Thermal Expansion Calculator (Linear/Area/Volume)
Find how much a solid grows or shrinks when its temperature changes, for length, area or volume.
Expansion type
m
1/K
K
Effective coefficient: 1α
- 1
Effective coefficient: factor × α
1 × 0.000012 = 0.000012Linear expansion uses α directly. - 2
Thermal change = (factor × α) × L0 × ΔT
0.000012 × 1 × 100 = 0.001200
How does this calculator work?
Thermal expansion change equals the coefficient times original size times temperature change. Use ΔL = α·L0·ΔT for length, ΔA = 2α·A0·ΔT for area, and ΔV = 3α·V0·ΔT for volume. Pick the mode, enter L0/A0/V0, α in 1/K, and ΔT in kelvin to get the change and final size.
Formula
How this is calculated
Enter the original size (length L0, area A0 or volume V0), the material linear expansion coefficient α in 1/K, and the temperature change ΔT in kelvin (a change of 1 K equals a change of 1 °C). The select field chooses whether you are expanding a 1D, 2D or 3D dimension.
Linear expansion uses ΔL = α·L0·ΔT, so the final length is L = L0(1 + α·ΔT). Because area scales with two lengths and volume with three, the area coefficient is approximately 2α and the volume (cubical) coefficient β is approximately 3α for an isotropic material. The tool simply multiplies α by 1, 2 or 3 depending on the selected mode and applies ΔX = (factor·α)·X0·ΔT.
The 2α and 3α relations are first-order approximations valid for small α·ΔT, which holds for almost all real solids over normal temperature ranges. A negative ΔT gives contraction (negative change). Coefficients are temperature dependent, so use a value appropriate to your working temperature for best accuracy.
Frequently asked questions
A solid expands in all three directions by the same fractional amount α·ΔT. Multiplying three nearly equal expansions gives roughly (1 + α·ΔT)³ ≈ 1 + 3α·ΔT, so the volumetric coefficient β ≈ 3α for isotropic materials.
Either works because it is a temperature difference. A change of 1 K equals a change of 1 °C, so ΔT is numerically identical in both scales.
It is a first-order approximation. The exact area factor is (1 + α·ΔT)² − 1 = 2α·ΔT + (α·ΔT)², but the squared term is negligible for typical materials, so 2α·ΔT is used.
Also known as
TG we-Calculate Editorial Team. (2026). Thermal Expansion Calculator (Linear/Area/Volume) [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/thermal-expansion-calculator
TG we-Calculate Editorial Team. "Thermal Expansion Calculator (Linear/Area/Volume)." TG we-Calculate. 2026. https://we-calculate.com/calculator/thermal-expansion-calculator.
TG we-Calculate Editorial Team, "Thermal Expansion Calculator (Linear/Area/Volume)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/thermal-expansion-calculator
@misc{wecalculate_thermal_expansion_calculator, title = {Thermal Expansion Calculator (Linear/Area/Volume)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/thermal-expansion-calculator}}, year = {2026}, note = {TG we-Calculate} }
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