In astronavigation, sight reduction is the process of deriving from a sight (in celestial navigation usually obtained using a sextant) the information needed for establishing a line of position, generally by intercept method.

Sight is defined as the observation of the altitude, and sometimes also the azimuth, of a celestial body for a line of position; or the data obtained by such observation.

The mathematical basis of sight reduction is the circle of equal altitude. The calculation can be done by computer, or by hand via tabular methods and longhand methods.

Given:

First calculate the altitude of the celestial body ${\displaystyle Hc}$ using the equation of circle of equal altitude:

$${\displaystyle \sin(Hc)=\sin(Lat)\cdot \sin(Dec)+\cos(Lat)\cdot \cos(Dec)\cdot \cos(LHA).}$$

The azimuth ${\displaystyle Z}$ or ${\displaystyle Zn}$ (Zn=0 at North, measured eastward) is then calculated by:

$${\displaystyle \cos(Z)={\frac {\sin(Dec)-\sin(Hc)\cdot \sin(Lat)}{\cos(Hc)\cdot \cos(Lat)}}={\frac {\sin(Dec)}{\cos(Hc)\cdot \cos(Lat)}}-\tan(Hc)\cdot \tan(Lat).}$$