Thermal Expansion Calculator — Linear Expansion Converter
Calculate thermal expansion of materials using the linear expansion formula ΔL = L₀αΔT. Essential for engineering design, construction, and materials science. See also our Specific Heat Calculator and Thermal Conductivity Calculator.
How to Calculate Thermal Expansion
- Select what you want to calculate from the dropdown menu.
- Enter the known values in the input fields.
- Click Calculate to solve for the unknown variable.
- Results show length change in meters and millimeters for precision.
Thermal Expansion Formula
ΔL = L₀ × α × ΔT
Where:
ΔL = Change in length (m)
L₀ = Original length (m)
α = Linear expansion coefficient (1/K)
ΔT = Temperature change (K or °C)
Rearranged forms:
α = ΔL / (L₀ × ΔT)
ΔT = ΔL / (L₀ × α)
Final Length = L₀ + ΔLExample Calculation
Problem: A 10-meter steel beam is heated from 20°C to 70°C. How much does it expand?
Given: L₀ = 10 m, α = 12 × 10⁻⁶ /K (steel), ΔT = 70 - 20 = 50 K
Solution: ΔL = 10 × 12 × 10⁻⁶ × 50 = 6.0 × 10⁻³ m = 6.0 mm
Answer: The beam expands by 6.0 mm.
Linear Expansion Coefficients Reference Table
| Material | α (× 10⁻⁶ /K) | α (× 10⁻⁶ /°F) |
|---|---|---|
| Aluminum | 23.1 | 12.8 |
| Steel (carbon) | 12.0 | 6.7 |
| Stainless Steel | 17.3 | 9.6 |
| Copper | 16.5 | 9.2 |
| Brass | 19.2 | 10.7 |
| Iron | 11.8 | 6.6 |
| Lead | 28.9 | 16.1 |
| Zinc | 30.2 | 16.8 |
| Concrete | 12.0 | 6.7 |
| Glass (soda-lime) | 9.0 | 5.0 |
| Quartz | 0.59 | 0.33 |
| Invar (Fe-Ni) | 1.2 | 0.67 |
Technical Details
Linear thermal expansion occurs when materials change length due to temperature changes. The expansion coefficient α is a material property that varies with temperature but is often treated as constant for small temperature ranges. Most materials expand when heated (positive α) but some, like water below 4°C, contract. The formula assumes uniform heating and no phase changes. For large structures, expansion joints accommodate thermal movement to prevent stress and cracking. Temperature differences in Kelvin and Celsius are identical for ΔT calculations.
Frequently Asked Questions
What is thermal expansion?
Thermal expansion is the tendency of materials to increase in size when heated. As temperature rises, atoms vibrate more and take up more space, causing the material to expand in all directions.
Why do different materials expand at different rates?
The expansion coefficient depends on the material's atomic structure and bonding strength. Materials with weaker bonds (like aluminum) expand more than those with stronger bonds (like steel or glass).
How do expansion joints work?
Expansion joints are gaps or flexible connections that allow structures to expand and contract without damage. They're essential in bridges, buildings, and pipelines to accommodate thermal movement.
What happens if thermal expansion is constrained?
If expansion is prevented, thermal stress develops. This can cause buckling, cracking, or failure. The stress equals E × α × ΔT, where E is the elastic modulus.
Are there materials that don't expand?
Invar (iron-nickel alloy) has extremely low expansion. Some ceramics and composites can be engineered to have near-zero or even negative expansion coefficients for specialized applications.