{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"thermal-expansion"},"result":{"entity_type":"calculator","id":"thermal-expansion","calculator_id":"thermal-expansion","canonical_url":"https://tttkmbb.com/physics/thermal-expansion","name":"Thermal Expansion Calculator","title":"Thermal Expansion Calculator – Linear, Area and Volume Expansion ΔL = α·L₀·ΔT by Material","category":"physics","category_name":"Physics","tool_name":"calculate_thermal_expansion","featured_mcp_tool":false,"description":"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.","use_when":"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.","inputs":[{"name":"material","label":"Material","type":"enum","required":true,"values":[{"value":"steel","label":"Steel (12 × 10⁻⁶/K)","aliases":["iron","carbon steel"]},{"value":"stainless_steel","label":"Stainless steel (304) (17.3 × 10⁻⁶/K)","aliases":["stainless"]},{"value":"aluminium","label":"Aluminium (23.1 × 10⁻⁶/K)","aliases":["aluminum","al"]},{"value":"copper","label":"Copper (17 × 10⁻⁶/K)","aliases":["cu"]},{"value":"brass","label":"Brass (19 × 10⁻⁶/K)"},{"value":"concrete","label":"Concrete (12 × 10⁻⁶/K)"},{"value":"glass","label":"Glass, soda-lime (8.5 × 10⁻⁶/K)","aliases":["window glass"]},{"value":"pyrex","label":"Borosilicate glass (Pyrex) (3.3 × 10⁻⁶/K)","aliases":["borosilicate"]},{"value":"pvc","label":"PVC (52 × 10⁻⁶/K)","aliases":["polyvinyl chloride"]},{"value":"wood_along_grain","label":"Wood, along the grain (5 × 10⁻⁶/K)","aliases":["wood","timber"]},{"value":"ice","label":"Ice (51 × 10⁻⁶/K)"},{"value":"custom","label":"Custom (use coefficient_per_k)"}],"description":"Material, selecting a typical linear expansion coefficient near room temperature; choose custom to supply coefficient_per_k.","example":"steel"},{"name":"coefficient_per_k","label":"Linear expansion coefficient","type":"number","unit":"1/K","required":false,"max":0.01,"exclusive_min":0,"description":"Linear coefficient of thermal expansion α in 1/K (e.g. 0.000012 for steel); required for material = custom and overrides the preset otherwise.","example":0.000012},{"name":"initial_length_m","label":"Initial length (area, volume)","type":"number","unit":"m","required":true,"exclusive_min":0,"description":"Initial length in metres; for expansion_type area give the initial area in m², for volume the initial volume in m³.","example":10},{"name":"temperature_change_k","label":"Temperature change","type":"number","unit":"K","required":true,"min":-1000,"max":5000,"description":"Temperature rise in kelvin (same as the °C difference); negative for cooling, which gives contraction.","example":40},{"name":"expansion_type","label":"Expansion type","type":"enum","required":false,"default":"linear","values":[{"value":"linear","label":"Linear (length, α)","aliases":["length"]},{"value":"area","label":"Area / superficial (2α)","aliases":["superficial","surface"]},{"value":"volume","label":"Volume / cubical (3α)","aliases":["volumetric","cubical"]}],"description":"Which dimension expands: a length (α), an area (2α) or a volume (3α of an isotropic solid).","example":"linear"}],"outputs":[{"name":"coefficient_per_k","label":"Linear coefficient α","type":"number","unit":"1/K","decimals":9,"description":"Linear expansion coefficient used."},{"name":"coefficient_ppm_per_k","label":"Linear coefficient α","type":"number","unit":"µm/(m·K)","decimals":2,"description":"The same coefficient in parts per million per kelvin (× 10⁶)."},{"name":"change","label":"Change in size","type":"number","unit":"m / m² / m³","decimals":8,"description":"Change in length (m), area (m²) or volume (m³) according to expansion_type; negative for contraction."},{"name":"change_mm","label":"Change in length","type":"number","unit":"mm","decimals":4,"description":"Length change in millimetres (linear expansion only)."},{"name":"final_length_m","label":"Final length","type":"number","unit":"m","decimals":6,"description":"initial_length_m + change (linear expansion only)."},{"name":"percent_change","label":"Relative change","type":"number","unit":"%","decimals":4,"description":"change / initial size × 100."},{"name":"formula_used","label":"Formula used","type":"string","decimals":4,"description":"The expansion formula applied (linear, area or volume)."