Moon Phase on Any Date

What causes lunar phases and how are they calculated?

Lunar phases happen because the Moon’s orbit changes the angle between the Sun, the Moon and Earth, so we see more or less of its sunlit half. The cycle through New Moon, First Quarter, Full Moon and Last Quarter takes 29.53 days on average, the synodic month. The fraction of the disc lit is k = (1 + cos i) / 2, where i is the phase angle.

How the picture is worked out

The calculator works out where the Sun and the Moon were at the instant you choose, using the methods in Jean Meeus’s Astronomical Algorithms: the Moon from the 120 periodic terms of chapter 47, good to about 10 seconds of arc, and the Sun from chapter 25. The angle Sun, Moon, Earth is the phase angle i, and the share of the disc in sunlight follows from it, k = (1 + cos i) / 2. At i = 0 the whole face is lit, at i = 90° exactly half, at i = 180° none of it. That is the cosine of an angle read off a circle, which the unit circle explorer lets you drag round.

On Meeus’s own test date, 12 April 1992 at 0h dynamical time, the full calculation gives k = 0.6786, the book’s figure. His shortcut, which skips the two positions, gives 0.6801, which is why it is not used here.

The fraction lit is the same, to within a percentage point, from everywhere on Earth at one instant. The tilt is not. Which way the lit edge points on your sky is its position angle χ, measured from north, less the parallactic angle q, which says how far north is turned from straight up where you stand. So the same waxing Moon is lit on its right in London and on its left in Sydney. The picture is NASA’s map of the Moon, turned to show the face that pointed at you, tipped by the tilt of the Moon’s axis, and lit from the point where the Sun stood overhead on the Moon. Each patch is shaded by the Lommel-Seeliger law, which is why the full Moon looks flat rather than like a ball.

Worked example: the full moon of 26 October 2026

This is the night the page opens on before it moves to your own: New Delhi, 28.61° N, 77.21° E, at 21:00 IST on 26 October 2026. The Moon was exactly full at 09:42 IST, 04:12 UT, so the day takes the name Full Moon.

1. Its age. The last new moon fell at 21:20 IST on 10 October, 15.99 days earlier, which the readout rounds to 16.0 days.
2. The phase angle. 11 hours 18 minutes after full, the Sun, Moon and Earth are 7.91° out of line, so k = (1 + cos 7.91°) / 2 = 0.9952: the disc is 99.5 percent lit.
3. Where it stands. The Moon is 172.1° west of the Sun, about 367,400 km away, 4.4 percent nearer than its 384,400 km average, and so 32.5 arcminutes across. From New Delhi it stands 42° up, due east.
4. Its day. It rose at 17:34 and had set that morning at 06:27, and it did not cross the meridian at all on 26 October: it passes due south at 00:31 the next day. The US Naval Observatory’s data give the same times to the minute.
5. The tithi. The Moon is 186.3° ahead of the Sun in ecliptic longitude, so the tithi at that moment is the 16th, Krishna Pratipada.

The orbit view

The right-hand panel looks down on the Earth from above its North Pole, with sunlight from the left. The Moon goes round anticlockwise, and the angle from the Sun’s direction to the Moon’s is the elongation, the violet arc. Drag the Moon round its orbit and the date moves to the moment in this lunation when the Moon really was at that angle; the Moon does not move at a steady pace, so the dates are found from its true motion.

One turn against the stars, the sidereal month, takes 27.321662 days. New moon to new moon, the synodic month, takes 29.530589 days on average, because meanwhile the Earth has carried the Moon about 29° round the Sun and it has that far still to go to line up again. Switch on the Earth’s own motion to see the two lines. The Moon also turns on its axis once every 27.321662 days, once per orbit, so the same face always points at the Earth: that is tidal locking, marked by the notch on the Moon’s near side. Its slightly tilted, slightly oval orbit lets us see a little round each edge in turn, the libration, and from somewhere on Earth, over the years, about 59 percent of its surface comes into view. With the orbit drawn to scale, the Earth is about 30 of its own diameters from the Moon.

Gravity sets that orbit. The orbit simulator shows why a body launched sideways falls round in an ellipse, and the gravitational force calculator gives the pull between the Earth and the Moon that holds it there.

Reading the calendar

Each day is named the way the US Naval Observatory names days. A day that contains the instant of a new moon, first quarter, full moon or last quarter takes that name, and the instant’s local time is printed under it. Every other day is a waxing or waning crescent, under half lit, or gibbous, over half lit. Because the names follow the local calendar, a full moon can fall on different dates in different places: the full moon of 26 October 2026 at 09:42 IST in New Delhi was at 21:12 on 25 October in Los Angeles.

Each disc is drawn as it looks at 21:00 local time, turned as it hangs in that place’s sky or north up, as you choose. Times are rounded to the nearest minute, as almanacs print them. Choose the year to see a whole year of Moons at once, and save either as an image.

For a whole year in one city, every phase on its own clock with moonrise on each full moon day, see the moon phase calendars for New York, Los Angeles, Chicago, Toronto, London and Sydney.

The tithi readout is the tithi at that moment, one for every 12° the Moon gains on the Sun. A panchang names the whole day by the tithi in force at local sunrise, which can be the one before.

What it leaves out

• The air. Near the horizon, refraction lifts the Moon about half a degree and the air dims and reddens it. The rise and set times allow for the lift, 34 arcminutes, as almanacs do; the altitude readout is the plain geometric one, and the picture is not reddened.
• Eclipses. The Earth’s shadow is not drawn. The full moon of 3 March 2026 passed within half a degree of the point opposite the Sun, a total eclipse of the Moon, and here it looks like any other full moon.
• Earthshine. Sunlight reflected by the Earth faintly lights the Moon’s dark side, brightest on a thin crescent. It is drawn far brighter than it really is, so that it can be seen at all, and the picture says so.
• Clock drift. The Earth’s spin is not quite steady, and the correction for it, Delta T, is a forecast after about 2025. The forecast used here already runs about 6 seconds ahead in 2026, which shifts a phase time by those 6 seconds. Phase times agree with the US Naval Observatory’s to within a minute from 1900 to 2050, and to about two minutes by 2100, where the two forecasts part.
• The stars. The stars behind the Moon are a fixed backdrop that comes out as the sky darkens, not a map of the real sky.

The Moon map is the CGI Moon Kit colour map made by NASA’s Scientific Visualization Studio from images by the Lunar Reconnaissance Orbiter’s camera, used here in greyscale; it is in the public domain, and the credit, NASA’s Scientific Visualization Studio, appears on the stage and in every saved image. NASA does not endorse this tool. The city list comes from Natural Earth and each time zone’s own place from the tz database, both public domain.