Moon Phase Calculator

What a moon phase is, geometrically

The Moon has no light of its own. Half of it is lit by the Sun at all times, and the phase you see is the fraction of that lit half turned toward Earth. Stand between a lamp and a ball and move the ball around your head: you see the same sequence of shapes, and nothing about the ball changes.

Phase is an angle, not a shape. Astronomers call it the elongation, the angle between the Sun and the Moon as seen from Earth, measured from 0 degrees at new moon to 180 at full. Illumination follows from that angle with one cosine: lit fraction = (1 - cos(elongation)) / 2. At 90 degrees the fraction is 0.5, which is a first or last quarter.

The Moon's orbit is tilted about 5 degrees to the plane of Earth's orbit, which is why the Moon usually passes above or below the Sun at new moon instead of covering it. Eclipses happen only when a new or full moon falls near one of the two points where the orbits cross, and NASA's moon phase overview is a good plain language reference for the eight names.

Two months: 29.53 days and 27.32 days

The Moon takes 27.32 days to circle Earth once relative to the stars. That is the sidereal month, and it is the true orbital period. The cycle of phases takes longer, 29.53 days, because Earth moves about 27 degrees around the Sun in the same time, so the Moon has to travel a bit further to line up with the Sun again.

Those 2.21 extra days are the synodic month, and it is the one that governs phases, tides and every lunar calendar. Twelve synodic months come to 354.4 days, which is why Islamic calendar dates drift about 11 days earlier each solar year.

Neither number is constant. The Moon's orbit is elliptical, so the synodic month varies between about 29.2 and 29.9 days, and the interval from new moon to full moon ranges from roughly 13.9 to 15.6 days. NASA's Goddard page on the Moon's orbit works through the geometry.

Counting from a known new moon

Any phase calculation starts from a reference. The calculator uses the new moon of January 6, 2000 at 18:14 UTC, the standard epoch for lunar formulas, and computes every later new moon from it with the synodic month plus a set of periodic corrections for the Moon's elliptical orbit and the Sun's pull. That is the method in Jean Meeus's Astronomical Algorithms, accurate to a few minutes.

The quick version is one subtraction: days since that reference, divided by 29.5306, and the remainder is the Moon's age. Age 0 is new, 7.4 is first quarter, 14.8 is full and 22.1 is last quarter. Multiply age by 360/29.5306 and you have an approximate phase angle.

The quick version drifts because the Moon does not move at a constant angular speed. On October 17, 2026 the age is 6.84 days, which the quick formula turns into 83 degrees. The true angle that day is 77 degrees, so the estimate is off by 6 degrees and the illumination estimate is off by 4 percentage points. The calculator uses the real angle, which is why its percentage matches an almanac.

One more subtlety: the phase is not exactly half of the lunation at full moon. The new to full interval is shorter than the full to new interval when the Moon is near perigee, and longer near apogee, which is why the calendar date of a full moon can sit a day off the midpoint between two new moons.

Worked example: October 17, 2026

Pick a date, any date. For October 17, 2026 at noon UTC, the last new moon was October 10 at 15:51 UTC, so the Moon is 6.8 days old. Its angle from the Sun is 77 degrees, and (1 - cos 77) / 2 gives 39 percent lit.

At 39 percent and growing, the phase is a waxing crescent, with the lit edge on the right in the northern hemisphere. The next full moon is October 26, 2026, 8.7 days later, and the next new moon is November 9, 2026.

Ten days on, November 5, the age is 25.8 days, the angle 316 degrees and the illumination 14 percent: a waning crescent, rising a couple of hours before the Sun. It is the same shape as a 14 percent waxing crescent on the other side of the cycle, but the lit edge is on the left and the Moon is in the morning sky rather than the evening sky.

That is the part people miss when they use a phase chart. A crescent at 25 percent looks identical in shape whether it is waxing or waning, and the direction of the lit edge plus the time of day is what tells you which half of the cycle you are in.

The eight phases and their boundaries

Almanacs name eight phases: four instants and four stretches between them. The instants are new, first quarter, full and last quarter, each lasting a moment. The stretches are the crescents and the gibbous phases, each lasting about a week.

The boundaries are a convention. At 49 percent lit the Moon is a waxing crescent and at 51 percent it is a waxing gibbous, even though the two look identical to the eye. The calculator treats a moon within about half a day of an instant as that instant, which is how an almanac labels the night of a full moon.

Why the southern hemisphere sees it upside down

The Moon's lit side points at the Sun, and where that is in your sky depends on your latitude. In the northern hemisphere a waxing moon is lit on the right and a waning moon on the left. South of the equator the same moon appears rotated 180 degrees: waxing is lit on the left.

The flip is not a different moon, it is the same moon seen from the other side of the plane of its orbit. Someone in Sydney and someone in New York looking at the same instant see the same illuminated fraction and the same phase name, with the crescent pointing the other way. Near the equator the crescent lies almost on its back, like a bowl, which is the image on several flags.

Latitude also changes how high the Moon climbs. A crescent that sits low and fat near the horizon in Miami can stand nearly upright in Toronto on the same night, because the ecliptic meets the horizon at a steeper angle the further north you go.

Illumination does not move in a straight line

The lit fraction follows a cosine, so it changes slowly near new and full and quickly near the quarters. Between age 0 and 3.7 the Moon goes from 0 to 14.6 percent. Between 11.1 and 14.8 it goes from 85.4 to 100. The middle week is where the shape changes every night in a way you can see.

That curve is why "half full" feels rare. Half lit happens twice a month and lasts a single night at each pass, while the crescent and gibbous stretches each last about a week. A moon that looks three quarters full is somewhere between 60 and 80 percent illuminated, which is a wide band.

What this calculator does not do

It gives the phase at noon UTC on the date you pick, so a date near a phase boundary can be off by a day in your local time zone. It does not give moonrise or moonset, which depend on your latitude and longitude, and it does not predict eclipses, which need the Moon's position relative to the orbital nodes.

It also does not correct for the fact that the Moon's disk is slightly larger than the Sun's, or for atmospheric refraction near the horizon, which flattens the Moon and shifts its color toward orange. For those, use the U.S. Naval Observatory data or a full ephemeris. For "what will the Moon look like on my birthday", noon UTC is close enough.

One thing the calculator does get right that a wall calendar often gets wrong: the date of a full moon depends on your time zone. A full moon at 02:00 UTC on the 26th is still the evening of the 25th in California, so a calendar printed for the East Coast can be a day ahead of what you see in the sky.