Thermal Expansion Calculator

This thermal expansion calculator can be used for the calculation of the linear thermal expansion of any material for a specific initial length and variation in temperature.

Instructions:

  1. Select units (either imperial or metric)
  2. Either choose a material or manually input the linear thermal expansion coefficient
  3. Input the original (initial) material length and input the temperature change
  4. Clicking on the "Calculate" button will provide the length change

* N.B. The thermal expansion coefficients employed are highly dependent on initial temperatures and may undergo significant change. Most values provided are for temperatures of 77°F (25°C).

Thermal Expansion Calculator

°C

×10-6/°C

What is Thermal Expansion?

Thermal expansion refers to the way in which any given substance (either gas, liquid, or solid) will undergo modifications of shape (either volume, area, or length) as temperatures vary. Thermal expansion is caused by particles expanding or contracting within particular substances according to different temperatures.

There are three forms of thermal expansion:

  1. Linear thermal expansion
  2. Areal thermal expansion
  3. Volumetric thermal expansion

Linear Thermal Expansion

We can clearly see that an object's length is dependent on temperature. If we heat something up or cool it, the length changes in proportion to the original length and the temperature change.

ΔL = α × L × ΔT

with:

ΔL being the variation in object length (in, m)

α being the linear expansion coefficient (1/°F, 1/°C)

L being the object's original length (in, m)

ΔT being the temperature change (°F, °C).

The linear thermal expansion coefficient (CTE) is dependent on the material from which an object is made. Generally, linear thermal expansion is most applicable to solids. The CTE employs reciprocal temperature units (°K-1, °F-1, °C-1, etc.) representing the length change per degree per unit length, e.g., in./in./°F or mm/mm/°C. The table at the foot of the page lists the conversion factors.

When we heat or cool an object and it does not have freedom of expansion or contraction (i.e., it is secured at both ends), thermal stress can be powerful enough to cause damage. Holes will undergo expansion or contraction matching that of the material surrounding them.

Thermal expansion can present significant challenges for designers in certain areas, for example when constructing spacecraft, aircraft, buildings, or bridges, but it can have positive uses.

Example:  Calculate the length change of a bronze bar (L = 5m, α = 10 ×10-6/°C), if the temperature rises from 25°C to 75°C.

Solution: The length changes provided by the formula above:

ΔL = 10 × 10-6/°C × 5 × (75°C − 25°C)

ΔL = 0.0025 m.

 

Conversion Factors
Convert From Convert To Multiply By
10-6/°K 10-6/°F 0.55556
10-6/°F 10-6/°K 1.8
10-6/°F 10-6/°C 1.8
10-6/°R 10-6/°K 1.8
10-6/°C 10-6/°F 0.55556
10-6/°C 10-6/°K 1
ppm/°C 10-6/°K 1
(µm/m)/°C 10-6/°K 1
(µm/m)/°F 10-6/°K 1

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