Physics
Linear thermal expansion
The change in one dimension, proportional to length and to temperature change.
The Formula
dL = alpha x L x dT
The change in one dimension, proportional to length and to temperature change.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| dL | Change in length | metres | How much longer, or shorter if negative. |
| alpha | Expansion coefficient | per degree Celsius | Fractional growth per degree. |
| L | Original length | metres | The length before the temperature change. |
| dT | Temperature change | degrees Celsius | Positive for warming, negative for cooling. |
What Each Symbol Means
dLmetres
Change in length
How much longer, or shorter if negative.
alphaper degree Celsius
Expansion coefficient
Fractional growth per degree.
Lmetres
Original length
The length before the temperature change.
dTdegrees Celsius
Temperature change
Positive for warming, negative for cooling.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate thermal expansion page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate Thermal Expansion, filed under Science. Every number the guide produces comes from substituting into this one line.