Linear Thermal Expansion Calculator

Calculate Linear Thermal Expansion Parameters
Select Answer Mode	T0 T1 αL L0 L1
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)
CLTE (αL) [?]
Select CLTE 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 Length (L0) [?]
⟳ Select length unit microns (µm) thousandths of an inch (thou) millimetres (mm) centimetres (cm) inches (in) feet (ft) yards (yd) metres (m) kilometres (km) miles (mi) nautical miles (nmi) yoctometres (ym) zeptometres (zm) attometres (am) femtometres (fm) picometres (pm) nanometres (nm) micrometres (µm) millimetres (mm) centimetres (cm) decimetres (dm) metres (m) decametres (dam) hectometres (hm) kilometres (km) megametres (Mm) gigametres (Gm) terametres (Tm) petametres (Pm) exametres (Em) zettametres (Zm) yottametres (Ym) thousandths of an inch (thou) inches (in) feet (ft) yards (yd) miles (mi) nautical miles (nmi) astronomical units (au) light-years (ly) parsecs (pc) kiloparsecs (kpc) megaparsecs (Mpc) gigaparsecs (Gpc)
End Length (L1) [?]
Select length unit microns (µm) thousandths of an inch (thou) millimetres (mm) centimetres (cm) inches (in) feet (ft) yards (yd) metres (m) kilometres (km) miles (mi) nautical miles (nmi) yoctometres (ym) zeptometres (zm) attometres (am) femtometres (fm) picometres (pm) nanometres (nm) micrometres (µm) millimetres (mm) centimetres (cm) decimetres (dm) metres (m) decametres (dam) hectometres (hm) kilometres (km) megametres (Mm) gigametres (Gm) terametres (Tm) petametres (Pm) exametres (Em) zettametres (Zm) yottametres (Ym) thousandths of an inch (thou) inches (in) feet (ft) yards (yd) miles (mi) nautical miles (nmi) astronomical units (au) light-years (ly) parsecs (pc) kiloparsecs (kpc) megaparsecs (Mpc) gigaparsecs (Gpc)

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User Guide

This tool will calculate any parameter from the formula for linear thermal expansion, 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:

T₀ = T₁ – (L₁ / L₀ – 1) / α_L

T₁ = T₀ + (L₁ / L₀ – 1) / α_L

α_L = (L₁ / L₀ – 1) / (T₁ – T₀)

L₀ = L₁ / (1 + α_L · (T₁ – T₀))

L₁ = L₀ · (1 + α_L · (T₁ – T₀))

Symbols

• T₀ = Start temperature
• T₁ = End temperature
• α_L = Coefficient of linear thermal expansion (CLTE)
• L₀ = Start length
• L₁ = End length

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 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 (L₀)

This is the length of the object when it is at the start temperature T₀ .

End Length (L₁)

This is the length of the object following thermal expansion caused by an increase in temperature from T₀ to T₁ .

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