Clock Time to Solar Time (Equation of Time and Longitude)
Converts the time on a clock to true solar time, the time the sun-angle calculators run on.
Example
You enter
- Clock hour (0-23) 10
- Clock minute (0-59) 30
- Day of year (1-365; Feb 3 = 34) 34
- Longitude (deg, west negative) -89.4
- Clock's UTC offset (h; CST -6, CDT -5) -6
You get
- Equation of time (min) -13.5
- Longitude correction (min) 2.4
- Total correction (min) -11.1
- Solar time hours 10.3167
No published worked example is on file for this calculation. It is checked against a hand-worked derivation of its method and an independent reference test.
Details, formula, and sources
ScopeIt adds 4 minutes per degree the site sits east of its time-zone meridian and the equation of time for the date. In Madison, Wisconsin (89.4 W) on February 3, 10:30 Central Standard is 10:19 solar time, 1.68 hours before solar noon, and solar noon falls at 12:11 on the clock. Enter the offset the clock is keeping, so daylight time needs no extra step. Good to about half a minute; an ephemeris governs.
Formula or tableSolar time = clock time + 4 (longitude - 15 x UTC offset) + E, in minutes, longitude in degrees with west negative. Equation of time E = 229.2 (0.000075 + 0.001868 cos B - 0.032077 sin B - 0.014615 cos 2B - 0.04089 sin 2B), B = (n - 1) 360/365 for day of year n. Hours from solar noon = solar time - 12. Solar noon on the clock = 12:00 minus the total correction.
Source and editionSpencer (1971) equation of time and the standard-to-solar time relation as given in Duffie and Beckman, Solar Engineering of Thermal Processes, eqs. 1.5.2 and 1.5.3, cited by name. The book writes longitudes in degrees west, solar time = standard time + 4 (Lst - Lloc) + E; with west negative and the standard meridian at 15 degrees per hour of UTC offset this is the same relation.
Free accessThe series is five terms and is reproduced in NOAA's General Solar Position Calculations with nearly identical coefficients. Duffie and Beckman Example 1.5.1 (Madison, Wisconsin, 89.4 W, February 3, 10:30 Central Standard) gives E = -13.5 min and a solar time of 10:19; this tile returns -13.49 min and 10:19.
What governsEstimate. AHJ and licensed professional govern.
API field namesclock_hour, clock_minute, day_of_year, longitude_deg, utc_offset_hours, equation_of_time_min, longitude_correction_min, total_correction_min, solar_time_hours
- Equation of time Spencer's five-term series on day of yearDuffie and Beckman eq. 1.5.3
- Clock meridian 15 degrees per hour of the entered UTC offsetdefinition of zone time
- Sign convention longitude and UTC offset negative west of Greenwich, as in solar-timesscope of this tile