How to calculate thermal expansion in length
Two bars of the same material experience the same temperature rise. The longer bar changes length more because the same small fractional change acts over more material.
What the formula is saying
Calculate thermal strain αΔT first. Multiply that strain by the original length L to find the free length change, not the final total length.
Read the symbols in plain language
- α
- Thermal expansion coefficient1/K
- L
- Lengthm
- ΔT
- Temperature changeK
Sort out the units first
Enter L in m and α in 1/K. Temperature differences in °C and K have the same numerical value. Multiply the answer in m by 1,000 for mm.
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
- L · Length
- 10 m
- ΔT · Temperature change
- 30 K
Find the fractional thermal change
This is how much one unit of length changes relative to itself.
(0.000012) × (30) = 0.00036Apply the fraction to the full length
Multiply by L because the whole bar expands.
(0.00036) × (10) = 0.0036 m
Does this worked answer make sense?
The example moves 3.6 mm. Doubling length or the temperature difference doubles free movement.
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
- L · Length
- 20 m
- ΔT · Temperature change
- 40 K
Find: thermal expansion in length
A hint, not the answer
Calculate thermal strain αΔT first. Multiply that strain by the original length L to find the free length change, not the final total length.
Enter L in m and α in 1/K. Temperature differences in °C and K have the same numerical value. Multiply the answer in m by 1,000 for mm.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Find the fractional thermal change
This is how much one unit of length changes relative to itself.
(0.00001) × (40) = 0.0004Apply the fraction to the full length
Multiply by L because the whole bar expands.
(0.0004) × (20) = 0.008 m
Avoid the common trap
The answer ΔL is a change, not Lfinal. Add it to the original length only when the question asks for final length.
When this method applies — and when it does not
Free expansion with constant α and uniform temperature. Do not use this alone to select an expansion joint or assess a restrained structure.
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.