The Celsius temperature scale is based off of the freezing point of water (0*). Kelvin is based off of absolute zero, or the lowest temperature that is attainable. To convert from Celsius to Kelvin, you add 273.15. Kelvin does not use a degree sign.
Freezing Point of Water: 0*C or 273.15
Boiling Point of Water: 100*C or 373.15
It is easy to tell wether or not a temperature can exist. If it falls below 0 on the Kelvin scale, it can not be possible! This is because 0 is the lowest temperature attainable. So if it falls below -273.15*C, it doesn't exist!