Many nuclides can decay in more than one way (e.g. by both alpha and beta decays). In this case each decay process is characterised by its own decay constant. We consider decay by two processes with decay constants and . This is easily generalised. Then
where is that number decaying by path 1, etc.
Let . Then the overall decay is determined by this sum of decay constants,
It follows that
The ratio gives the fraction of nuclei decaying by path 1 and is known as the branching ratio.