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.

What is the coefficient of thermal expansion of steel?

Mild carbon steel is about 12 ppm/°C (6.7 µin/in·°F), so a 30 m steel rail warmed by 40 °C grows 12 × 10⁻⁶ × 30,000 mm × 40 = 14.4 mm. Austenitic stainless steels expand more: 304 is about 17.2 and 316 about 16.0 ppm/°C, while ferritic 430 (10.4) and martensitic 410 (9.9) are close to carbon steel.

What is the CTE of aluminum?

Typical room-temperature values are 23.1 ppm/°C for pure aluminum, 22.9 for alloy 2024, 23.6 for 6061 and 23.4 for 7075, about 12.7–13.1 ppm/°F. A 1 m aluminum bar heated by 50 °C grows roughly 1.14–1.18 mm.

What is the coefficient of thermal expansion of glass in ppm?

It depends on the glass type: soda-lime (window and container) glass is about 9.0 ppm/°C, while borosilicate glass is about 3.3 ppm/°C, which is why borosilicate tolerates rapid temperature changes better. Check the supplier datasheet for a specific glass grade.

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

It is a constant-CTE estimate. Accuracy depends on whether the selected coefficient represents the exact grade, condition, direction and temperature interval. Because α changes with temperature, critical work should use manufacturer or measured data over the actual interval and, when necessary, an integrated temperature-dependent model.

Why does CTE matter in electronics?

Materials with different CTEs expand by different amounts during thermal cycling. In a constrained assembly, that mismatch can contribute to strain in solder joints, traces and interfaces. Actual reliability depends on the complete stack-up, material directions, geometry, temperature history and manufacturing process.

What is CTE mismatch and why is it a problem?

CTE mismatch occurs when joined materials expand at different rates. If the assembly constrains that movement, interfacial stress, warpage or delamination can result. This calculator estimates free dimensional change only; predicting stress requires a mechanical model with geometry, constraints and temperature-dependent material properties.

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 and shows the matching volume change in the results: an aluminum block (α = 23.1) heated by 100 °C grows about 0.69% in volume. Use linear CTE for length, diameter, or gap calculations; use volumetric CTE for sealed fluid or reservoir volume calculations.

How do I calculate the gap change between two materials?

Differential expansion is (α₁ − α₂) · L₀ · ΔT. An aluminum 6061 part (23.6) inside a 304 stainless housing (17.2), both 100 mm long, heated by 80 °C grows 0.0512 mm more than the housing. Choose the second material in the calculator to get this mismatch directly.

Do polymers have higher CTE than metals?

Many polymers have higher CTE values than common structural metals, but the value can vary substantially with formulation, reinforcement, moisture, direction and temperature. Use grade-specific supplier data when evaluating a metal-to-polymer assembly.

Coefficient of Thermal Expansion by Material

Look up CTE (α) for 80+ materials, calculate how much a part grows or shrinks over a temperature change, see the area and volume change, and compare two materials to get the gap change from CTE mismatch.

Aluminum CTE is about 23 ppm/°C (23 × 10⁻⁶/°C, or 23 µm per meter per °C): 23.1 for pure aluminum, 22.9 for 2024, 23.6 for 6061 and 23.4 for 7075.

CTE Reference Table

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

Values are typical reference estimates, not certified values for every grade or temperature. CTE can vary with temperature, composition, processing, moisture and direction. Verify critical designs against supplier or measured data. Reference context: NIST selected metals at 295 K and NIST materials-data guidance.

Expansion Calculator

ΔL = α · L₀ · ΔT

CTE — α (ppm/°C)

Click or focus a table row and press Enter/Space to fill this automatically. Negative CTE values are allowed.

Original length — L₀

Start temp — T₁

End temp — T₂

Compare with material 2 (optional)

Gives the mismatch ΔL₁ − ΔL₂ for two parts of the same length L₀.

Quick answer

Aluminum CTE is about 23 ppm/°C (23 × 10⁻⁶/°C, or 23 µm per meter per °C): 23.1 for pure aluminum, 22.9 for 2024, 23.6 for 6061 and 23.4 for 7075. That is roughly twice mild carbon steel (12.0) and seven times borosilicate glass (3.3).

Examples

Material	CTE (ppm/°C)	1 m bar, +50 °C
Aluminum (pure)	23.1	+1.155 mm
Aluminum 6061	23.6	+1.180 mm
Stainless steel 304	17.2	+0.860 mm
Mild carbon steel	12.0	+0.600 mm
Borosilicate glass	3.3	+0.165 mm

Search any material, then click its row to calculate expansion for your part.

Summary

This tool provides linear coefficient of thermal expansion (CTE, symbol α) values in µm/(m·°C) — equivalently 10⁻⁶/°C, 10⁻⁶/K or ppm/°C — for over 80 engineering and building materials. The calculator applies ΔL = α · L₀ · ΔT, reports the matching area and volume change, and, when a second material is chosen, the differential expansion that opens or closes a gap between two parts. Values are typical near room temperature; always consult manufacturer data for critical design work.

How it works

Type a material name in the search box to filter the reference table instantly.
Click any table row to pre-fill its CTE into the expansion calculator.
Enter the original part length, start temperature, and end temperature.
Click Calculate to see the dimensional change (ΔL) and the final length.
Use the category filter to browse metals, polymers, ceramics, composites, and more.
Results include both metric (mm, µm) and imperial (in, mil) unit views.
Area and volume change use the exact factors (1 + αΔT)² − 1 and (1 + αΔT)³ − 1, which are about 2αΔT and 3αΔT for an isotropic solid.
Pick an optional second material to get ΔL₁ − ΔL₂: the change in clearance between two parts of the same starting length.

Use cases

Calculating clearance fits for shafts and housings across operating temperature ranges.
Estimating pipe expansion in process piping and selecting expansion joints.
Evaluating bi-material stress in printed circuit boards or bonded assemblies.
Selecting materials for precision instruments that must remain dimensionally stable.
Designing thermal actuators that rely on controlled expansion.
Comparing CTE mismatch between a substrate and a coating or adhesive.
Quick look-up during FEA model setup or structural thermal analysis.

Frequently Asked Questions

Last updated: 2026-10-09 · Reviewed by Nham Vu