Area Thermal Expansion Calculator

Calculate Area Thermal Expansion Parameters
Select Answer Mode	T0 T1 αA A0 A1
Start Temperature (T0) [?]
⟳ Select temperature unit degrees Celsius (°C) degrees Fahrenheit (°F) kelvins (K) degrees Rankine (°R) yoctokelvins (yK) zeptokelvins (zK) attokelvins (aK) femtokelvins (fK) picokelvins (pK) nanokelvins (nK) microkelvins (µK) millikelvins (mK) centikelvins (cK) decikelvins (dK) kelvins (K) decakelvins (daK) hectokelvins (hK) kilokelvins (kK) megakelvins (MK) gigakelvins (GK) terakelvins (TK) petakelvins (PK) exakelvins (EK) zettakelvins (ZK) yottakelvins (YK)
End Temperature (T1) [?]
Select temperature unit degrees Celsius (°C) degrees Fahrenheit (°F) kelvins (K) degrees Rankine (°R) yoctokelvins (yK) zeptokelvins (zK) attokelvins (aK) femtokelvins (fK) picokelvins (pK) nanokelvins (nK) microkelvins (µK) millikelvins (mK) centikelvins (cK) decikelvins (dK) kelvins (K) decakelvins (daK) hectokelvins (hK) kilokelvins (kK) megakelvins (MK) gigakelvins (GK) terakelvins (TK) petakelvins (PK) exakelvins (EK) zettakelvins (ZK) yottakelvins (YK)
CATE (αA) [?]
Select CATE unit per degree Celsius (/°C) per degree Fahrenheit (/°F) per kelvin (/K) per degree Rankine (/°R) ppm per degree Celsius (ppm/°C) ppm per degree Fahrenheit (ppm/°F) ppm per kelvin (ppm/K) ppm per degree Rankine (ppm/°R) per yoctokelvin (/yK) per zeptokelvin (/zK) per attokelvin (/aK) per femtokelvin (/fK) per picokelvin (/pK) per nanokelvin (/nK) per microkelvin (/µK) per millikelvin (/mK) per centikelvin (/cK) per decikelvin (/dK) per kelvin (/K) per decakelvin (/daK) per hectokelvin (/hK) per kilokelvin (/kK) per megakelvin (/MK) per gigakelvin (/GK) per terakelvin (/TK) per petakelvin (/PK) per exakelvin (/EK) per zettakelvin (/ZK) per yottakelvin (/YK) ppm per yoctokelvin (ppm/yK) ppm per zeptokelvin (ppm/zK) ppm per attokelvin (ppm/aK) ppm per femtokelvin (ppm/fK) ppm per picokelvin (ppm/pK) ppm per nanokelvin (ppm/nK) ppm per microkelvin (ppm/µK) ppm per millikelvin (ppm/mK) ppm per centikelvin (ppm/cK) ppm per decikelvin (ppm/dK) ppm per kelvin (ppm/K) ppm per decakelvin (ppm/daK) ppm per hectokelvin (ppm/hK) ppm per kilokelvin (ppm/kK) ppm per megakelvin (ppm/MK) ppm per gigakelvin (ppm/GK) ppm per terakelvin (ppm/TK) ppm per petakelvin (ppm/PK) ppm per exakelvin (ppm/EK) ppm per zettakelvin (ppm/ZK) ppm per yottakelvin (ppm/YK)
Start Area (A0) [?]
⟳ Select area unit sq millimetres (mm²) sq centimetres (cm²) sq inches (in²) sq feet (ft²) sq yards (yd²) sq metres (m²) acres (ac) hectares (ha) sq kilometres (km²) sq miles (mi²) sq nautical miles (nmi²) sq yoctometres (ym²) sq zeptometres (zm²) sq attometres (am²) sq femtometres (fm²) sq picometres (pm²) sq nanometres (nm²) sq micrometres (µm²) sq millimetres (mm²) sq centimetres (cm²) sq decimetres (dm²) sq metres (m²) sq decametres (dam²) sq hectometres (hm²) sq kilometres (km²) sq megametres (Mm²) sq gigametres (Gm²) sq terametres (Tm²) sq petametres (Pm²) sq exametres (Em²) sq zettametres (Zm²) sq yottametres (Ym²) sq thousands of an inch (thou²) sq inches (in²) sq feet (ft²) sq yards (yd²) acres (ac) sq miles (mi²) sq nautical miles (nmi²) centiares (ca) deciares (da) ares (a) decares (daa) hectares (ha) sq astronomical units (au²) sq light-years (ly²) sq parsecs (pc²) sq kiloparsecs (kpc²) sq megaparsecs (Mpc²) sq gigaparsecs (Gpc²)
End Area (A1) [?]
Select area unit sq millimetres (mm²) sq centimetres (cm²) sq inches (in²) sq feet (ft²) sq yards (yd²) sq metres (m²) acres (ac) hectares (ha) sq kilometres (km²) sq miles (mi²) sq nautical miles (nmi²) sq yoctometres (ym²) sq zeptometres (zm²) sq attometres (am²) sq femtometres (fm²) sq picometres (pm²) sq nanometres (nm²) sq micrometres (µm²) sq millimetres (mm²) sq centimetres (cm²) sq decimetres (dm²) sq metres (m²) sq decametres (dam²) sq hectometres (hm²) sq kilometres (km²) sq megametres (Mm²) sq gigametres (Gm²) sq terametres (Tm²) sq petametres (Pm²) sq exametres (Em²) sq zettametres (Zm²) sq yottametres (Ym²) sq thousands of an inch (thou²) sq inches (in²) sq feet (ft²) sq yards (yd²) acres (ac) sq miles (mi²) sq nautical miles (nmi²) centiares (ca) deciares (da) ares (a) decares (daa) hectares (ha) sq astronomical units (au²) sq light-years (ly²) sq parsecs (pc²) sq kiloparsecs (kpc²) sq megaparsecs (Mpc²) sq gigaparsecs (Gpc²)

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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:

T₀ = T₁ – (A₁ / A₀ – 1) / α_A

T₁ = T₀ + (A₁ / A₀ – 1) / α_A

α_A = (A₁ / A₀ – 1) / (T₁ – T₀)

A₀ = A₁ / (1 + α_A · (T₁ – T₀))

A₁ = A₀ · (1 + α_A · (T₁ – T₀))

Symbols

• T₀ = Start temperature
• T₁ = End temperature
• α_A = Coefficient of area thermal expansion (CATE)
• A₀ = Start area
• A₁ = End area

Start Temperature (T₀)

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

End Temperature (T₁)

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 (A₀)

This is the two dimensional area of a region on the object when it is at the start temperature T₀ .

End Area (A₁)

This is the two dimensional area of a region on the object following thermal expansion caused by an increase in temperature from T₀ to T₁ .

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