Linear Thermal Expansion Calculator
Calculate one-dimensional free length change using a mean linear coefficient of thermal expansion supplied for the exact material condition and temperature interval. The tool does not invent a material coefficient or perform a piping-code stress analysis.
Calculated free length change
Arithmetic only: apply the uncertainty of L₀, both temperatures and the supplied mean CTE. A negative ΔL means contraction along the stated direction.
Definition, formula and unit treatment
Therefore: ΔL = L₀ · (ᾱ × 10⁻⁶ K⁻¹) · ΔT
Final free length: L₂ = L₀ + ΔL
The equation is the rearranged definition of the mean coefficient over the stated interval. It is not an ISO pipe-design formula. For Celsius endpoints, ΔT in kelvins equals T₂−T₁. For Fahrenheit endpoints, ΔT in kelvins equals (T₂−T₁)×5/9. The international inch is exactly 25.4 mm.
Required evidence
- Exact material and condition.
- Direction if anisotropic.
- Mean CTE source and interval.
Rejected
- Temperatures below absolute zero.
- Zero/negative original length.
- Exponent, grouping or unit suffix.
- A result with non-positive final length.
Non calculé
- Stress, force or yield margin.
- Volumetric/fluid expansion.
- Pipe loops or expansion joints.
- Any code acceptance decision.
Primary sources and standards boundary
- ASTM E228-22, Standard Test Method for Linear Thermal Expansion of Solid Materials With a Push-Rod Dilatometer — active. ASTM states that accurate expansion determination requires a calibrated dilatometer and accurate length and temperature measurements. This calculator does not implement that test method.
- ISO 11359-2:2021, Plastics — Thermomechanical analysis — Part 2 — Edition 2, published, stage 90.60 after systematic review. Its public scope is a TMA method for solid-state plastics; it is not a universal material-property table.
- NIST Engineering Metrology Toolbox FAQ — explains why an actual manufacturer/material source and its temperature range are needed instead of an unidentified handbook coefficient.
- NIST/SEMATECH e-Handbook, Thermal Expansion of Copper case study — provides measured CTE as a function of temperature, demonstrating that a single coefficient is not generally universal.
- BIPM SI Brochure, 9th edition, version 4.01 (2026), page 129 — distinguishes temperature values from temperature differences and states the kelvin/degree-Celsius interval relation.
- NIST SP 811, Appendix B.8 — exact temperature-interval and international-inch conversion factors.
Classification : general engineering calculation from a user-controlled mean coefficient. It is not a conformity assessment, material database, stress analysis or implementation of ASTM E228 or ISO 11359-2.
