Back to Tools
🌡️

Linear Thermal Expansion

// CALCULATE STRAIN & LENGTH CHANGE

A one-line estimate with a generic coefficient. Not a thermal stress analysis and not a design allowance. ΔL = α × L0 × ΔT assumes the coefficient is constant over the range, the material is isotropic, and nothing is holding the part. All three are usually false, and a constrained part does not expand, it loads. Open for the full scope limits.

What this tool actually does

Educational and estimation purposes only. This page produces a first-pass number, not a design figure.

Applies the linear thermal expansion formula to one dimension of one material over one temperature change, using a typical published coefficient of thermal expansion.

ΔL = α × L0 × ΔT

The model assumes a constant CTE across the whole temperature range, which is not always accurate, and it assumes the part is free to move.

Key factors not accounted for

  • Non-linearity: CTE varies with temperature. Plastics change dramatically near the glass transition (Tg), and every material behaves differently near a melting point or other phase transition.
  • Material variance: The listed values are generic and typical. Specific alloys, tempers, additives, fillers, reinforcements and processing methods all shift expansion behaviour, and the datasheet for the grade you actually bought governs.
  • Anisotropy: many materials expand differently in different directions:
    • Wood: radial against tangential against longitudinal grain
    • Composites: along the fibres against across them
    • 3D prints: layer adhesion direction effects
    • Metals: rolling and extrusion direction effects
  • Thermal hysteresis: some materials do not return to their original dimensions after temperature cycling.
  • Constraint effects: a real assembly is usually restrained, so the temperature change produces stress rather than free movement. That stress is the number that breaks things, and this tool does not compute it.
  • Moisture and environment: hygroscopic materials such as wood and several plastics expand and contract with humidity independently of temperature.
  • Time-dependent effects: creep, stress relaxation and viscoelastic behaviour change dimensions over time under load and temperature.

Application-specific considerations

  • Pressure vessels and piping: must follow the ASME Boiler and Pressure Vessel Code, ASME B31 piping codes, the applicable ASTM material standards and local regulations.
  • Structural components: expansion joints, flexible connections and movement allowances require professional engineering analysis, not a single length change.
  • Precision assemblies: tolerance stack-up must include thermal variation across the whole operating range, not the nominal condition.
  • Dissimilar materials: bimetallic effects can generate significant stress at joints and interfaces even when each part is free on its own.
  • Extreme temperatures: CTE at cryogenic or elevated temperatures can differ substantially from room-temperature data, which is what most published tables report.

Never use this as the design allowance for

  • Pressure equipment, load-bearing structures, aerospace hardware or medical devices.
  • Any case where the failure carries property damage, injury or a regulatory consequence.
  • Complex geometries, or assemblies combining several materials.
  • Environments outside normal atmospheric conditions.
  • Anything requiring a certified calculation or a professional engineer's stamp.

Consult a qualified professional engineer for all of the above. Verify every value against the specific material datasheet and the applicable industry standard before it informs a tolerance, a gap or a joint.

No warranty. No liability. You assume all risk. This page, its coefficient table and its outputs are provided as-is and as-available, without warranty of any kind, express or implied, including accuracy, completeness, timeliness, reliability, fitness for a particular purpose, merchantability, engineering or professional suitability, regulatory or code acceptability, or non-infringement. To the maximum extent permitted by law, the author accepts no liability for any loss, injury, death, damage, cost or claim arising from use of or reliance on this page.

Independent verification required. Check every coefficient against the datasheet for the exact grade and condition you are using, and have the result reviewed by a qualified engineer before it informs any design, tolerance or purchase. Local building codes, industry standards and professional engineering judgement take precedence; where this page disagrees with them, this page is wrong.

Consequential damages excluded. To the maximum extent permitted by law, in no event will the author or maintainers be liable for any direct, indirect, incidental, special, exemplary, punitive or consequential damages, including loss of use, data, profits or business interruption, however caused and on any theory of liability, whether in contract, strict liability or tort including negligence, arising out of or in connection with this page, even if advised of the possibility of such damage.

Indemnity. By using this page you agree to indemnify and hold harmless the author and maintainers against any claim, demand, loss or expense arising out of your use of it or of anything derived from it.

Severability. If any part of this notice is held unenforceable, the remainder continues to apply, and the unenforceable part is limited to the least extent necessary rather than struck out.

Material Properties
µm/m·°C
Initial Dimensions
Temperatures
Temperature Change (ΔT)
100 °C
Change in Length (ΔL)
+0.1175 m
Final Length (L)
100.1175 m
Percentage Change
+0.1175%

A free length change, not a design allowance. The coefficient is a typical published value for a generic material, held constant across the range; a restrained part turns this movement into stress instead. Check the datasheet for the grade you are actually using, and get a professional engineer involved for pressure equipment, structures, precision assemblies and anything requiring a stamped calculation.

L₀
Start
L₀
ΔL
Visual is true-to-scale. (Expansion may be too small to see).

What is Linear Thermal Expansion?

Cold / Contracted
Low Kinetic Energy
Hot / Expanded
High Kinetic Energy

Put simply: When things get hot, they get longer.

Notice in the animation above how the "Hot" atoms vibrate more aggressively? To maintain that movement without colliding, they push their neighbors further away (shown by the larger gaps).

Across billions of atoms, these microscopic gaps add up to a measurable change in length.

At the atomic level, heat is just energy. As a material gets warmer, its atoms vibrate more vigorously. This vibration creates "personal space" issues - the atoms push their neighbors slightly further away. Across billions of atoms, these microscopic pushes add up to a noticeable change in length. This is why bridges have "expansion joints" (gaps with teeth) and why power lines sag more on hot summer days.

Understanding the Formula

Engineers use a simple formula to estimate this growth:

ΔL = α · L₀ · ΔT
  • ΔL (Delta L): The change in length (how much it grew).
  • α (Alpha): The Coefficient of Thermal Expansion. This is a material property that says "how sensitive is this stuff to heat?"
  • L₀: The original starting length.
  • ΔT (Delta T): The change in temperature (Final - Initial).