Thermal Expansion Calculator

Linear Thermal Expansion

Linear Expansion Formula:

ΔL = αL₀ΔT
L = L₀(1 + αΔT)
Where: ΔL = change in length, α = coefficient of linear expansion, L₀ = original length, ΔT = temperature change

Original Length (L₀) - meters:

Coefficient of Linear Expansion (α) - /°C:

Temperature Change (ΔT) - °C:

Change in Length (ΔL) - meters:

Linear Expansion Coefficients (×10⁻⁶ /°C):
Steel: 11-13
Aluminum: 23
Copper: 17
Brass: 19
Glass (ordinary): 9
Concrete: 12
Wood (along grain): 3-5
Invar (steel alloy): 1.2

Area Thermal Expansion

Area Expansion Formula:

ΔA = βA₀ΔT
A = A₀(1 + βΔT)
β ≈ 2α (for small expansions)
Where: ΔA = change in area, β = coefficient of area expansion, A₀ = original area

Original Area (A₀) - m²:

Coefficient of Area Expansion (β) - /°C:

Temperature Change (ΔT) - °C:

Change in Area (ΔA) - m²:

Area Expansion Coefficients (×10⁻⁶ /°C):
Steel: 22-26
Aluminum: 46
Copper: 34
Brass: 38
Glass: 18

Note: β ≈ 2α for isotropic materials

Volume Thermal Expansion

Volume Expansion Formula:

ΔV = γV₀ΔT
V = V₀(1 + γΔT)
γ ≈ 3α (for solids, small expansions)
Where: ΔV = change in volume, γ = coefficient of volume expansion, V₀ = original volume

Original Volume (V₀) - m³:

Coefficient of Volume Expansion (γ) - /°C:

Temperature Change (ΔT) - °C:

Change in Volume (ΔV) - m³:

Volume Expansion Coefficients (×10⁻⁶ /°C):
Steel: 33-39
Aluminum: 69
Copper: 51
Water (0-4°C): -68
Water (20°C): 214
Ethanol: 1120
Mercury: 182
Air: 3670

Thermal Stress Analysis

Thermal Stress Formula:

σ = EαΔT (for constrained expansion)
Where: σ = thermal stress, E = Young's modulus, α = linear expansion coefficient, ΔT = temperature change

Young's Modulus (E) - GPa:

Linear Expansion Coefficient (α) - /°C:

Temperature Change (ΔT) - °C:

Thermal Stress (σ) - MPa:

Young's Modulus (GPa):
Steel: 200
Aluminum: 70
Copper: 120
Concrete: 30
Glass: 70

Note: Thermal stress occurs when expansion is constrained