How to calculate thermal strain
An unconstrained material can change size as its temperature changes. Thermal strain measures the fractional length change, before you multiply by the actual length.
What the formula is saying
The expansion coefficient α tells you the strain per degree of temperature change. Multiply it by ΔT, which is final temperature minus initial temperature.
Read the symbols in plain language
- α
- Thermal expansion coefficient1/K
- ΔT
- Temperature changeK
Sort out the units first
α is in 1/K. A temperature difference of 30°C equals a difference of 30 K; do not add 273.15 to a temperature difference. Here α = 0.000012 per K is a supplied example value.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
- α · Thermal expansion coefficient
- 0.000012 1/K
- ΔT · Temperature change
- 30 K
Find the temperature change
Use the difference, not the final temperature by itself.
(30) = 30 KMultiply by the expansion coefficient
The inverse-temperature unit cancels K, leaving a ratio.
(0.000012) × (30) = 0.00036
Does this worked answer make sense?
For a positive α, warming gives positive free strain; cooling gives negative free strain. The worked ratio 0.00036 is 0.036%.
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Use these new values. Work it out first, then check your answer.
- α · Thermal expansion coefficient
- 0.00001 1/K
- ΔT · Temperature change
- 40 K
Find: thermal strain
A hint, not the answer
The expansion coefficient α tells you the strain per degree of temperature change. Multiply it by ΔT, which is final temperature minus initial temperature.
α is in 1/K. A temperature difference of 30°C equals a difference of 30 K; do not add 273.15 to a temperature difference. Here α = 0.000012 per K is a supplied example value.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Find the temperature change
Use the difference, not the final temperature by itself.
(40) = 40 KMultiply by the expansion coefficient
The inverse-temperature unit cancels K, leaving a ratio.
(0.00001) × (40) = 0.0004
Avoid the common trap
Confusing the final temperature with ΔT changes the answer. The result is a strain ratio, not millimetres of movement.
When this method applies — and when it does not
Uniform temperature change and approximately constant α over the range. Actual movement depends on restraints and material behaviour.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Lesson updated: · Worked examples checked against the implemented formula; not an independent engineering certification.