Calculators
Thermal Expansion Calculator
Calculate linear thermal expansion, final length, and strain from initial length, expansion coefficient, and temperature change.
Calculate length changes from heating or cooling.
Linear thermal expansion is ΔL = αL₀ΔT and final length L = L₀ + ΔL. Here L₀ is initial length in meters and ΔT is final minus initial temperature in °C; a temperature difference in kelvins has the same numerical value. Enter the linear coefficient in micrometers per meter per degree Celsius: 12 means 12 × 10⁻⁶ /°C. A 1 m bar with coefficient 12 and a 50 °C rise expands by 0.0006 m (0.6 mm) to 1.0006 m. Cooling gives a negative change for positive coefficients; negative coefficients are accepted for materials that contract on heating. Zero coefficient or zero temperature change gives no expansion. The model assumes a uniform temperature change, constant linear coefficient, a freely expanding unconstrained material, and small strain. It does not calculate thermal stress, area or volume expansion, or phase changes. Use a coefficient appropriate to your material and temperature range. Nonpositive predicted lengths are rejected; a positive result alone does not establish physical validity. Inputs are finite numbers up to 1e12 in magnitude, with initial length greater than zero. Results use browser floating-point arithmetic rounded to 12 significant digits. All inputs remain on your device.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
What is the linear thermal expansion formula?
ΔL = αL₀ΔT. Add the signed length change to initial length to obtain final length. Linear strain is αΔT.
How do I enter the expansion coefficient?
Enter the coefficient in µm/(m·°C). A coefficient of 12 × 10⁻⁶ /°C should be entered as 12, not 0.000012. Use a material-specific linear coefficient.
Can I calculate contraction during cooling?
Yes. Enter a negative temperature change for cooling. Negative coefficients are also supported. Zero temperature change or coefficient leaves length unchanged.
What is a worked example?
For a 1 m bar, coefficient 12 µm/(m·°C), and temperature rise of 50 °C, length increases by 0.6 mm to 1.0006 m. Strain is 0.0006, or 0.06%.
When does this model apply?
Use small strains, uniform temperature change, constant linear coefficient, and free expansion. Constraints, thermal stress, changing coefficients, and phase transitions require other models. A positive final length is not sufficient to validate extreme inputs.
Are my inputs uploaded?
No. Calculation and copying run locally in your browser. Reset restores the worked example.