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_tChange in Length (mm)
expansion_mm = alpha * original_length * delta_t * 1000Final Length
final_length = original_length + alpha * original_length * delta_tVariables
| Variable | Description | Default |
|---|---|---|
alpha | Coefficient of Linear Expansion(1/°C) | 0.000012 |
original_length | Original Length(m) | 10 |
delta_t | Temperature 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.
- 01DeltaL = alpha * L0 * DeltaT
- 02DeltaL = 12e-6 * 10 * 40
- 03DeltaL = 0.0048 m = 4.8 mm
Frequently Asked Questions
Why do bridges have expansion joints?
Steel and concrete expand and contract with temperature changes. Expansion joints allow this movement to prevent structural damage.
What is the coefficient of expansion for common materials?
Steel: ~12e-6, aluminum: ~23e-6, copper: ~17e-6, glass: ~9e-6, concrete: ~12e-6 (all in 1/°C).
Is there also volumetric expansion?
Yes. For isotropic materials, the volumetric coefficient is approximately three times the linear coefficient: beta ≈ 3*alpha.
Learn More
Guide
Thermal Expansion Guide: Calculating Length, Area, and Volume Changes
Understand thermal expansion in engineering materials. Learn to calculate linear, area, and volumetric expansion, handle expansion joints, and avoid thermal stress failures.
Ready to run the numbers?
Open Thermal Expansion Calculator