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

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## Related Tools

- Linear thermal expansion calculations
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- Thermal coefficient units conversion

## User Guide

This tool will calculate any parameter from the formula for area thermal expansion, which includes the start temperature, end temperature, coefficient of area thermal expansion (CATE), start area and end area.

The area thermal expansion formula is used to calculate the change in area of a two dimensional region on an object, due to a change in temperature. The precision of area expansion is very good if the change in area is small compared to the overall area of the region on the 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 area thermal expansion calculator to determine each individual parameter are:

T_{0} = T_{1} – (A_{1} / A_{0} – 1) / α_{A}

T_{1} = T_{0} + (A_{1} / A_{0} – 1) / α_{A}

α_{A} = (A_{1} / A_{0} – 1) / (T_{1} – T_{0})

A_{0} = A_{1} / (1 + α_{A} · (T_{1} – T_{0}))

A_{1} = A_{0} · (1 + α_{A} · (T_{1} – T_{0}))

#### Symbols

- T
_{0}= Start temperature - T
_{1}= End temperature - α
_{A}= Coefficient of area thermal expansion (CATE) - A
_{0}= Start area - A
_{1}= End area

### 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 Area Thermal Expansion (CATE, α_{A})

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

### Start Area (A_{0})

This is the two dimensional area of a region on the object when it is at the start temperature T_{0} .

### End Area (A_{1})

This is the two dimensional area of a region on the object following thermal expansion caused by an increase in temperature from T_{0} to T_{1} .

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