Thermal Expansion Calculator
Calculate linear thermal expansion, thermal strain, and restrained thermal stress for engineering materials subjected to temperature changes.
Inputs
Results
Length Change (ΔL)
0.07 in
Restrained Thermal Stress
18,850 psi
How to Use This Calculator
- Enter the Original Length in inches at the reference (installation) temperature.
- Enter the Temperature Change (ΔT) in °F — positive for heating, negative for cooling.
- Set the Expansion Coefficient (α) for your material: steel ≈ 6.5×10⁻⁶, aluminum ≈ 12.8×10⁻⁶, copper ≈ 9.3×10⁻⁶ per °F.
- For restrained thermal stress calculations, enter the Cross-Sectional Area in in² and Elastic Modulus (E) in psi (steel ≈ 29×10⁶ psi).
- Read the Length Change (ΔL) in inches to determine required expansion loop, joint, or gap size.
- Check Restrained Thermal Stress (psi) and Thermal Force (lb) if the member is anchored — compare to the material allowable stress.
How the result changes with Original Length
| Original Length | Length Change (ΔL) | Restrained Thermal Stress |
|---|---|---|
| 10,000 | 6.5 in | 18,850 psi |
| 35,000 | 22.75 in | 18,850 psi |
| 65,000 | 42.25 in | 18,850 psi |
| 90,000 | 58.5 in | 18,850 psi |
What each input means
- Original Length
- Initial length of the member at the reference temperature.
- Temperature Change (ΔT)
- Change in temperature from the installation temperature. Positive = heating, negative = cooling.
- Expansion Coefficient (α)
- Coefficient of thermal expansion. Steel ≈ 6.5×10⁻⁶; aluminum ≈ 12.8×10⁻⁶; copper ≈ 9.3×10⁻⁶ per °F.
- Cross-Sectional Area
- Cross-sectional area of the member. Used to calculate restrained thermal force.
- Elastic Modulus (E)
- Young's modulus of the material. Steel ≈ 29×10⁶; aluminum ≈ 10×10⁶; copper ≈ 17×10⁶ psi.
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersOriginal Length = 100, Temperature Change (ΔT) = 100, Expansion Coefficient (α) = 0.0000065, Cross-Sectional Area = 1 = 5 input(s) provided
- Calculate Length ChangeLength Change0.065 = 0.065
- Calculate Restrained Thermal StressRestrained Thermal Stress18850 = 18850
- Calculate Thermal StrainThermal Strain0.00065 = 0.00065
- Calculate New LengthNew Length100.065 = 100.065
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