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THERMAL EXPANSION CALCULATOR

Home>Tools>Thermal Expansion Calculator

THERMAL EXPANSION CALCULATOR

Thermal expansion is normally calculated in two ways, as a linear (single dimension) or volumetric (3 dimensional) measurement. Depending on the case, each method is useful, as finding out how a beam would extend due to heat would only require a linear method, however when trying to find out how a body of liquid expands with temperature, volumetric might be best.

Linear Thermal Expansion Calculator

Linear Thermal Expansion is calculated using the following formula:
Linear thermal expansion formula: Change in length = coefficient of linear thermal expansion x change in temperature x initial length
Where:
L = Initial Length

ΔL = The change in Length 
αL = Coefficient of Linear Thermal Expansion
ΔT = Change in temperature 
This thermal expansion calculator uses the most common formula used to estimate the expansion caused by a change in temperature. The linear thermal expansion equation calculates the increase or decrease in a single dimension of a body as a result of a change in temperature, it is calculated by multiplying the dimension of the material by the Coefficient of Linear Thermal Expansion for that material. The Coefficient of Linear Thermal Expansion, or CLTE, is commonly displayed as a product of a length/length per temperature unit. As this is the case, the unit of length does not matter provided both units of length are the same. Once you have your coefficient, you need the length of the expansion to be measured, and the temperature range for the scenario, put it all into the calculator and go!

Volumetric Thermal Expansion Calculator

Volumetric Thermal Expansion is calculated using the following formula:
Volumetric thermal expansion formula: Change in volume = coefficient of volume thermal expansion x change in temperature x initial volume
Where:
V = Initial Volume
ΔV = The change in Volume 
αV = Coefficient of Volumetric Thermal Expansion
Volumetric Thermal Expansion is calculated in a very similar fashion to Linear expansion, only with measurements of volume, not length! Coefficients of Volumetric Expansion are proportional to Linear coefficients, being triple the value of linear expansion, so its easy to convert from one to the other if you cant find the correct coefficient.

Area Thermal Expansion

Area Thermal Expansion is calculated using the following formula:
area thermal expansion formula: Change in area = coefficient of linear thermal expansion x change in temperature x initial area
Where:
A = Initial Area

ΔA = The change in Area 
αA = Coefficient of Area Thermal Expansion
As with linear it Area Expansion is calculated the same way as above, normally double that of linear expansion.
Hot metal glowing - thermal expansion

Linear Thermal Expansion Calculator

Initial Length
Difference in Temperature
  Coefficient of Linear Thermal Expansion




     Expansion

CalculateClear















Volumetric Thermal Expansion Calculator

Initial Volume
Difference in Temperature
  Coefficient of Linear Thermal Expansion



     Volumetric Expansion

CalculateClear

Table Of Thermal Expansion Coefficients

Thermal Expansion of Common Materials
Material Coefficient of thermal expansion (CTE) Reference
Linear Expansion
(X10^-6 K^-1)
Volume Expansion
(X10^-6 K^-1)
Low Carbon Steel 10.1 - 14.9 30.3 - 44.7 Matweb
High Carbon Steel 9.9 - 14.8 29.7 - 44.4 Matweb
Stainless Steel (316) 18.5 55.5 Matweb
Aluminium (pure) 23.6 70.8 Chicago University
Water (293 Kelvin) 69 207 efunda
Water (277 Kelvin) 0 0 University of Oregon
Copper 16.4 49.2 Matweb
Brass 18 - 26 54 - 78 Matweb
ABS 60 - 100 180 - 300 Roechling

Important Notes for Thermal Expansion Calculations!

Its important to remember when using thermal expansion coefficients, figures quoted are normally at 20°C, its important to know the coefficients vary with temperature! for example, thermal expansion of water is a curve, with centre at approximately 4°C. At this point, the thermal expansion is zero, however either side the expansion coefficient increases. In most cases, the difference is very small, but worth checking, especially near the melting point of the material.


Thermal Expansion Examples

Linear Thermal Expansion Example

In this example, we take a stainless steel bar 1000mm long, 100mm wide and 50mm thick. If we heat the bar from 20°C to 300°C, we can calculate the amount the bar will expand in each direction using the linear thermal expansion calculator.
If:
​L = 1000mm 
αL = 18.5 X 10^-6 K^-1, or 0.0000185mm/mm°C
ΔT = 300-20 = 280°C


Stainless Steel Bar Thermal Expansion example
By multiplying our three  variables according the the linear thermal expansion equation, we can find that the bar will expand by approximately 5.2mm, bringing the overall length to 1005.2mm.​

​Volumetric Thermal Expansion Example

Stainless Steel Bar Thermal Expansion example
Using the same example,  a stainless steel bar 1000mm long, 100mm wide and 50mm thick heated to 300°C, we can calculate the amount the volume of the bar will change using the volumetric thermal expansion calculator.
If:
​L = 1000mm 
W = 100mm
D = 50mm
αV = 55.5 X 10^-6 K^-1, or 0.0000185mm/mm°C
ΔT = 300-20 = 280°C

First we need to find the Volume:
V = L x W x D = 5,000,000mm^3
Using the calculator above, we can calculate that the Volume of the bar will expand by 77,000 cubic millimetres, bringing the volume to 5,077,000 cubic millimetres.

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Photo used under Creative Commons from Ross Elliott
  • NEWS
  • Calculators/Tools
    • Inch To Metric Conversion Table
    • Thermal Expansion Calculator
    • Stress, Strain and Young's Modulus
    • Beam Deflection Calculators >
      • Single Load Cantilever Beam Deflection Calculator
      • Single load supported beam deflection calculator
      • Even load cantilever beam deflection calculator
      • Even load supported beam deflection calculator
    • Cutting Speed, Spindle, Feed Rate MRR Calculators
    • Pressure Calculator
    • MTBF, MTTR and Reliability
    • Ohm's Law Calculator
    • Capacitance Calculator
    • Laws of Thermodynamics
    • Heat Transfer >
      • Radiation, Absorbance, Emissivity and Reflectivity
    • Theory of Constraints
    • Entropy and Specific Entropy Calculators
    • Alloying Elements of Steel
    • Kinetic Energy Calculator
    • Potential Energy Calculator
    • Refractive Index Calculator
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