Thermal expansion: coefficients of materials and calculator
Published October 18, 2026 — thermal expansion coefficients of common materials, the formula ΔL = α·L₀·ΔT, the stress in a restrained part, clearances between two materials, shrink-fit temperature and a calculator.
In short: a heated part grows by ΔL = α · L₀ · ΔT. The coefficient α is about 12 × 10⁻⁶ /K for steel, 16 for austenitic stainless and 23 for aluminium: 1 m of steel heated by 100 °C grows by 1.2 mm, 1 m of aluminium by 2.3 mm. If the part is restrained, it does not grow but is stressed instead: σ = E · α · ΔT.
1. Thermal expansion calculator
Pick a material or enter your own coefficient, then the length and both temperatures. With a Young's modulus E, the calculator also gives the stress if the part is fixed at both ends.
2. Thermal expansion coefficients of materials
Mean linear expansion coefficients between 20 and 100 °C, in 10⁻⁶ /K (that is, µm per metre per degree). These are common design values: the exact value depends on the grade, condition and temperature range, and the coefficient rises with temperature. For a critical part, use the value from the material's datasheet.
For the densities of the same materials, see the density chart; for steel grades, S235, S275 and S355.
3. Thermal expansion formulas
Example: a 1,000 mm steel bar goes from 20 to 70 °C. ΔL = 12 × 10⁻⁶ × 1,000 × 50 = 0.6 mm. The same bar in aluminium grows by 23 × 10⁻⁶ × 1,000 × 50 = 1.15 mm.
4. Restrained expansion: thermal stress
Stress in a part fixed at both ends, in the elastic range, for a 50 °C change. E: 210 GPa for steel (Eurocode 3), 200 GPa for austenitic stainless, 70 GPa for aluminium (Eurocode 9).
- The stress does not depend on length: a 20 mm spacer clamped between two flanges sees the same stress as a 10 m beam.
- 126 MPa for 50 °C is already more than half the yield strength of S235 (235 MPa up to 16 mm thick); for 100 °C, 252 MPa exceeds it. Provide a sliding support, a slotted hole or a bellows.
- A slender part restrained in compression can also buckle before reaching that stress.
5. Clearances between two materials and shrink fits
When the bore and the shaft are in different materials, the clearance changes with temperature: Δj = (αbore − αshaft) · D · ΔT. Example: a Ø50 H7/g6 fit, clearance 0.009 to 0.050 mm at 20 °C, taken to 100 °C (clearances in mm).
- Aluminium housing, steel shaft: the clearance increases by 0.044 mm when hot. A bearing press-fitted in an aluminium housing can creep in its seat.
- Steel housing, aluminium shaft: the clearance decreases by 0.044 mm. The min clearance turns negative, −0.035 mm: the sliding fit becomes an interference and can seize.
- Shrink fitting: to fit a Ø50 H7/p6 steel hub (max interference 0.042 mm) with 0.03 mm of assembly clearance, you need ΔT = (0.042 + 0.03) / (12 × 10⁻⁶ × 50) = 120 °C, so heat the hub to 140 °C from 20 °C.
- The H7, g6 and p6 deviations come from the ISO 286 fits chart; to add expansion to other dimensions, see the tolerance stack-up.
Printable version: the coefficient chart and formulas as a PDF (A4, no sign-up), to keep at your desk.
6. Why dimensions are specified at 20 °C
ISO 1 sets 20 °C as the reference temperature for geometrical product specifications: a drawing dimension is the size of the part at 20 °C. Measured at another temperature, it must be corrected, especially when the part and the instrument have different coefficients.
- Steel part measured with a steel instrument, both at 25 °C: both expand alike and the error almost cancels out.
- 500 mm aluminium part measured at 25 °C with a steel instrument: error of (23 − 12) × 10⁻⁶ × 500 × 5 ≈ 0.03 mm, nearly half an IT7 tolerance at that size (0.063 mm).
- A part fresh off the machine is often warmer than the shop: let it return to temperature before inspection.
7. FAQ
What is the thermal expansion formula?
ΔL = α · L₀ · ΔT: the change in length is the product of the expansion coefficient α, the initial length L₀ and the temperature change ΔT. A 1 m steel bar heated from 20 to 70 °C grows by 12 × 10⁻⁶ × 1,000 × 50 = 0.6 mm.
What is the thermal expansion coefficient of steel?
About 12 × 10⁻⁶ /K for structural and carbon steel, the value used in Eurocode 3: 1.2 mm per metre for 100 °C. Austenitic stainless (304, 316L) expands more, about 16 × 10⁻⁶ /K; ferritic stainless (430) less, about 10 × 10⁻⁶ /K.
What is the thermal expansion coefficient of aluminium?
About 23 × 10⁻⁶ /K, the value used in Eurocode 9, nearly twice steel: 2.3 mm per metre for 100 °C. This is why clearances change between an aluminium housing and a steel shaft.
Does a hole get bigger or smaller when the part is heated?
It gets bigger. Heated uniformly, the part scales up like a photographic enlargement: the hole grows by the same factor as if it were filled with material. This is how shrink fitting works.
What are the units of the thermal expansion coefficient?
In 1/K, which equals 1/°C, because a change of 1 K is a change of 1 °C. It is often written × 10⁻⁶ /K, or µm/(m·K): 12 × 10⁻⁶ /K is 12 µm per metre per degree. For a coefficient per °F, divide by 1.8.