Thermal Expansion Calculator
Thermal expansion is ΔL = α L₀ ΔT: 10 m of carbon steel (α = 12 × 10⁻⁶ /K) heated by 50 °C grows by 12 × 10⁻⁶ × 10 × 50 = 6 mm.
A change, not a reading: heating from 20 °C to 70 °C is ΔT = 50. Use a negative value for cooling.
6 mm
- α = 12 ppm/K = 6.667 ppm/°F
- ΔL = 0.000012 K⁻¹ × 10 m × 50 K = 0.006 m
- New length L = L₀ + ΔL = 10.006 m
Linear Thermal Expansion Formula
ΔL = α · L₀ · ΔT L = L₀ (1 + α ΔT)
ΔL change in length, α coefficient of linear thermal expansion (1/K), L₀ original length, ΔT temperature change (K or °C)
α varies slightly with temperature, so the values below are averages near room temperature (about 20–100 °C). For large temperature ranges use the mean coefficient over that range from the material data.
| Material | ppm/K (µm/m·°C) | ppm/°F (µin/in·°F) | ΔL of 1 m per 100 °C |
|---|---|---|---|
| Carbon steel | 12 | 6.67 | 1.2 mm |
| Stainless steel 304 | 17.3 | 9.61 | 1.73 mm |
| Aluminium | 23.1 | 12.8 | 2.31 mm |
| Copper | 16.5 | 9.17 | 1.65 mm |
| Brass | 19 | 10.6 | 1.9 mm |
| Titanium | 8.6 | 4.78 | 0.86 mm |
| Cast iron | 10.5 | 5.83 | 1.05 mm |
| Concrete | 12 | 6.67 | 1.2 mm |
| Soda-lime glass | 9 | 5 | 0.9 mm |
| PVC | 52 | 28.9 | 5.2 mm |
| HDPE | 120 | 66.7 | 12 mm |
Typical values; alloys, grades and fillers change α. Use the material specification for design.
Worked Examples
- Steel beam, 10 m, heated by 50 °C: ΔL = 12 × 10⁻⁶ × 10 m × 50 = 6 mm.
- Aluminium extrusion, 6 m, ΔT = 40 °C: ΔL = 23.1 × 10⁻⁶ × 6 × 40 = 5.54 mm.
- 100 ft of carbon steel pipe with α = 6.5 × 10⁻⁶ /°F and a 120 °F rise: ΔL = 6.5 × 10⁻⁶ × 1200 in × 120 = 0.936 in.
- A 25 m rail cooling by 30 °C shortens by 9 mm if it is free to move.
Frequently asked questions
What is the formula for linear thermal expansion?
ΔL = α × L₀ × ΔT, where α is the coefficient of linear expansion, L₀ the original length and ΔT the temperature change. The new length is L₀ + ΔL.
Do I use °C or K for ΔT?
Either: a change of 1 °C is the same as a change of 1 K. For °F, multiply the change by 5/9 to get K, or use α in 1/°F. Do not use the temperature readings themselves, only their difference.
How do I convert α from 1/°C to 1/°F?
Divide by 1.8: steel at 12 × 10⁻⁶ /°C is 6.67 × 10⁻⁶ /°F. No 32 °F offset is involved because α is per degree of change.
What about area and volume expansion?
For isotropic solids the area coefficient is about 2α and the volume coefficient about 3α, valid when α ΔT is small.
What happens if expansion is restrained?
If a part cannot move, it builds up a thermal stress of about σ = E α ΔT. For steel that is roughly 2.4 MPa per °C (E = 200 GPa, α = 12 ppm/K), which is why pipes and bridges need expansion joints or loops.
What is the coefficient of thermal expansion of steel?
Carbon steel is about 11–13 × 10⁻⁶ /°C (12 ppm/K is a common design value) and stainless steel 304 about 17.3 × 10⁻⁶ /°C. Aluminium is about 23 × 10⁻⁶ /°C, copper about 16.5–17 × 10⁻⁶ /°C and concrete about 10–13 × 10⁻⁶ /°C.
How do I calculate the thermal expansion of a pipe?
Use ΔL = α L ΔT along the pipe length: 100 m of carbon steel pipe (α = 12 × 10⁻⁶ /°C) heated by 60 °C grows by 12 × 10⁻⁶ × 100 × 60 = 0.072 m, or 72 mm. Expansion loops or joints must absorb this movement.
Does the diameter of a pipe or hole also expand?
Yes. Every dimension grows by the same fraction, Δd = α d ΔT, so a hole in a heated plate gets larger, not smaller. This is why shrink fits are assembled by heating the outer part.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
- Guide for the Use of the International System of Units (SI), NIST Special Publication 811, 2008 Edition, National Institute of Standards and Technology .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Thermal Expansion Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/thermal-expansion/
IEEE
Scientific Converters, "Thermal Expansion Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/thermal-expansion/