Sun and Moon Position Calculator

How to use the sun and moon calculator

1. Pick a city in Place, type a Latitude and Longitude in decimal degrees (south and west are negative), or click Use my location. Your browser then asks for permission; the position is used only on this page and is never sent to a server.
2. Choose the Date, the Time and the Time zone in which you want to read the results. Click Now to jump to the current time.
3. Under Position at the chosen time, read the sun and moon altitude above the horizon, their azimuth (compass direction), the moon phase, the illuminated fraction of the disc, the moon’s age and its distance.
4. The two tables list the day’s events: dawn and dusk for each twilight, sunrise, solar noon and sunset with their direction, day length, moonrise and moonset, and the next full and new moons.

Altitude, azimuth and twilight

Altitude is the angle of the body above the horizon: 0° on the horizon, 90° straight overhead, negative below it. Azimuth is measured clockwise from true north: 90° is east, 180° south, 270° west. Photographers use them to plan the light, gardeners and solar panel owners to study shadows, astronomers to know when a target is high enough.

Sunrise and sunset are the moments when the upper edge of the sun touches the horizon. Because the atmosphere bends light by about 34 arcminutes near the horizon and the sun’s radius is 16 arcminutes, this happens when the centre of the sun is 0.833° below the horizon. Twilight follows three standard definitions:

• Civil twilight: sun down to 6° below the horizon; outdoor activities are possible without lights.
• Nautical twilight: down to 12°; the horizon is still visible at sea.
• Astronomical twilight: down to 18°; beyond this the sky is fully dark.

At high latitudes some of these events simply don’t happen: in summer the sun may stay above the horizon all day (midnight sun), and in winter it may not rise at all. The tables then show “Above all day” or “Below all day”.

How the calculation works

The sun’s position comes from the formulas of Jean Meeus’s Astronomical Algorithms, the same method as the NOAA solar calculator, accurate to about 0.01°. The moon uses Meeus’s lunar theory with its largest periodic terms, then a correction for parallax, since the moon is close enough for its position to depend on where you stand on Earth. Rise and set times are found by following the altitude through the local day and refining each horizon crossing to the second, then rounding to the minute. The moon phase comes from the angle between the moon and the sun; the illuminated fraction uses the true phase angle.

Results assume a sea-level horizon and standard atmospheric refraction. Mountains, buildings, altitude and unusual temperatures can shift the visible sunrise by a few minutes.