How to use the thermal expansion calculator
- Pick the material, or choose your own coefficient and enter it in millionths per degree Celsius.
- Enter the length and choose its unit: millimeters, centimeters, meters, inches or feet.
- Enter the starting and final temperatures and choose Celsius or Fahrenheit.
- Read the change in length and the new length. In the advanced options, enter a change you can allow to see the temperature change that causes it.
Formula
change in length = alpha x length x change in temperature
new length = length + change in length
change in temperature in Celsius = change in Fahrenheit x 5 / 9
temperature change for a given length change = change / (alpha x length)
alpha is the linear coefficient of thermal expansion, written here in millionths per degree Celsius. The material values on the page are rounded examples near room temperature.
A steel rail and an aluminum rod
A 10 m steel part (alpha 12 millionths per degree Celsius) warmed from 20 to 60 degrees Celsius changes by 12 x 10^-6 x 10 x 40 = 0.0048 m, or 4.8 mm, so it ends at 10.0048 m. That is a change of 0.048 percent of its length. The temperature change that would move it by 2.4 mm is 20 degrees Celsius, which is 36 degrees Fahrenheit.
A 2 ft aluminum rod (alpha 23) warmed from 70 to 100 degrees Fahrenheit is a change of 30 degrees Fahrenheit, which is 16.67 degrees Celsius. It grows by 23 x 10^-6 x 2 x 16.67 = 0.00076667 ft, about 0.0092 inches. A 30 m concrete slab (alpha 12) going from -10 to 35 degrees Celsius changes by 16.2 mm, which is why slabs have joints.
Where expansion causes trouble
Long pipes, bridges, rails, fences, decking, window glass and metal roofing all need room to grow and shrink. Without a gap, the stress can buckle the part or crack what it is attached to. Plastics such as PVC expand several times as much as steel, so a plastic pipe run needs more room than a steel one of the same length.
Choosing a coefficient
The listed values are examples. Real coefficients differ with the alloy, the mix or the grade, and they change with the temperature range. If the result matters, take the coefficient from the data sheet for your material. The coefficient for area is about twice the linear value and the coefficient for volume is about three times, but this tool covers length only.
More motion and materials tools
For other motion and material effects, try the Pulley Belt Length Calculator, Terminal Velocity Calculator and Buoyancy and Hydrostatic Pressure Calculator.
Assumptions and limits
- The part is free to expand and is not held at both ends.
- The whole part is at one temperature, and the coefficient stays the same over the range.
- The expansion is small enough that the straight-line formula is accurate.
- The material coefficients are rounded examples, not data for a particular product.
- The length and temperatures in the form are examples to replace with your own.
Frequently asked questions
Why does a Fahrenheit change get multiplied by 5 over 9?
One degree Celsius equals 1.8 degrees Fahrenheit, so a change of 30 degrees Fahrenheit is only 16.67 degrees Celsius. The coefficient is per degree Celsius, so the tool converts the change before using it.
Does the starting temperature matter, or only the change?
Only the change matters in this simple model. Heating from 20 to 60 degrees and from 0 to 40 degrees give the same expansion.
What if the part is held rigidly at both ends?
Then it cannot expand and builds up stress instead. This tool shows how far it would have grown if it were free, which is a way to judge how much stress or how large a gap to expect.
Do materials always expand when heated?
Nearly all do, but a few shrink over narrow temperature ranges, such as water between 0 and 4 degrees Celsius. This tool treats the coefficient as positive for ordinary solids.