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In quantum mechanics, a spin-orbital is a one-particle wavefunction taking both the position and spin angular momentum of a particle as its parameters.
The spinorbital of a single electron, for example, is a complex-valued function of four real variables: the three scalars used to define its position, and a fourth scalar, ms, which can be either +1/2 or -1/2:
- ?(x,y,z,ms)
We can also write it more compactly as a function of a position vector  and the quantum number ms:
 .
For a general particle with spin s, ms can take values between -s to s in integer steps. The electron has s=1/2.
A spinorbital is usually normalized, such that the probability of finding the particle anywhere in space with any spin is equal to 1:
From a normalized spinorbital, one can calculate the probability that the particle is in an arbitrary volume of space V and has an arbitrary spin ms:
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