Equation of time from Duffie & Beckman and attributed to Spencer (1971) and Iqbal (1983).

The coefficients correspond to the online copy of the Fourier paper 1 in the Sundial Mailing list that was posted in 1998 by Mac Oglesby from his correspondence with Macquarie University Prof. John Pickard who added the following note.

In the early 1970s, I contacted Dr Spencer about this method because I was trying to use a hand calculator for calculating solar positions, etc. He was extremely helpful and gave me a reprint of this paper. He also pointed out an error in the original: in the series for E, the constant was printed as 0.000075 rather than 0.0000075. I have corrected the error in this version.

There appears to be another error in formula as printed in both Duffie & Beckman’s 2 and Frank Vignola’s 3 books in which the coefficient 0.04089 is printed instead of 0.040849, corresponding to the value used in the Bird Clear Sky model implemented by Daryl Myers 4 and printed in both the Fourier paper from the Sundial Mailing List and R. Hulstrom’s 5 book.


dayofyear (numeric) –


equation_of_time (numeric) – Difference in time between solar time and mean solar time in minutes.



J. W. Spencer, “Fourier series representation of the position of the sun” in Search 2 (5), p. 172 (1971)


J. A. Duffie and W. A. Beckman, “Solar Engineering of Thermal Processes, 3rd Edition” pp. 9-11, J. Wiley and Sons, New York (2006)


Frank Vignola et al., “Solar And Infrared Radiation Measurements”, p. 13, CRC Press (2012)


Daryl R. Myers, “Solar Radiation: Practical Modeling for Renewable Energy Applications”, p. 5 CRC Press (2013)


Roland Hulstrom, “Solar Resources” p. 66, MIT Press (1989)