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Thermal Expansion Calculator

Computes how much a length, area or volume of a solid changes with temperature from ΔL = α·L₀·ΔT (area coefficient 2α, volume coefficient 3α), using tabulated linear expansion coefficients for common materials or a custom coefficient.

MaterialMaterial, selecting a typical linear expansion coefficient near room temperature; choose custom to supply coefficient_per_k. Linear expansion coefficient (1/K) (optional)Linear coefficient of thermal expansion α in 1/K (e.g. 0.000012 for steel); required for material = custom and overrides the preset otherwise. Initial length (area, volume) (m)Initial length in metres; for expansion_type area give the initial area in m², for volume the initial volume in m³. Temperature change (K)Temperature rise in kelvin (same as the °C difference); negative for cooling, which gives contraction. Expansion type (optional)Which dimension expands: a length (α), an area (2α) or a volume (3α of an isotropic solid).

When to use

You need the growth or shrinkage of a steel beam, rail, pipe, concrete slab, glass pane or metal part over a temperature change, or the volume change of a solid.

Do not use when: The material is a liquid or gas (enter its volumetric coefficient as custom with expansion_type volume, or use ideal-gas-law for gases), the temperature range crosses a phase change, or you need thermal stress in a constrained part rather than free expansion.

Formula

linear: change = α × initial_length_m × temperature_change_k; area: change = 2α × A₀ × ΔT; volume: change = 3α × V₀ × ΔT; change_mm = change × 1000; final_length_m = initial_length_m + change; percent_change = change / initial × 100. α (× 10⁻⁶/K): steel 12, stainless steel 17.3, aluminium 23.1, copper 17, brass 19, concrete 12, glass 8.5, Pyrex 3.3, PVC 52, wood along grain 5, ice 51

First-order (small α·ΔT) expansion of an isotropic solid free to expand; coefficients are room-temperature values from the Wikipedia table and vary with alloy, composition and temperature (steel 11–13, brass 18–19 × 10⁻⁶/K).

Inputs

Parameter	Type	Unit	Required	Description
`material`	enum: steel \| stainless_steel \| aluminium \| copper \| brass \| concrete \| glass \| pyrex \| pvc \| wood_along_grain \| ice \| custom		yes	Material, selecting a typical linear expansion coefficient near room temperature; choose custom to supply coefficient_per_k.
`coefficient_per_k`	number	1/K	no	Linear coefficient of thermal expansion α in 1/K (e.g. 0.000012 for steel); required for material = custom and overrides the preset otherwise. Range: > 0, ≤ 0.01
`initial_length_m`	number	m	yes	Initial length in metres; for expansion_type area give the initial area in m², for volume the initial volume in m³. Range: > 0
`temperature_change_k`	number	K	yes	Temperature rise in kelvin (same as the °C difference); negative for cooling, which gives contraction. Range: ≥ -1000, ≤ 5000
`expansion_type`	enum: linear \| area \| volume		default linear	Which dimension expands: a length (α), an area (2α) or a volume (3α of an isotropic solid).

Outputs

Output	Type	Unit	Description
`coefficient_per_k`	number	1/K	Linear expansion coefficient used.
`coefficient_ppm_per_k`	number	µm/(m·K)	The same coefficient in parts per million per kelvin (× 10⁶).
`change`	number	m / m² / m³	Change in length (m), area (m²) or volume (m³) according to expansion_type; negative for contraction.
`change_mm`	number	mm	Length change in millimetres (linear expansion only).
`final_length_m`	number	m	initial_length_m + change (linear expansion only).
`percent_change`	number	%	change / initial size × 100.
`formula_used`	string		The expansion formula applied (linear, area or volume).

Example

10 m steel rail heated by 40 K: {"material":"steel","initial_length_m":10,"temperature_change_k":40} → {"coefficient_per_k":0.000012,"coefficient_ppm_per_k":12,"change":0.0048,"change_mm":4.8,"final_length_m":10.0048,"percent_change":0.048}

1 m³ of aluminium heated by 50 K (volume): {"material":"aluminium","initial_length_m":1,"temperature_change_k":50,"expansion_type":"volume"} → {"coefficient_ppm_per_k":23.1,"change":0.003465,"percent_change":0.3465}

GET https://tttkmbb.com/api/v1/calculate/thermal-expansion?material=steel&initial_length_m=10&temperature_change_k=40

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/thermal-expansion (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/thermal-expansion · Markdown: https://tttkmbb.com/physics/thermal-expansion.md · JSON definition: https://tttkmbb.com/physics/thermal-expansion.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="thermal-expansion"
OpenAPI operationId: calculate_thermal_expansion
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Wikipedia – Thermal expansion (coefficient table) (reference)
HyperPhysics – Thermal expansion (reference)

FAQ

Why is the volume coefficient 3α?

Each of the three dimensions of an isotropic solid grows by a factor (1 + α·ΔT); the product is 1 + 3α·ΔT plus terms in (α·ΔT)² that are negligible for the small values of α·ΔT met in practice.

Is the temperature change in °C the same as in K?

Yes: a difference of 40 °C is a difference of 40 K, so temperature_change_k can be taken directly from Celsius readings.

What if the part cannot expand freely?

It develops thermal stress σ = E·α·ΔT instead (E = Young's modulus); a fully restrained steel bar heated by 40 K sees about 100 MPa, which this calculator does not compute.

Related calculators

Mixing Temperature Calculator — Temperature reached when bodies exchange heat.
Specific Heat Calculator — Heat needed to produce the temperature change.
Temperature Converter — Convert temperatures between °C, °F and K.