Thermal Expansion Calculator Formula

Understand the math behind the thermal expansion calculator. Each variable explained with a worked example.

Formulas Used

Change in Length

expansion = alpha * original_length * delta_t

Change in Length (mm)

expansion_mm = alpha * original_length * delta_t * 1000

Final Length

final_length = original_length + alpha * original_length * delta_t

Variables

VariableDescriptionDefault
alphaCoefficient of Linear Expansion(1/°C)0.000012
original_lengthOriginal Length(m)10
delta_tTemperature Change(°C)40

How It Works

Thermal Expansion

Most materials expand when heated. Linear thermal expansion predicts the change in length.

Formula

DeltaL = alpha * L_0 * DeltaT

where alpha is the coefficient of linear expansion, L_0 is the original length, and DeltaT is the temperature change.

Worked Example

A 10 m steel beam (alpha = 12e-6 /°C) heated by 40°C.

alpha = 0.000012original_length = 10delta_t = 40
  1. 01DeltaL = alpha * L0 * DeltaT
  2. 02DeltaL = 12e-6 * 10 * 40
  3. 03DeltaL = 0.0048 m = 4.8 mm

Ready to run the numbers?

Open Thermal Expansion Calculator