Why Does Metal Expand When Heated?
Most metals expand when heated because their atoms vibrate more and their average separation increases. Those tiny changes add up across the part. The atoms do not simply get bigger. How much the metal grows depends on its alloy, starting size and temperature change—and whether it is free to move.
What changes between the atoms?
In a solid metal, atoms vibrate around positions in a crystal lattice: an ordered arrangement of atoms. Heating increases the energy of that motion. The forces between neighboring atoms resist pushing them very close together more sharply than they resist a modest increase in separation.
That imbalance shifts their average spacing outward as the vibration grows. Physicists call this anharmonicity. Larger vibration alone is not the whole explanation: a perfectly symmetric spring model would allow more motion without changing the average spacing.
The sketches show average positions. The change is exaggerated so it is visible; ordinary thermal expansion does not require the metal to melt.
Solid circles represent atoms at their average positions. Dashed circles indicate vibration schematically, not atom size. Both drawings use the same atom diameter.
Mechanism: Princeton’s thermal expansion explanation and MIT’s atomistic model.
How much will a metal part expand?
For a uniformly heated, freely moving part, estimate the change in a length or diameter with the mean linear coefficient of thermal expansion, usually shortened to CTE.
L₀ is the dimension at the starting temperature T₀; L₁ is the dimension at T₁. Use a mean coefficient ᾱ applicable to that temperature interval.
A CTE of 12 µm/(m·K) means approximately 12 micrometers of growth per meter of length for each kelvin of temperature rise. In the formula, enter it as 12 × 10⁻⁶ K⁻¹. A temperature difference has the same numerical value in kelvins and degrees Celsius.
Twice the lengthWith the same alloy and temperature change, a part twice as long has twice the free growth.
Cooling reverses the signFor a positive CTE, a lower final temperature gives a negative ΔL: contraction.
Keep units consistentLength in millimeters gives ΔL in millimeters. Convert a °F difference to kelvins by dividing by 1.8.
Worked example: a 10 m steel member
Assume a uniform rise from 20°C to 100°C, no restraint and a constant illustrative CTE of 12 µm/(m·K). Then ΔT = 80 K:
= 0.0096 m = 9.6 mm
The final length is 10.0096 m. This is an assumed calculation, not a measured result or a certified property for every steel grade. It also does not specify where that movement occurs in an installed assembly.
Formula and representative steel coefficient: OpenStax, Thermal Expansion.
How do alloy and temperature range affect CTE?
Different atomic bonding and alloy structures produce different expansion behavior. A value labelled only “metal” or “stainless steel” is too vague for a tight clearance calculation. Even the same grade can have different reported CTE values because the temperature intervals differ.
| Material in the source | Mean linear CTE µm/(m·K) | Temperature interval | How to use the value |
|---|---|---|---|
| 6061 aluminum Kaiser tube and pipe data | 23.6 | 20–100°C | Typical alloy value; the CTE entry is not separated by temper. |
| 304 stainless steel Annealed, Atlas data | 17.2 | 0–100°C | Typical mean value for the stated interval. |
| 304 stainless steel Same data sheet | 18.4 | 0–538°C | An average over the wider interval, not the instantaneous CTE at 538°C. |
On a narrow screen, scroll the table sideways to see the conditions.
Data: Kaiser 6061 data sheet, physical properties; Atlas 304 data sheet, typical annealed properties. These are typical reference values, not lot-specific test certificates.
The figures show why 6061 aluminum generally grows more than 304 stainless near ambient temperatures. Their source intervals are not identical, so use matched interval data when a small difference will determine fit or acceptance.
Low-expansion alloys are a special case. Invar 36 is designed for low expansion near room temperature, but its CTE rises as the temperature range increases. It is not a zero-expansion material at every temperature. See Carpenter’s Invar 36 data.
CTE and thermal conductivity answer different questions. CTE describes dimensional response to temperature. Thermal conductivity describes heat flow through the material. Conductivity can affect how quickly and evenly a part heats; it is not the coefficient to put into an expansion formula.
Thermal expansion calculator
Estimate the free change in a length or diameter. Enter the mean CTE for your alloy and temperature interval. The starting example uses an assumed steel value of 12 µm/(m·K); change it when your material data requires a different value.
Change in dimension
Enter valid values to calculate.
Final dimension
Temperature change
Thermal strain
Model: uniform temperature, free movement and small strain, with a valid mean CTE over the entered interval. Results do not predict stress, buckling, weld distortion, melting or phase-change behavior. Displayed digits are calculation detail, not material accuracy.
Does a hole get bigger when metal is heated?
