Daily Almanac Calculator

The equation of time (EoT) is the difference between mean solar time (clock time) and apparent solar time (sundial time): EoT = mean time - apparent time. It results from Earth's elliptical orbit and its axial tilt. A positive EoT means solar noon occurs before clock noon. The EoT is zero around April 15, June 13, September 1, and December 25.

Solar noon is the moment when the Sun reaches its highest point in the sky, crossing the local meridian. It corresponds to 12:00 local apparent solar time (sundial time). In clock time, solar noon varies by up to 30 minutes from 12:00 depending on your longitude within your time zone and the equation of time.

Day length depends on the hour angle at sunrise/sunset: cos(HA) = -tan(lat)*tan(dec). Near the poles, summer brings near-continuous daylight and winter brings near-continuous darkness. At the equator, day length is always close to 12 hours. The Arctic/Antarctic Circles mark the latitudes where continuous daylight or darkness first occur at the solstices.

Equinoxes occur when solar declination is 0 (around March 20 and September 22-23). Day and night are approximately equal everywhere on Earth. Solstices occur at maximum declination (+23.45 in June, -23.45 in December). The summer solstice is the longest day in the Northern Hemisphere; the winter solstice is the shortest.

The EoT is used to set sundials accurately and to predict when the Sun will be at a specific altitude for photography (golden hour), solar energy production peak times, and astronomical observations of the Sun. Solar trackers in photovoltaic systems use the EoT to aim panels precisely at the Sun throughout the year.

The analemma is the figure-8 curve traced on a globe or globe-like diagram showing the Sun's position at the same clock time each day throughout the year. Its horizontal axis represents the equation of time; its vertical axis represents solar declination. It is used to correct sundial readings to clock time and is visible as a decorative feature on globes.

The solar (tropical) year is the time from one vernal equinox to the next: 365.2422 days. The sidereal year is Earth's orbital period relative to distant stars: 365.2564 days. They differ by about 20 minutes because precession of Earth's axis slowly shifts the equinox point westward relative to the stars. Our calendar (Gregorian) tracks the tropical year.

Twilight is the period when the Sun is below the horizon but still illuminates the sky. Civil twilight: Sun 0 to -6 degrees (enough light for outdoor activities). Nautical twilight: -6 to -12 degrees (horizon visible at sea). Astronomical twilight: -12 to -18 degrees (sky not yet fully dark). When Sun is below -18 degrees, the sky is astronomically dark for observing.

The formula is accurate to within 1-2 minutes for all dates between 1900 and 2100. For higher accuracy (seconds), use the USNO Solar Position Algorithm or the Astronomical Almanac, which account for obliquity changes, aberration, atmospheric refraction, and the precise shape of Earth's orbit. For most practical purposes — sundials, solar energy, visual astronomy — this calculator is more than sufficient.