Thermal Expansion Coefficient & Material Strain Calculator

Materials Science, Lattice Dynamics & Thermal Expansion Metrology

Thermal expansion is the fractional dimensional change of a material per degree of temperature change:

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• CTE Unit Conversion Relationships (ASTM Standards)**:

α_µin/(in·^) = α_µm/(m·K)1.8 = α_ppm/K × 0.555556

α_K^-1 = α_ppm/K × 10^-6

α_F^-1 = α_K^-11.8 = α_K^-1 × 0.555556

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• Elongation, Volume & Thermal Stress Formulas**:

Δ L = α × L_0 × Δ T (Linear Elongation in mm)

β ≈ 3α (Volumetric Expansion Coefficient)

σ = E × α × Δ T (Constrained Thermal Stress in MPa)

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• Standard Engineering Material CTE Benchmarks**:

• Invar 36 (Ni-Fe Alloy): 1.2 µm/(m·K) 0.67 µin/(in·^) (Near-zero expansion)

• Pyrex Borosilicate Glass: 3.3 µm/(m·K) 1.83 µin/(in·^) (High thermal shock resistance)

• Structural Carbon Steel: 12.0 µm/(m·K) 6.67 µin/(in·^) 12.0 mm on 20m @ 50°C

• Pure Copper: 16.5 µm/(m·K) 9.17 µin/(in·^)

• Aluminum 6061-T6: 23.0 µm/(m·K) 12.78 µin/(in·^) (2× steel expansion)

How to Use This Calculator

Enter your Linear CTE Magnitude (α) (e.g. 12.0 in CTE), From CTE Unit — choose from Micrometers per Meter-Kelvin (µm/(m·K) = ppm/K = 10⁻⁶/K), Fractional per Kelvin (1/K - SI Base Unit), Fractional per Degree Celsius (1/°C), To CTE Unit — choose from µm/(m·K) = ppm/K, 1/K, 1/°F, Initial Component Length (L₀ in meters) (e.g. 20 in m), Temperature Change (ΔT in °C / K) (e.g. 50 in Δ°C), and Engineering Material Benchmark — choose from Custom Material CTE, Structural Carbon Steel (12.0 µm/(m·K), E=200 GPa) → 6.67 µin/(in·°F) | ΔL = 12.0 mm (20m @ 50°C) | σ = 120.0 MPa, Aluminum 6061-T6 (23.0 µm/(m·K), E=69 GPa) → 12.78 µin/(in·°F) | ΔL = 23.0 mm | σ = 79.35 MPa. Results update instantly as you type — adjust any value to compare scenarios.

The Formula

E in GPa = 10^9 Pa, sigma in MPa = 10^6 Pa -> sigma_MPa = E_GPa 1000 alpha * Delta_T

Worked Example

A civil engineer designing a 20.0-meter steel bridge span subject to a 50°C seasonal temperature swing calculates the span will expand by exactly 12.0 mm, requiring a minimum 15 mm expansion joint gap to prevent buckling.

Understanding Your Result

Unit conversions are exact by definition within a given measurement system (e.g., 1 km = exactly 1,000 m). Cross-system conversions (metric to imperial) use defined exchange factors: 1 inch = exactly 2.54 cm; 1 pound = 0.45359237 kg. Round your converted result to match the precision of your original measurement — expressing more decimal places than your input justifies implies false accuracy. For regulatory, legal, or safety-critical applications, verify which measurement system is required by the applicable standard.