Thermal Expansion Calculator

Calculate dimensional change due to temperature. Input length, CTE, and temperature change.

Calculator

Reference CTE Values

Material CTE (µm/m·°C)

How to Use

  1. 1
    Select the Alloy and Temperature Range

    Choose the alloy from the database and enter the initial temperature T₁ and final temperature T₂ in either Celsius or Fahrenheit.

  2. 2
    Input the Initial Dimension

    Enter the length, diameter, or other relevant dimension of the component in millimeters or inches; for area expansion, enter the surface area.

  3. 3
    Read the Dimensional Change and Fit Tolerance Impact

    The calculator outputs the thermal expansion ΔL, the final dimension at T₂, and an assessment of whether the expansion will violate specified dimensional tolerances or cause interference fits to loosen.

About

Thermal expansion is a fundamental material behavior that engineers must account for wherever components operate across a temperature range. From the expansion loops designed into cross-country pipelines to the clearances specified between turbine blades and their casings, dimensional changes due to temperature govern the integrity and function of countless engineered systems.

Accurate CTE data for the specific alloy, temper, and temperature range is essential — CTE varies with temperature, and mean values quoted in datasheets may differ significantly from instantaneous values at extreme temperatures. The AlloyFYI Thermal Expansion Calculator provides both mean and instantaneous CTE values where available, and automatically flags situations where CTE mismatch between joined dissimilar materials may generate stresses exceeding the material's yield strength. The tool supports applications ranging from precision metrology (where even sub-micron expansion matters) to large structural assemblies operating over a 200°C service temperature range.

FAQ

What is the coefficient of thermal expansion and why does it matter?
The coefficient of thermal expansion (CTE, symbol α) quantifies how much a material expands per unit length per degree of temperature change, typically expressed in μm/(m·°C) or 10⁻⁶/°C. For most engineering metals, α is approximately constant over moderate temperature ranges: aluminum alloys average 23 μm/(m·°C), carbon steel 11–12, stainless steel 16–17, and Invar (FeNi36) a remarkable 1.5 μm/(m·°C). CTE governs thermal stress in constrained components, dimensional changes in precision mechanisms, and compatibility requirements in dissimilar-metal joints.
How does thermal expansion cause stress in constrained structures?
When a structural member is prevented from expanding freely — as in a pipe fixed between rigid supports or a component bonded to a stiffer substrate — the constrained thermal expansion generates compressive thermal stress proportional to E × α × ΔT. For a steel beam heated 100°C, this stress is approximately 200 GPa × 12×10⁻⁶ × 100 ≈ 240 MPa, approaching yield. Expansion joints, bellows, and flexible couplings in piping systems are designed specifically to absorb this expansion while allowing the pipe to carry only intended operating loads.
Why do dissimilar metal joints develop stress during thermal cycling?
When two metals with different CTEs are bonded together (as in bimetal thermostats, brazed joints, or electronic packages), a temperature change causes differential expansion that cannot be accommodated without stress. The interface experiences shear stress proportional to the CTE mismatch, the temperature change, and the elastic moduli of the constituents. Repeated thermal cycling induces fatigue at the interface or in the lower-ductility material. This is the primary failure mechanism in soldered electronic joints (particularly in power cycling applications) and in ceramic-to-metal seals used in vacuum electronics.
What are Invar and other low-expansion alloys used for?
Invar (FeNi36) has a CTE of approximately 1.5 μm/(m·°C) near room temperature due to the magnetostrictive Invar effect that partially cancels lattice thermal expansion. It is used in precision optical instruments, laser interferometers, satellite structures, and clock pendulums where dimensional stability with temperature is critical. Super Invar (FeNiCo) further reduces CTE to near zero at a specific temperature. Kovar and similar iron-nickel-cobalt alloys are designed to match the CTE of borosilicate glass, enabling reliable hermetic glass-to-metal seals in electronic packages.
How do I calculate interference fit changes with temperature?
An interference (press) fit is designed with a specific diametral interference at assembly temperature. When the assembly is heated, the shaft expands by α_shaft × D × ΔT and the hub bore expands by α_hub × D × ΔT. If the shaft CTE exceeds the hub CTE (e.g., aluminum shaft in steel hub), the fit tightens with temperature; if the hub expands faster, the fit loosens and may allow relative rotation or axial slip. The thermal expansion calculator evaluates this scenario automatically when two different alloys are selected for shaft and hub, computing the residual interference at the operating temperature.
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