The Equation Of Time is a correction applied to Solar Time. It is mainly used today in celestial navigation, but was also used as a correction applied to sundials. Sundials would have a table or graph of the equation of time printed on them, so the observer could adjust the observed time to the true time.
The equation below is a simplified version, published by W. M. Smart in "Textbook On Spherical Astronomy". A more accurate version would require a nutation series, and precise RA and Dec of the Sun. But this version is accurate to within a few seconds over 60 centuries.
An even more simplified version is produced below. It differs by Smart's version by a few minutes at most, and is based only on the day of the year, so no correction for precession or other factors are made. The Astronomical Almanac publishes a simplefied version for each year. In the code, I have included versions from 1982 and 2016 purely to illustrate how it changes with time.
Where \( d \) is the day of the year.
Result is in minutes