}],"input_schema":{"type":"object","properties":{"material":{"description":"Material, selecting a typical linear expansion coefficient near room temperature; choose custom to supply coefficient_per_k.","type":"string","enum":["steel","stainless_steel","aluminium","copper","brass","concrete","glass","pyrex","pvc","wood_along_grain","ice","custom"],"examples":["steel"]},"coefficient_per_k":{"description":"Linear coefficient of thermal expansion α in 1/K (e.g. 0.000012 for steel); required for material = custom and overrides the preset otherwise. Unit: 1/K.","type":"number","maximum":0.01,"exclusiveMinimum":0,"examples":[0.000012],"x-unit":"1/K"},"initial_length_m":{"description":"Initial length in metres; for expansion_type area give the initial area in m², for volume the initial volume in m³. Unit: m.","type":"number","exclusiveMinimum":0,"examples":[10],"x-unit":"m"},"temperature_change_k":{"description":"Temperature rise in kelvin (same as the °C difference); negative for cooling, which gives contraction. Unit: K.","type":"number","minimum":-1000,"maximum":5000,"examples":[40],"x-unit":"K"},"expansion_type":{"description":"Which dimension expands: a length (α), an area (2α) or a volume (3α of an isotropic solid).","type":"string","enum":["linear","area","volume"],"default":"linear","examples":["linear"]}},"additionalProperties":false,"required":["material","initial_length_m","temperature_change_k"]},"output_schema":{"type":"object","properties":{"coefficient_per_k":{"description":"Linear expansion coefficient used. Unit: 1/K.","type":"number","x-unit":"1/K"},"coefficient_ppm_per_k":{"description":"The same coefficient in parts per million per kelvin (× 10⁶). Unit: µm/(m·K).","type":"number","x-unit":"µm/(m·K)"},"change":{"description":"Change in length (m), area (m²) or volume (m³) according to expansion_type; negative for contraction. Unit: m / m² / m³.","type":"number","x-unit":"m / m² / m³"},"change_mm":{"description":"Length change in millimetres (linear expansion only). Unit: mm.","type":"number","x-unit":"mm"},"final_length_m":{"description":"initial_length_m + change (linear expansion only). Unit: m.","type":"number","x-unit":"m"},"percent_change":{"description":"change / initial size × 100. Unit: %.","type":"number","x-unit":"%"},"formula_used":{"description":"The expansion formula applied (linear, area or volume).","type":"string"}}},"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","method":"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).","sources":[{"name":"Wikipedia – Thermal expansion (coefficient table)","url":"https://en.wikipedia.org/wiki/Thermal_expansion","type":"reference","retrieved_at":"2026-09-24"},{"name":"HyperPhysics – Thermal expansion","url":"http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thexp.html","type":"reference","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"10 m steel rail heated by 40 K","inputs":{"material":"steel","initial_length_m":10,"temperature_change_k":40},"expected":{"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},"url":"https://tttkmbb.com/api/v1/calculate/thermal-expansion?material=steel&initial_length_m=10&temperature_change_k=40"},{"name":"1 m³ of aluminium heated by 50 K (volume)","inputs":{"material":"aluminium","initial_length_m":1,"temperature_change_k":50,"expansion_type":"volume"},"expected":{"coefficient_ppm_per_k":23.1,"change":0.003465,"percent_change":0.3465},"url":"https://tttkmbb.com/api/v1/calculate/thermal-expansion?material=aluminium&initial_length_m=1&temperature_change_k=50&expansion_type=volume"}],"faq":[{"q":"Why is the volume coefficient 3α?","a":"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."},{"q":"Is the temperature change in °C the same as in K?","a":"Yes: a difference of 40 °C is a difference of 40 K, so temperature_change_k can be taken directly from Celsius readings."},{"q":"What if the part cannot expand freely?","a":"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."}],"tags":["thermal expansion","linear expansion","expansion coefficient","expansion joint","steel expansion","volume expansion"],"related":[{"calculator_id":"mixing-temperature","reason":"Temperature reached when bodies exchange heat."},{"calculator_id":"specific-heat","reason":"Heat needed to produce the temperature change."},{"calculator_id":"temperature","reason":"Convert temperatures between °C, °F and K."}],"links":{"html":"https://tttkmbb.com/physics/thermal-expansion","markdown":"https://tttkmbb.com/physics/thermal-expansion.md","json":"https://tttkmbb.com/physics/thermal-expansion.json","api":"https://tttkmbb.com/api/v1/calculate/thermal-expansion","schema":"https://tttkmbb.com/api/v1/calculators/thermal-expansion","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T03:46:41Z","next_actions":[{"tool":"run_calculator","calculator_id":"thermal-expansion","reason":"Run Thermal Expansion Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/physics/thermal-expansion.md"}}