Zenith angle calculator

What the zenith angle is

The solar zenith angle is the angle between the sun and directly overhead (the zenith). At solar noon on the equator during an equinox it approaches 0° - the sun is nearly overhead. At sunrise and sunset it is 90° - the sun is on the horizon. Solar elevation, shown alongside it, is simply 90° minus the zenith angle - the sun's height above the horizon, which is often the more intuitive number to read.

What it is calculated from

Latitude and longitude fix where you are; the date fixes the sun's declination (how far north or south of the equator the sun is directly overhead that day, which is why the sun sits higher in summer); the time of day, combined with longitude, fixes the sun's hour angle (how far it has moved across the sky since solar noon). This uses the standard solar position equations built from those three inputs - the same approach behind sundial design, solar panel tilt calculations and photography's "golden hour" timing.

Time zone care

Solar position depends on true solar time, not clock time, which is offset from clock time by both the time zone and the equation of time (a few minutes of seasonal drift caused by Earth's elliptical orbit and axial tilt). The time entered is treated as local clock time in the time zone you specify, and both corrections are applied internally rather than left for you to work out.

Related tools

See the Qibla direction finder for another location-and-angle calculation, and the Zulu time converter if you need to convert the time itself first.