How to Calculate Thermal Expansion

Calculating linear thermal expansion and contraction, or change of size due to change in temperature, is a common engineering calculation. Materials that will be welded, glued, or rigidly fastened together should have similar coefficients of thermal expansion, or breakage and cracking may occur. Knowing the expansion due to temperature change is extremely importnat in mold design, and can cause problems with running fits, location misalignment, and more.

Fortunately, the calculation for size change due to temperature change is fairly simple:

Size Change = initial size x temperature change x coefficient of expansion.

The important thing to remember, as with all calculations, is to keep all of the terms of the equation in the same units.

In order to use this equation, you need to know the coefficient of thermal expansion for the material in question. Here is a list of some common coefficients of thermal expansion, for different materials, in inches per inch per degree Fahrenheit:

Aluminum - .000013 or 12.8 x 10^-6 in scientific notation
Beryllium Copper - .0000093 or 9.3 x 10^-6
Brass - .000014 or 10.4 x 10^-6
Brick - .0000032 or 3.2 x 10^-6
Cement - .000006 or 6.0 x 10^-6
Concrete - .000008 or 8.0 x 10^-6
Glass, hard - .0000033 or 3.3 x 10^-6
Glass, Plate - .000005 or 5.0 x 10^-6
Glass, Pyrex - .0000022 or 2.2 x 10^-6
Gold - .0000084 or 8.4 x 10^-6
Graphite - .0000044 or 4.4 x 10^-6
Lead - .0000151 or 15.1 x 10^-6
Marble - .0000065 or 6.5 x 10^-6
Porcelain - .0000017 or 1.7 x 10^-6
Rubber - .0000428 or 42.8 x 10^-6
Silver - .0000107 or 10.7 x 10^-6
Steel - .0000064 or 6.4 x 10^-6
Tin - .000013 or 13.0 x 10^-6
Titanium - .0000048 or 4.8 x 10^-6
Wood, oak parallel to grain - .0000027 or 2.7 x 10^-6
Wood, oak across the grain - .000003 or 3.0 x 10^-6
Zinc - .0000165 or 16.5 x 10^-6

You can use the internet, the Machinists Handbook, Marks Standard Handbook for Mechanical Engineers, and many other resources to find the coefficient of thermal expansion for materials not listed here.

OK, suppose you have a piece of steel that is 12.0000 inches long, and has a 100 degree increase in temperature. What will the new length be?

The change in length = 12.0000 x 100 x .0000064 = .00768

The new length will be 12.0000 = .00768 = 12.00768

As shown in the list, .0000064 inch/inch/degree F is the coefficient of thermal expansion for steel. This can also be represented as 6.4 x 10^-6 in scientific notation.

If you want software to automate this calculation, go to www.dzynsource.com