Thermal Expansion Calculator
The Thermal Expansion Calculator predicts how a solid object grows or shrinks as its temperature changes. Pick whether you are tracking a length, a surface area, or a volume, then supply the original size, the material coefficient of expansion, and the temperature change in degrees Celsius. The tool returns the change in size, the resulting new size, and the effective coefficient applied for that dimension, so you can plan expansion gaps, tolerances, and clearances with confidence.
Formula
linear: dL = a*L0*dT ; area: dA = 2a*A0*dT ; volume: dV = 3a*V0*dT ; newSize = original + delta
- a
- Linear coefficient of thermal expansion (per degree Celsius)
- L0 / A0 / V0
- Original length, area, or volume of the object
- dT
- Temperature change (final minus initial), in degrees Celsius
- delta
- Change in size for the selected dimension
How it works
- Choose a mode — linear for a length, area for a flat surface, or volume for a three-dimensional solid. The mode decides whether the calculator multiplies the linear coefficient by 1, 2, or 3.
- Enter the original size, the linear coefficient of expansion (alpha, per degree Celsius), and the temperature change. A positive temperature change expands the object while a negative one contracts it.
- The calculator computes the change in size, adds it to the original to find the new size, and reports the effective coefficient (alpha, 2-alpha, or 3-alpha) used for the selected dimension.
Worked example
An aluminium beam 10 m long is heated by 40 degrees Celsius. Aluminium has a linear coefficient of about 23e-6 per degree Celsius.
- Linear mode keeps the coefficient as a = 23e-6 per degree Celsius.
- Change in length: dL = 23e-6 x 10 x 40 = 0.0092 m (9.2 mm).
- New length: 10 + 0.0092 = 10.0092 m.
The beam lengthens by 0.0092 m (9.2 mm) to a new length of 10.0092 m.
Frequently asked questions
- Why does area use 2-alpha and volume use 3-alpha?
- Expansion happens along every dimension at once. A surface grows in two directions, so its fractional change is roughly twice the linear value, and a solid grows in three directions, giving roughly three times the linear value. These factors assume the material is isotropic and the temperature change is moderate.
- What units should I use for the coefficient and temperature?
- Enter the linear coefficient in units of per degree Celsius (for example 12e-6 for steel) and the temperature change in degrees Celsius. Because the coefficient and the temperature both use Celsius, a Kelvin change of the same magnitude gives an identical result.
- Can the calculator model cooling and contraction?
- Yes. Enter a negative temperature change to model cooling. The change in size becomes negative, and the new size is smaller than the original, which is exactly how materials shrink as they lose heat.
- How accurate is the linear approximation for large temperature swings?
- The formula treats the coefficient as constant, which is accurate for everyday temperature ranges. Over very large swings or near phase transitions the coefficient itself changes, so for precision engineering you should use temperature-dependent material data.