The velocity of a star relative to the sun can be broken down into perpendicular components: the radial velocity and transverse velocity. The transverse velocity results in a change of angular position, which can be measured in arc seconds per year. This is called the proper motion of the star, denoted . If the star is located at a distance d, then the transverse velocity v will b

where the factor 206265 converts from arc seconds per year to radians per year.
When d is expressed in terms of the star's parallax p, i.e.,

where A is one astronomical unit and p is measured in arc seconds,

Finally, if A is expressed in kilometers and the year is expressed in seconds the expression becomes

km/s.