Quick answer
Linear thermal expansion is ΔL = α L₀ ΔT. A 10 m steel bar (α = 12 × 10⁻⁶ /K) heated by 50 K grows 6 mm, to 10.006 m.
Enter the coefficient of linear expansion, original length and temperature change. The calculator returns the change in length and the new length.
Related tools: Specific Heat Calculator: Specific heat capacity or heat required from Q = m c ΔT. Thermodynamic Processes Calculator: Work, heat and internal energy for an ideal gas process. EER Calculator: Energy efficiency ratio of an air conditioner and its COP equivalent.
How to use the Thermal Expansion Calculator
- Enter coefficient of linear expansion (µm/(m·K)) (above 0).
- Enter original length (m) (above 0).
- Enter temperature change (K or °C).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Coefficient of linear expansion | A number, in µm/(m·K) | > 0 |
| Original length | A number, in m | > 0 |
| Temperature change | A number, in K or °C | — |
Formula and method
Formula
ΔL = α L₀ ΔT
IEEE-754 double precision; shown to the decimals indicated.
Enter the coefficient for your material from a reliable table.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Coefficient of linear expansion = 12; Original length = 10; Temperature change = 50.
| Result | Value |
|---|---|
| Change in length | 6 mm |
| New length | 10.006 m |
Example 2
Inputs: Coefficient of linear expansion = 23; Original length = 2.5; Temperature change = 80.
| Result | Value |
|---|---|
| Change in length | 4.6 mm |
| New length | 2.5046 m |
Example 3
Inputs: Coefficient of linear expansion = 9; Original length = 1.2; Temperature change = -30.
| Result | Value |
|---|---|
| Change in length | -0.324 mm |
| New length | 1.199676 m |
The first line is the headline result (change in length). Below it the thermal Expansion Calculator lists new length, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Typical coefficients
Steel is about 12 × 10⁻⁶ per kelvin, aluminium 23, concrete 10 to 14 and glass 9. Bridges, rails and pipes need expansion joints for this reason.
Where this estimate stops applying
The linear formula is valid for small changes. Area expansion is about 2α and volume expansion about 3α. A 100 m rail heated by 40 K expands 48 mm, enough to buckle if constrained.
How the result changes with coefficient of linear expansion
Holding every other input at the first worked example, this table changes only coefficient of linear expansion. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Coefficient of linear expansion | Change in length | New length |
|---|---|---|
| 6 | 3 mm | 10.003 m |
| 12 | 6 mm | 10.006 m |
| 24 | 12 mm | 10.012 m |
| 48 | 24 mm | 10.024 m |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Coefficient of linear expansion: entering "0" shows "Coefficient of linear expansion must be greater than 0." beside that field and no result.
- Original length: entering "0" shows "Original length must be greater than 0." beside that field and no result.
Choosing between the Thermal Expansion Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Specific Heat Calculator](/science/specific-heat-calculator/) | solve for, mass and temperature change | Specific heat |
| [Thermodynamic Processes Calculator](/science/thermodynamic-processes/) | process, gas and amount of gas | Work done by the gas |
| [EER Calculator](/science/energy-efficiency-ratio-calculator/) | cooling capacity and power input | EER |
| [Heat Pump COP Calculator](/science/heat-pump-cop-calculator/) | use | COP |
| [Heat Transfer Calculator](/science/heat-transfer-calculator/) | thermal conductivity, area and temperature difference | Heat flow |
Background: heat and temperature
The basic heat relation is Q = m × c × ΔT: heat in joules equals mass times specific heat capacity times temperature change. A positive Q means heat absorbed and a negative Q heat released, and a change in °C is numerically the same as a change in K.
It covers a change in temperature only. During melting or boiling the temperature stays constant while heat still flows (latent heat), which needs a separate term.
Assumptions and limitations
- Valid for small changes
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for coefficient of linear expansion and original length to confirm this.
Frequently asked questions
What is the unit of α?
α is in per kelvin (1/K), equivalent to per °C; steel is about 12 × 10⁻⁶ /K.
Why do rails have gaps?
Rails have gaps so they can expand in hot weather; a 100 m rail heated 40 K grows about 48 mm and would buckle if constrained.
Is cooling a negative change?
Yes. A fall in temperature makes ΔT negative, so ΔL is negative and the object contracts.
What does the Thermal Expansion Calculator calculate?
Change in length from a temperature change. It returns Change in length and New length.
What formula does the Thermal Expansion Calculator use?
ΔL = α L₀ ΔT. Enter the coefficient for your material from a reliable table.
What do I need to enter in the thermal Expansion Calculator?
You enter Coefficient of linear expansion (µm/(m·K)), Original length (m) and Temperature change (K or °C).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Valid for small changes.
What is an example of a thermal Expansion result?
With coefficient of linear expansion 12, original length 10 and temperature change 50, the change in length is 6 mm.
Related calculators
- Specific Heat Calculator — Specific heat capacity or heat required from Q = m c ΔT.
- Thermodynamic Processes Calculator — Work, heat and internal energy for an ideal gas process.
- EER Calculator — Energy efficiency ratio of an air conditioner and its COP equivalent.
- Heat Pump COP Calculator — Coefficient of performance from heat output and power input, or the Carnot limit.
- Heat Transfer Calculator — Conductive heat flow through a flat wall.
- Dew Point Calculator — Dew point from temperature and relative humidity.
Sources
- OpenStax, University Physics Volume 1 (Rice University): mechanics
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.