Are °C and K interchangeable here?
For temperature differences, yes: 10 °C of change equals 10 K of change. This is not true for absolute temperature values.
Can I use RPM or heat energy in this calculator?
No. Thermal expansion depends on dimensional change, expansion coefficient, and temperature change. Heat energy and rotational motion are separate physical quantities.
Does this predict exact real-world dimensions?
It is a first-order estimate. Real materials can have temperature-dependent coefficients, anisotropy, constraints, joints, manufacturing tolerances, or phase changes that require more detailed analysis.
Where do I get the expansion coefficient?
Use a reliable material datasheet, engineering handbook, or supplier specification for the material and relevant temperature range. Check the units before entering it.
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