Case 1
- Expansion coefficient α
- 0.0000121/K
- Original length L₀
- 10m
- Temperature change ΔT
- 50K
0.006000m
Open with these valuesThermal Expansion Calculator
Change any value to update the result.
0.006000m
Change in length ΔL: 0.006000 mExamples
Linear expansion in one line: ΔL = α × L₀ × ΔT. A 10 m steel beam warmed by 50 K grows 6 mm, and a 25 m rail cooled by 40 K shrinks 12 mm. The temperature change is a difference, so kelvin and degrees Celsius are interchangeable here; enter a negative value for cooling.
The numbers at a glance
Held fixed: Expansion coefficient α 0.0000120 1/K, Original length L₀ 10.000 m.
| Temperature change ΔT (K) | Change in length ΔL (m) |
|---|---|
| 0.00 | 0.000000 |
| 20.00 | 0.002400 |
| 40.00 | 0.004800 |
| 50.00Your value | 0.006000 |
| 60.00 | 0.007200 |
| 80.00 | 0.009600 |
| 100.00 | 0.012000 |
Worked examples
Case 2
- Expansion coefficient α
- 0.0000231/K
- Original length L₀
- 2m
- Temperature change ΔT
- 30K
0.001380m
Open with these valuesCase 3
- Expansion coefficient α
- 0.0000121/K
- Original length L₀
- 25m
- Temperature change ΔT
- -40K
-0.012000m
Open with these valuesHow it's calculated
ΔL = α × L₀ × ΔT
- StepEnter the linear expansion coefficient of the material, per kelvin.Expansion coefficient α=0.0000121/K
- StepEnter the length before the temperature changed, in metres.Original length L₀=10m·Temperature change ΔT=50K
- StepEnter the temperature change; negative means cooling.Temperature change ΔT=50K
- ResultRead the change in length; add it to L₀ for the final length.Temperature change ΔT=50K·Original length L₀=10m→0.006000m
Reference table
| α, L₀, ΔT | Final length | Change in m |
|---|---|---|
| 0.000012, 25, -40 | 24.988 m | -0.012000 |
| 0.000012, 100, 0 | 100 m, unchanged | 0.000000 |
| 0.000023, 2, 30 | 2.00138 m | 0.001380 |
| 0.000017, 1.5, 100 | 1.50255 m | 0.002550 |
| 0.000012, 10, 50 | 10.006 m | 0.006000 |
Questions
How do I calculate thermal expansion?
Multiply the expansion coefficient by the original length and the temperature change: ΔL = α × L₀ × ΔT. A 10 m steel beam with α = 0.000012 per K warmed by 50 K grows 0.006 m, reaching 10.006 m.
What is the coefficient of thermal expansion?
It is how much a material stretches per unit length for each degree of temperature change, in units of 1 per kelvin. Reference tables give aluminium 23, copper 16 to 17, concrete 13 to 14 and steel about 11 to 12, all in millionths per kelvin.
Kelvin or Celsius for the temperature change?
Either. A change of 1 K is exactly a change of 1 °C, and the coefficient carries the same number per °C, so a 50 K rise and a 50 °C rise give the same answer.
What happens when the object cools?
The temperature change goes negative, so the change in length is negative and the object contracts. A 25 m steel rail cooled by 40 K shrinks about 12 mm, which is why bridges and rails are built with expansion gaps.
Does this cover area and volume too?
No, this is linear expansion along one direction. For the same material, area expands at roughly twice the linear coefficient and volume at roughly three times.