How do you calculate the right ascension and declination?

Hint: In astronomy, the right ascension is the east-west coordinate through which the position of a celestial body is measured more accurately. The Declination is analogous to the latitude and it is measured as south or north of the celestial equator.

Complete step by step answer:
The right ascension is the angular distance of a body’s hour circle east of the vernal equinox which is measured along the celestial equator.
The total range of the right ascension is 24 hours = 360 degree / 15 degree / hour. The 15 degrees/hour conversion factor rises from the rotation rate of the Earth.
We can calculate the right ascension by converting it into a decimal form by using the formula,
$hour + \dfrac{{minute}}{{60}} + \dfrac{{second}}{{3600}} = decimal value$
For example, if the right ascension is 4 hours, 20 minutes, and 40 seconds, then this in decimal form is
$4 + \dfrac{{20}}{{60}} + \dfrac{{40}}{{3600}} = 4.344.$
Then multiply this by 15 degrees.
The declination can be calculated by assuming that the Earth’s orbit is circular. Then the solar declination for any day of the year can be determined by using,
$\Delta = \varphi cos\left[ {\dfrac{{C\left( {d - {d_r}} \right)}}{{{d_y}}}} \right]$
Where $\varphi $is the tilt angle of 23.5 degrees and C is 360 degrees and d is the Julian day.
The declination is expressed in degrees and it is the celestial sphere’s equivalent of the latitude. The celestial equator is $0^\circ $ declination and the poles are $ + 90^\circ and - 90^\circ $ respectively. Here + and – refer to north and south accordingly.

Note:
1. For the right ascension, any units of the angular measure can be chosen.
2. The Earth’s declination varies from 23.45 degrees north to 23.45 degrees south which gives rise to seasons.