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Change the answer mode for this tool by selecting start temperature (T_{0}), end temperature (T_{1}), coefficient of linear thermal expansion (α_{L}), start length (L_{0}) or end length (L_{1}) as the parameter to calculate instead

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## User Guide

This tool will calculate any parameter from the formula for linear thermal expansion L₁=L₀(1+αₗ(T₁-T₀)), which includes the start temperature, end temperature, coefficient of linear thermal expansion (CLTE), start length and end length.

The linear thermal expansion formula is used to calculate the change in length of an object, due to a change in temperature. It has been widely proven and accepted by the scientific and engineering community that in many cases the change in length to overall length ratio is directly proportional to the change in temperature of the object. However, it is only an approximation, and will only produce a precise value if the change in length is small compared to the overall length of an object, and the thermal coefficient of expansion of the material does not change by much, within the range of temperature change.

### Formulas

The formulas used by this linear thermal expansion calculator to determine each individual parameter are:

T_{0} = T_{1} – (L_{1} / L_{0} – 1) / α_{L}

T_{1} = T_{0} + (L_{1} / L_{0} – 1) / α_{L}

α_{L} = (L_{1} / L_{0} – 1) / (T_{1} – T_{0})

L_{0} = L_{1} / (1 + α_{L} · (T_{1} – T_{0}))

L_{1} = L_{0} · (1 + α_{L} · (T_{1} – T_{0}))

#### Symbols

- T
_{0}= Start temperature - T
_{1}= End temperature - α
_{L}= Coefficient of linear thermal expansion (CLTE) - L
_{0}= Start length - L
_{1}= End length

### Start Temperature (T_{0})

This is the temperature of the object before the temperature is increased.

### End Temperature (T_{1})

This is the temperature of the object after the temperature has been increased

### Coefficient Of Linear Thermal Expansion (CLTE, α_{L})

This is a fixed value which is used to determine how much a small change in temperature will affect the length of a particular substance. The coefficient defines the fractional change in length of a substance per unit change in its temperature.

### Start Length (L_{0})

This is the length of the object when it is at the start temperature T_{0} .

### End Length (L_{1})

This is the length of the object following thermal expansion caused by an increase in temperature from T_{0} to T_{1} .