Linear Thermal Expansion Calculator
Find how much a rod, pipe or rail grows or shrinks with temperature using linear thermal expansion, deltaL = alpha times L times deltaT. Enter a coefficient, length and temperature change to get the change in length and the new length.
How to calculate linear thermal expansion
- Enter the linear expansion coefficient alpha in per kelvin (1/K).
- Enter the initial length in metres.
- Enter the temperature change in kelvin, using a negative value for cooling.
- Read the change in length and the final length.
Examples
Steel beam heated
alpha = 12e-6, L = 10 m, deltaT = 50 K
deltaL = 0.006 m = 6 mm, final = 10.006 m
Steel beam cooled
alpha = 12e-6, L = 10 m, deltaT = -50 K
deltaL = -0.006 m, final = 9.994 m
Frequently asked questions
What is the linear thermal expansion formula?
deltaL = alpha * L * deltaT, where deltaL is the change in length, alpha is the linear expansion coefficient in 1/K, L is the original length and deltaT is the temperature change in kelvin.
What units should I use?
Use SI units: the coefficient in per kelvin, length in metres and temperature change in kelvin. A change in kelvin equals a change in degrees Celsius, so either works for deltaT.
What are typical expansion coefficients?
Roughly 12e-6 per K for steel, 23e-6 for aluminium, 17e-6 for copper, 9e-6 for glass and about 0.5e-6 for fused quartz. Larger values expand more for the same heating.
What happens when deltaT is negative?
A negative temperature change means cooling, so deltaL is negative and the material contracts. The final length is shorter than the original length.
Is this linear, area or volume expansion?
This is linear (one dimensional) expansion. Area expansion is about 2 times alpha and volume expansion is about 3 times alpha for an isotropic solid.
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