Radiometric dating using the naturally-occurring radioactive elements is simple in concept even though technically complex. If we know the number of radioactive parent atoms present when a rock formed and the number present now, we can calculate the age of the rock using the decay constant.

The number of parent atoms originally present is simply the number present now plus the number of daughter atoms formed by the decay, both of which are quantities that can be measured. Samples for dating are selected carefully to avoid those that are altered, contaminated, or disturbed by later heating or chemical events.

In addition to the ages of Earth, Moon, and meteorites, radiometric dating has been used to determine ages of fossils, including early man, timing of glaciations, ages of mineral deposits, recurrence rates of earthquakes and volcanic eruptions, the history of reversals of Earth's magnetic field, and the age and duration of a wide variety of other geological events and processes.

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The age equation

The mathematical expression that relates radioactive decay to geologic time is^{}

*D* = *D*_{0} + *N*(t) (e^{λt} − 1)

**where**

**t** is age of the sample,

**D** is number of atoms of the daughter isotope in the sample,

**D0** is number of atoms of the daughter isotope in the original composition,

**N** is number of atoms of the parent isotope in the sample at time t (the present), given by **N(t)** = Noe-λt, and

**λ** is the decay constant of the parent isotope, equal to the inverse of the radioactive half-life of the parent isotope times the natural logarithm of 2.

The equation is most conveniently expressed in terms of the measured quantity N(t) rather than the constant initial value No.

The above equation makes use of information on the composition of parent and daughter isotopes at the time the material being tested cooled below its closure temperature. This is well-established for most isotopic systems.
However, construction of an isochron does not require information on the original compositions, using merely the present ratios of the parent and daughter isotopes to a standard isotope. Plotting an isochron is used to solve the age equation graphically and calculate the age of the sample and the original composition.