Linear Thermal Expansion CalculatorFree online other calculator — instant results, no sign-up
Estimate length change from a constant expansion coefficient.
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About the Linear Thermal Expansion Calculator
The Linear Thermal Expansion Calculator estimates how much an object's length changes when its temperature increases, using a constant linear expansion coefficient. Enter the initial length in meters, the coefficient in µm/(m·K), and the temperature increase in kelvins to calculate the length change in meters.
- Initial length (m)
- The object's length at the starting temperature, measured in meters; the default is 2 m.
- Expansion coefficient (µm/(m·K))
- The linear length change in micrometers per meter of initial length per kelvin of temperature change; the default is 12 µm/(m·K).
- Temperature increase (K)
- The final temperature minus the starting temperature, measured in kelvins; the default is 50 K.
Formula and method
ΔL = L₀ × (α × 10⁻⁶) × ΔT = 2 × (12 × 10⁻⁶) × 50 = 0.0012 m
- ΔLCalculated length change in meters.
- L₀Initial length in meters.
- αEntered linear expansion coefficient in µm/(m·K); multiplying by 10⁻⁶ converts it to K⁻¹.
- ΔTTemperature change in kelvins, calculated as final temperature minus initial temperature.
Convert the entered expansion coefficient from µm/(m·K) to K⁻¹ by multiplying by 10⁻⁶, then multiply it by the initial length and temperature increase. With the default inputs, 12 × 10⁻⁶ K⁻¹ × 2 m × 50 K gives a length change of 0.0012 m.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Initial length2 m
- Expansion coefficient12 µm/(m·K)
- Temperature increase50 K
Results
- Result0.0012 m
How to use the Linear Thermal Expansion Calculator
- 1Enter the object's initial length in meters; use 2 for the default example.
- 2Enter a linear expansion coefficient appropriate to the material and temperature range; use 12 µm/(m·K) for the default example.
- 3Enter the temperature increase in kelvins; use 50 for the default example.
- 4Calculate the result and read the length change in meters: the default inputs produce 0.0012 m.
Reading your result
The Result row reports ΔL, the change in length, not the final length. The default result of 0.0012 m means the object lengthens by 1.2 mm. Adding this change to the initial 2 m gives a final length of 2.0012 m. A positive result indicates expansion, a negative result indicates contraction, and zero indicates no predicted length change.
Limitations
This estimate assumes a constant linear expansion coefficient over the temperature interval, a uniform temperature change, and an object free to expand along the measured direction. It is a small-strain approximation and does not account for temperature-dependent coefficients, phase changes, thermal gradients, or mechanical constraints. Constrained objects can develop thermal stress rather than undergoing the full predicted length change. For direction-dependent materials, use the coefficient for the measured direction; do not substitute an area or volume expansion coefficient.
Common questions
Why is the coefficient multiplied by 10⁻⁶?+
The coefficient is entered in micrometers per meter per kelvin, while the result is in meters. Since one micrometer is 10⁻⁶ meters, the default coefficient of 12 becomes 0.000012 K⁻¹ before multiplication.
Can I use a temperature increase measured in degrees Celsius?+
Yes. A temperature difference has the same numerical value in degrees Celsius and kelvins, so an increase of 50 °C is entered as 50 K. Enter the difference between temperatures, not the final temperature.
Does the default result of 0.0012 m represent the final length?+
No. It represents the added length. For the default initial length of 2 m, the final length is 2 + 0.0012 = 2.0012 m.
Can this formula estimate contraction during cooling?+
Yes, mathematically: cooling makes ΔT negative, so a positive expansion coefficient produces a negative length change. If the input accepts negative values, enter the temperature decrease as a negative temperature change.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.