In the pharmaceutical industry, Mean kinetic temperature (MKT) is a calculated temperature that represents the equivalent thermal effect of temperature variations over time, such that the degradation occurring under fluctuating conditions is equal to that which would occur at a constant MKT value.

The mean kinetic temperature can be expressed as:

T K = Δ H R − ln ⁡ ( t 1 e ( − Δ H R T 1 ) + t 2 e ( − Δ H R T 2 ) + ⋯ + t n e ( − Δ H R T n ) t 1 + t 2 + ⋯ + t n ) {\displaystyle T_{K}={\cfrac {\frac {\Delta H}{R}}{-\ln \left({\frac {{t_{1}}e^{\left({\frac {-\Delta H}{RT_{1}}}\right)}+{t_{2}}e^{\left({\frac {-\Delta H}{RT_{2}}}\right)}+\cdots +{t_{n}}e^{\left({\frac {-\Delta H}{RT_{n}}}\right)}}{{t_{1}}+{t_{2}}+\cdots +{t_{n}}}}\right)}}}

Where:

T K {\displaystyle T_{K}\,\!} is the mean kinetic temperature in kelvins

Δ H {\displaystyle \Delta H\,\!} is the activation energy (in kJ mol−1)

R {\displaystyle R\,\!} is the gas constant (in J mol−1 K−1)

T 1 {\displaystyle T_{1}\,\!} to T n {\displaystyle T_{n}\,\!} are the temperatures at each of the sample points in kelvins

t 1 {\displaystyle t_{1}\,\!} to t n {\displaystyle t_{n}\,\!} are time intervals at each of the sample points

When the temperature readings are taken at the same interval (i.e., t 1 {\displaystyle t_{1}\,\!} = t 2 {\displaystyle t_{2}\,\!} = ⋯ {\displaystyle \cdots } = t n {\displaystyle t_{n}\,\!}), the above equation is reduced to:

T K = Δ H R − ln ⁡ ( e ( − Δ H R T 1 ) + e ( − Δ H R T 2 ) + ⋯ + e ( − Δ H R T n ) n ) {\displaystyle T_{K}={\cfrac {\frac {\Delta H}{R}}{-\ln \left({\frac {e^{\left({\frac {-\Delta H}{RT_{1}}}\right)}+e^{\left({\frac {-\Delta H}{RT_{2}}}\right)}+\cdots +e^{\left({\frac {-\Delta H}{RT_{n}}}\right)}}{n}}\right)}}}

Where:

n {\displaystyle n\,\!} is the number of temperature sample points