Linear Thermal Expansion Calculator (Growth and Differential Growth)
Metals grow when heated, and different metals grow by different amounts. This calculator gives the growth of one part from its length, material and temperature change, and the differential growth against a mating part of another material, which is what drives fit, clearance and alignment problems.
Your numbers
Drawings and gauges are referenced to 20 C.
Your results
Uses average handbook coefficients, which vary with alloy, temperature range and heat treatment. For tight work use the supplier data and the actual part temperature, not the room temperature.
Growth versus operating temperature (um)
Sweeps Operating temperature from -40 to 200, holding your other inputs fixed.
Capture inspection conditions in your quality records
Optional: a short review of how temperature and gauge data are recorded with inspection results.
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How to use it
Enter the length at the 20 C reference, choose the material for each part, and set the operating temperature. Part 1 is the base part and part 2 the mating one. The outputs show each part's growth in micrometres, the difference between them, the new length of part 1 and its strain. The chart sweeps temperature from minus 40 to 200 C so you can see how fast the gap opens or closes. A 500 mm steel bar warmed from 20 to 60 C grows about 234 um.
The formula
Linear expansion is change in length equals original length times the coefficient of thermal expansion times the temperature change. With length in millimetres and the coefficient in micrometres per metre per degree, the result in micrometres is length times coefficient times temperature change divided by 1000. Strain in parts per million is just the coefficient times the temperature change. Values used are typical handbook averages near room temperature and rise slightly with temperature.
Reading the result
The differential figure is the number to design around. An aluminium housing around a steel bearing, 100 mm in diameter, opens up roughly 120 um more per 100 C rise than the steel, which can loosen a press fit or change preload. Precision assemblies handle this by choosing matched materials, allowing for float, or using Invar-type alloys for stability. For long parts, remember that measurement itself is affected, so check the companion measurement error calculator.
- Compare differential growth with the fit clearance or interference
- Use the part temperature, not the room temperature
- Allow for soak time, large parts lag the air temperature
Common mistakes
Common mistakes include using ambient temperature for a part that runs hot, mixing units so the answer is out by 1000, assuming one coefficient across a wide range, and ignoring that restrained parts build stress instead of growing. Another is checking dimensions on a part fresh from the machine, still warm from cutting, against a 20 C drawing size.
Frequently Asked Questions
What is the thermal expansion coefficient of steel?
Carbon steel is typically about 11 to 12 micrometres per metre per degree Celsius. Stainless 304 is higher at around 17, and aluminium alloys are about 23. These are averages and vary with alloy and temperature, so use supplier data when it matters.
How much does a steel part grow per degree?
About 11.7 micrometres per metre per degree Celsius, so a 1 m steel bar grows roughly 12 um per degree. A 100 mm part grows about 1.2 um per degree, which is why temperature control matters for micron-level work.
Why is 20 C the reference temperature?
ISO 1 sets 20 degrees Celsius as the standard reference temperature for dimensional measurement. Drawings, gauges and calibration certificates assume it, so parts measured at other temperatures need compensation or soak time to give comparable results.
Can I use this for plastics?
The formula works, but plastics expand several times more than metals, often 50 to 150 micrometres per metre per degree, and also absorb moisture. Enter the supplier coefficient by choosing the closest value or using the custom calculation by hand.
If temperature-sensitive parts are inspected at varying conditions and results are logged in your ERP, we can help add compensation and context to the records.
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