The element potassium (symbol K) has three nuclides, K39, K40, and K41. Only K40 is radioactive; the other two are stable. K40 can decay in two different ways: it can break down into either calcium or argon. The ratio of calcium formed to argon formed is fixed and known. Therefore the amount of argon formed provides a direct measurement of the amount of potassium-40 present in the specimen when it was originally formed.
Because argon is an inert gas, it is not possible that it might have been in the mineral when it was first formed from molten magma. Any argon present in a mineral containing potassium-40 must have been formed as the result of radioactive decay. F, the fraction of K40 remaining, is equal to the amount of potassium-40 in the sample, divided by the sum of potassium-40 in the sample plus the calculated amount of potassium required to produce the amount of argon found. The age can then be calculated from equation (1).
In spite of the fact that it is a gas, the argon is trapped in the mineral and can't escape. (Creationists claim that argon escape renders age determinations invalid. However, any escaping argon gas would lead to a determined age younger, not older, than actual. The creationist "argon escape" theory does not support their young earth model.)
The argon age determination of the mineral can be confirmed by measuring the loss of potassium. In old rocks, there will be less potassium present than was required to form the mineral, because some of it has been transmuted to argon. The decrease in the amount of potassium required to form the original mineral has consistently confirmed the age as determined by the amount of argon formed.