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Solar Culmination and Equation of Time Calculator

From a date plus latitude, longitude and time zone, compute the solar noon time, noon altitude, equation of time and solar declination, with an equation of time curve.

Input

Enter a date with longitude, latitude and time zone to compute the solar culmination time, noon altitude, equation of time and solar declination.

yr
mo
day
deg

East positive, west negative (−180 to 180)

deg

North positive, south negative (−90 to 90)

h

Offset from UTC, east positive (for example Japan is 9)

Result

Culmination time (local standard time)

11:42:59

When the Sun crosses the local meridian

Equation of time

-1.742699 min

Noon altitude

77.747961 deg

Solar declination

23.437961 deg

Julian day

2,461,212.625

+18-18minDay of year

The equation of time and declination use the Julian day and NOAA solar position formulas, and the culmination time is 12 hours minus the equation of time minus the longitude offset.

How it works

  • Culmination is the moment the Sun crosses the local meridian (due south or due north) and reaches its greatest altitude of the day. The tool reports that moment in local standard time.
  • The equation of time is apparent solar time minus mean solar time. It arises from the eccentricity of Earth orbit and the tilt of its axis, ranging roughly from −14 to +16 minutes over a year.
  • Solar declination and the equation of time use the NOAA solar position polynomials, referenced to the Julian day and the J2000.0 epoch (JD 2451545.0).
  • Noon altitude is computed as 90 minus the absolute difference between latitude and solar declination. Enter east longitude as positive and the time zone as the offset from UTC, with east positive.
  • Atmospheric refraction, terrain obstruction and observer elevation are not included. Dates are taken from text inputs and all results come from pure functions.

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