Yes—if the plate is heated uniformly, expands equally in each direction and is free to move. Its inside and outside dimensions increase together. The material does not simply expand inward to fill the opening.
A geometric way to check this is to apply one scale factor to the whole plate. If every distance from the center is multiplied by 1 + ᾱΔT, both the outer edge and the hole edge move outward. The hole’s diameter follows the same linear expansion formula.
Example: a 100 mm aluminum bore
Using 23.6 µm/(m·K) for a uniformly heated 6061 part from 20°C to 100°C:
= 0.1888 mm
The calculated bore diameter is 100.1888 mm. For an assembly, calculate the mating shaft’s change too. Heating both parts does not guarantee that the clearance increases.
What if the metal cannot expand freely?
Preventing thermal movement creates stress. For an initially stress-free, straight elastic bar with both ends held perfectly fixed, uniform heating with positive CTE produces axial compression. Under those ideal assumptions, its magnitude is approximately EαΔT, where E is Young’s modulus.
Restraint turns movement into load
For assumed values E = 200 GPa, α = 12 × 10⁻⁶ K⁻¹ and ΔT = 50 K, the ideal compressive stress is 120 MPa. This is an illustrative elastic calculation, not an allowable stress or a prediction for a real fixture.
Support flexibility, slip, yielding and buckling change the response. A component can stop following the simple elastic model before the calculated stress is reached.
Different growth changes fits and joints
Two connected materials may want to expand by different amounts. A temperature gradient can also make one part of a single component grow more than another. Either condition can cause bending or internal stress.
Check which dimensions are allowed to move, where movement is restrained and how temperatures vary. Slots, clearances or compliant supports need to follow that movement path and the assembly’s load requirements.
Basis: MIT, thermoelastic strain relations. For the ideal axial case, zero total extension requires the elastic strain to cancel αΔT. The numerical example uses the assumptions stated here.
How should you account for expansion in manufacturing?
Measure at a known temperature
A hot part can be dimensionally correct for its current temperature yet read outside a drawing tolerance referenced to another temperature. NIST’s dimensional metrology guidance identifies 20°C as the standard reference unless another temperature is specified.
For a calculated scale example, a 100 mm part with assumed α = 12 µm/(m·K) changes by 6 µm over 5 K. That is relevant to a micrometer-level tolerance even though the part does not feel especially hot.
Allow the workpiece and measuring equipment to stabilize. If measuring away from the reference temperature, account for both their temperatures and expansion behavior, including uncertainty in the CTE. Air temperature alone may not represent a part that has just been machined.
When CTE uncertainty dominates the decision, use material-specific data or a suitable measurement. ASTM E228-22 covers linear expansion of rigid solids measured with a push-rod dilatometer; it does not replace a thermal-stress analysis of the assembly.
Treat welding as a local thermal cycle
A weld heats a small region while much of the surrounding material remains cooler. The cooler structure restrains the hot region. As the joint cools, contraction and plastic deformation can leave residual stress and permanent distortion.
That is why multiplying the overall part length by one peak welding temperature does not predict its final bow or shrinkage. Joint shape, temperature distribution, material response, weld sequence and restraint all matter. TWI explains this distortion mechanism.
For laser welding, assess the actual joint and thermal cycle. Use the welding heat input calculator to compare energy per unit length, then check the laser-welding HAZ guide for material changes near the weld. Confirm dimensional results on representative parts after cooling.
Will it return to its original size? Ordinary reversible expansion returns toward the starting dimension when the original temperature is restored. Plastic deformation, creep or a change in material structure can leave a permanent dimensional change. A completed heat or weld cycle therefore needs a cooled-part measurement.
Share the alloy, thickness, joint drawing and dimensions that must hold after cooling with Oceanplayer Laser.
Technical references
- Princeton: thermal expansion — atomic spacing and anharmonicity.
- MIT: thermal expansion model — the asymmetric interatomic potential.
- OpenStax: thermal expansion — linear expansion and a representative steel coefficient.
- MIT: thermoelastic effects — thermal strain and its relation to elastic stress.
- Kaiser Aluminum: 6061 tube and pipe — typical physical properties over 20–100°C.
- Atlas Steels: 304 data sheet — mean CTE over different temperature intervals.
- Carpenter Technology: Invar 36 — temperature-dependent low-expansion behavior.
- NIST: Engineering Metrology Toolbox — dimensional reference temperature and CTE uncertainty.
- ASTM E228-22 — public scope of push-rod dilatometry.
- TWI: what causes distortion? — restraint, cooling contraction and plastic deformation in welding.