Thermal Expansion Guide
Linear Expansion Formula
The change in length due to temperature change is:
\u0394L = \u03B1 \u00D7 L\u2080 \u00D7 \u0394T
- \u0394L = change in length
- \u03B1 = coefficient of linear thermal expansion
- L\u2080 = original length
- \u0394T = change in temperature
Real-World Examples
- Bridges: A 100m steel bridge expanding 50\u00B0C grows about 60mm (2.4 inches). Expansion joints absorb this movement
- Railroad tracks: Continuous welded rail is pre-stressed to handle expansion. In extreme heat, improperly maintained track can buckle
- Pipes: Steam pipes use expansion loops or bellows to absorb thermal growth without creating stress
- Glass: Borosilicate glass (Pyrex) has a low CTE, making it resistant to thermal shock compared to regular soda-lime glass
- Bimetallic strips: Two bonded metals with different CTEs bend when heated, used in thermostats and circuit breakers
Material Comparison
| Material | CTE (\u00D710\u207B\u2076 /\u00B0C) |
|---|---|
| Lead | 29.0 (highest) |
| Aluminum | 23.1 |
| Brass | 19.0 |
| Copper | 16.5 |
| Steel | 12.0 |
| Titanium | 8.6 |
| Glass | 8.5 (lowest) |
Volumetric Expansion
For three-dimensional expansion, the volumetric coefficient is approximately 3 times the linear coefficient:
\u0394V \u2248 3\u03B1 \u00D7 V\u2080 \u00D7 \u0394T
This approximation is valid for small temperature changes. For liquids and gases, volumetric expansion is the primary concern.
Note: CTE values are averages for typical temperature ranges. Actual values may vary with specific alloy composition and temperature range.
Thermal Expansion, Quantified
Linear thermal expansion coefficients span a 20x range across common materials. Invar 36 (iron-nickel alloy): 1.3 × 10⁻⁶ /°C. Glass: 9 × 10⁻⁶ /°C. Concrete: 10-14 × 10⁻⁶ /°C. Mild steel: 12 × 10⁻⁶ /°C. Stainless 304: 17 × 10⁻⁶ /°C. Aluminum 6061: 23 × 10⁻⁶ /°C. Polyethylene: 200 × 10⁻⁶ /°C. This is why mismatched materials in bonded assemblies delaminate under temperature cycling.
The Sydney Harbour Bridge expands 18 cm end-to-end on a hot summer day, Golden Gate Bridge 41 cm at peak. Concrete highways include expansion joints every 10-15 m because asphalt expands ~15 × 10⁻⁶ /°C. The 'Interstate expansion gap' sized at 25 mm accommodates a 60°C seasonal range on a 25 m slab — miss the math and the slabs buckle (FHWA Highway Maintenance Manual 2018 tracks 2,200+ such events per year in the U.S.).
Modern aerospace uses precisely matched CTEs. Carbon fiber reinforced polymer (CFRP) has near-zero axial expansion (0.5-1 × 10⁻⁶ /°C) but transverse expansion of 25-30 × 10⁻⁶ /°C. The Hubble Space Telescope mirror is made of ULE glass (0.03 × 10⁻⁶ /°C) to hold its shape in orbit where temperatures swing 180°C every 90-minute orbit. A conventional mirror would distort 150x more — well beyond usable optical tolerance.
Sources: ASM Materials Handbook, FHWA Highway Maintenance Manual, NASA Hubble technical specs
Methodology & Assumptions
This calculator implements standard formulas drawn from primary-source authorities. Values are point-in-time estimates; consult a licensed professional for high-stakes decisions. See the per-input definitions and source citations below.
How this works
Computations are deterministic and run client-side — no inputs leave your
browser. Formulas are derived from
standard published formulas for the calculator's domain (mortgage,
taxes, energy, conversions, etc.). When the underlying agency publishes
updated rates or thresholds we refresh defaults and update the page's
lastmod timestamp.
| Input | Default | Source / authority |
|---|---|---|
| All inputs | Domain-typical defaults | Editorial methodology, CalcMesh 2026 |