What is the coefficient of thermal expansion?

The linear CTE (α) is a material property that describes the fractional change in length per degree of temperature change: ΔL/L₀ = α · ΔT. It is typically expressed in µm/(m·°C), which is the same as 10⁻⁶/°C or ppm/°C. A value of 12 ppm/°C means a 1 m bar grows 12 µm for every 1 °C rise.

How accurate is the formula ΔL = α·L₀·ΔT?

The linear approximation is accurate for small-to-moderate temperature changes (roughly ±200 °C from the reference). Over larger ranges, α itself changes with temperature and a temperature-integrated form should be used. For most workshop and design estimates the simple formula is sufficient.

Why does CTE matter in electronics?

Solder joints and PCB traces fail when materials with mismatched CTE cycle through temperature. FR-4 substrate has a CTE of ~14–17 ppm/°C in-plane, while ceramic components can be as low as 3–7 ppm/°C. The mismatch creates shear stress at every thermal cycle and is a leading cause of solder fatigue.

What is CTE mismatch and why is it a problem?

CTE mismatch occurs when bonded materials expand at different rates. The difference in expansion creates interfacial shear and normal stresses. The induced stress is proportional to (α₁ − α₂) × ΔT × E, so large temperature swings or large elastic moduli amplify the problem. Selecting materials with similar CTEs minimizes warpage and delamination.

Are the values here the same as volumetric thermal expansion?

No. Volumetric (cubic) expansion β ≈ 3α for isotropic materials. This tool lists the linear coefficient. Use linear CTE for length, diameter, or gap calculations; use volumetric CTE for sealed fluid or reservoir volume calculations.

Do polymers have higher CTE than metals?

Yes — most thermoplastics have CTE values of 50–200 ppm/°C, roughly 5–15× higher than structural metals (steel ~12, aluminum ~23 ppm/°C). This large mismatch must be accounted for in metal-to-plastic assemblies across temperature.

Coefficient of Thermal Expansion by Material

Name: Coefficient of Thermal Expansion by Material
Availability: InStock
Author: Nham Vu

Look up CTE (α) for 50+ materials and calculate how much a part expands or contracts over a temperature change.

CTE Reference Table

Material	CTE (ppm/°C)	CTE (ppm/°F)	Category

Expansion Calculator

ΔL = α · L₀ · ΔT

CTE — α (ppm/°C)

Click a table row to fill this automatically.

Original length — L₀

Start temp — T₁

End temp — T₂

Summary