Free Engineering Tool
Thermal Expansion Calculator
Calculate linear and volumetric thermal expansion for 20+ materials. Pipe expansion between anchors, expansion loop sizing, and thermal stress when constrained (σ = E·α·ΔT).
Expansion Results
Linear Expansion
Where α is the coefficient of thermal expansion (CTE) in 1/°C, L₀ is the original length, and ΔT is the temperature change.
Volumetric Expansion
For isotropic materials, the volumetric CTE is approximately 3× the linear CTE.
Thermal Stress (Constrained Member)
When expansion is completely prevented (e.g., pipe between two rigid anchors), the resulting stress can be very high. This is compressive for heating and tensile for cooling.
Expansion Loop Sizing (Rule of Thumb)
Where D is the pipe outer diameter (mm) and Δ is the expansion (mm); the result L is in mm. The factor 66 comes from the guided-cantilever formula L = √(3 · E · D · Δ / Sₐ) evaluated for carbon steel (E = 200 GPa, Sₐ = 138 MPa). For other materials or allowable stresses use the full formula (L scales as √(E/Sₐ)). This is a screening estimate, not a full code flexibility analysis.
Practical Example
Given: L₀ = 6000 mm, α = 12 × 10⁻⁶ /°C, ΔT = 80°C, E = 200 GPa
ΔL = 12e-6 × 6000 × 80 = 5.76 mm
Thermal stress if constrained: σ = 200,000 × 12e-6 × 80 = 192 MPa
Expansion loop (DN100/OD 114 mm): L ≈ 66 × √(114 × 5.76) ≈ 1,690 mm ≈ 1.7 m
Material CTE Database
| Material | α (×10⁻⁶ /°C) | E (GPa) | Notes |
|---|---|---|---|
| Carbon steel | 12.0 | 200 | SA-516, P265GH |
| Low-alloy steel | 12.5 | 200 | 16Mo3, SA-387 |
| Cr-Mo steel (2.25Cr) | 12.0 | 205 | SA-335 P22 |
| Stainless 304 | 17.3 | 193 | 1.4301, 18Cr-8Ni |
| Stainless 316 | 16.0 | 193 | 1.4401, 16Cr-10Ni-2Mo |
| Stainless 321 | 17.0 | 193 | 1.4541, Ti-stabilized |
| Duplex 2205 | 13.0 | 200 | 1.4462 |
| Aluminium 6061 | 23.6 | 69 | T6 temper |
| Copper | 17.0 | 117 | Pure, annealed |
| Brass (CuZn30) | 20.0 | 110 | Cartridge brass |
| Bronze (CuSn8) | 18.0 | 110 | Phosphor bronze |
| Titanium Gr.2 | 8.6 | 103 | Commercially pure |
| Nickel 200 | 13.3 | 207 | Pure nickel |
| Inconel 625 | 12.8 | 207 | Ni-Cr-Mo |
| Inconel 718 | 13.0 | 211 | Ni-Cr-Fe |
| Grey cast iron | 10.5 | 110 | GG25 |
| Ductile cast iron | 11.0 | 170 | GGG40 |
| Concrete | 12.0 | 30 | Varies with mix |
| Glass (soda-lime) | 9.0 | 72 | Window glass |
| PTFE (Teflon) | 120.0 | 0.5 | Very high CTE |
| HDPE | 150.0 | 1.0 | Polyethylene |
| PVC | 80.0 | 3.0 | Rigid PVC |
| Invar 36 | 1.2 | 145 | Ultra-low CTE alloy |
💡 Note: CTE values are mean values for 20–100°C. For high-temperature or cryogenic applications, use specific data from material standards.
Nikolai Shelkovenko
Nikolai Shelkovenko is a vibration analysis engineer and the founder and CEO of Vibromera. For more than 15 years he has balanced rotating equipment in the field rather than on a test bench: mulchers, industrial fans, crushers, centrifuges, shafts and spindles. That work is what the Balanset instruments grew out of — they were designed as a tool a specialist can carry to the machine and use alone, on site, not as laboratory equipment. Vibromera was founded in 2017 and has been based in Porto, Portugal, since 2023. Development, assembly and support of the Balanset line all happen here. The flagship instrument is the Balanset-1A, a portable analyser for single- and two-plane balancing and for vibration diagnostics. Nikolai is personally involved in customer support, in working through difficult balancing cases and in the development of the software. He works with customers worldwide, in any language.
