What this calculator does
Find out what the moon looks like on any date, and when the next full and new moons are. The moon's phase is how much of its sunlit half we can see from Earth. As the moon circles us, the angle between the Sun, the Moon and Earth changes. So the lit part grows from a thin sliver to a full circle, then shrinks back again. One full cycle, from new moon to new moon, takes about 29.5 days on average.
Pick a date, and the calculator works out the phase from where the Sun and Moon actually are, not from a table. It gives the phase name and the share of the moon that's lit. It also shows how many days have passed since the last new moon, and the date and time of the next full and new moons.
Where it's used
Why this math matters outside the classroom:
- Night photography. Photographers check the phase to plan Milky Way shots on moonless nights or a full moon rising at dusk.
- Tides. Boaters and anglers plan around spring tides, which come near new and full moon when the Sun and Moon line up.
- Night events. Event planners pick a full-moon date for night hikes so the trail is lit without extra lights.
- Festival dates. Several religious and cultural calendars set festival dates by the new or full moon, so organizers look phases up ahead.
- Classroom tracking. Science classes record the moon's lit fraction over a month and match it with the 29.5-day cycle.
How to use it
- Choose a date between 1800 and 2200. It starts on today's date.
- Read the phase name and the percent of the moon that's lit that day.
- Check the moon's age, its days since the last new moon, to see how far through the cycle it is. It's about 0 at new moon, 7.4 at first quarter, 14.8 at full moon and 22 at last quarter.
- Use the next full moon and next new moon lines to plan ahead. Remember they're given in Coordinated Universal Time (UTC), the world's standard clock time.
What the inputs mean
- Date
- The calculation is made for 12:00 UTC on the chosen day. The moon changes slowly. So the phase name only differs from your local evening sky near the switch from one phase to the next.
Formula and method
mean new moon = 2451550.09766 + 29.530588861 × k (Julian day, k = lunation number since January 2000) true new or full moon = mean phase + Σ periodic terms in the Sun's anomaly M, the Moon's anomaly M′, the argument of latitude F and the node Ω phase angle i ≈ 180° − D − 6.289° sin M′ + 2.100° sin M − 1.274° sin(2D − M′) − 0.658° sin 2D − 0.214° sin 2M′ − 0.110° sin D illuminated fraction = (1 + cos i) ÷ 2 moon age = time now − time of the most recent true new moon
Don't worry if the formulas look heavy; the idea behind them is simple. The method comes from Jean Meeus's book Astronomical Algorithms, a standard reference for amateur and professional astronomers. It starts from the average cycle, or lunation, of 29.530589 days. That gives the rough time of each new and full moon.
A Julian day is a running count of days that astronomers use instead of calendar dates, and k counts lunations since January 2000. The orbits of the Moon and Earth are ovals (ellipses), not circles, so the moon speeds up and slows down along its path. A series of small corrections, called periodic terms, adjusts for that.
In those corrections, M and M′ (the anomalies) track where the Sun and Moon are along their oval paths. F (the argument of latitude) tracks how far the Moon is above or below Earth's orbit, and Ω (the node) is where those two paths cross. D (the elongation) is how far the Moon appears from the Sun in the sky. Σ means "add up", and sin and cos are the sine and cosine from trigonometry.
The phase angle i is the angle at the Moon between the directions to the Sun and to Earth. It depends mostly on D, with smaller corrections for M and M′. When i is 0°, the side facing us is fully lit; at 180°, it's completely dark.
A day is called New Moon or Full Moon when the exact moment of that phase falls on it, in UTC. It's First Quarter or Last Quarter when the lit share passes 50% during it. Other days are crescent (under half lit) or gibbous (over half lit). They're waxing (growing) between new and full, and waning (shrinking) between full and new.
How accurate is it? For 1800 to 2200, the times of new and full moons match published almanac tables to within a few minutes. The lit share matches to within about one percentage point. A few very tiny corrections for the planets are left out. So is the slight difference between atomic clock time and time based on Earth's spin.
Worked example
What did the moon look like on March 14, 2025, the night of a total lunar eclipse?
- At 12:00 UTC the date is Julian day 2,460,749.
- The most recent true new moon was on February 28, 2025 at 00:47 UTC (Julian day 2,460,734.5325).
- Moon age: 2,460,749 − 2,460,734.5325 = 14.47 days.
- The phase angle is about 2.2°, so the lit fraction is (1 + cos 2.2°) ÷ 2 ≈ 0.9996, or 100%.
- The true full moon falls at 06:57 UTC that same day, so the day is labelled Full Moon.
Result: On March 14, 2025, the moon is full, about 100% lit and 14.5 days old. The next new moon follows on March 29, 2025 at 11:00 UTC.
Understanding the result
Waxing means the lit part grows each night. In the Northern Hemisphere, the right-hand side is lit. Waning means it's shrinking, and the left-hand side is lit. South of the equator, the picture is flipped.
Near full moon, the moon looks round to the eye for a day or two either side. But only one instant is the true full moon. The lit percentage shows how close to full it really is.
If you're planning around a full or new moon, convert the UTC time to your own time zone. For example, a full moon at 02:00 UTC falls on the evening before in the Americas.
Assumptions and limitations
- The phase is worked out for 12:00 UTC on the chosen date.
- Times are given in UTC. The astronomers' time scale used in the formulas (terrestrial dynamical time) is treated as equal to UTC. Today the two differ by about a minute.
- The calendar is the Gregorian calendar, the one in everyday use, for every date.
- Dates are limited to 1800–2200, where the method is reliable.
- It doesn't give moonrise or moonset times, which depend on exactly where you are.
- It doesn't predict eclipses or say whether the moon is above the horizon for you.
- Near the switch between two phases, a phase name can be a day off from a calendar that uses a different time zone.
Frequently asked questions
Why does my calendar show the full moon on a different day?
A full moon is a single moment, and its calendar date depends on the time zone. This calculator uses UTC. If the full moon is early in the morning UTC, it happens the evening before for anyone in North or South America.
Is the moon age the same as the phase?
They're closely linked. The age counts days since the last new moon. But the moon's speed along its orbit varies. So a full moon can come anywhere from about 13.9 to 15.6 days after new moon, and the age alone can't pin down the exact phase.
Why is a quarter moon half lit?
The name means the moon is a quarter of the way (or three quarters of the way) through its cycle. It isn't about how much is lit. At those points, we see half of the moon lit.
How long is a lunar cycle?
The average time from one new moon to the next is about 29.53 days. Single cycles can be several hours shorter or longer, roughly 29.3 to 29.8 days. That's because the orbits of the Moon and Earth aren't perfect circles.
How this calculator is checked
Method: Jean Meeus, Astronomical Algorithms (2nd ed.), chapter 49 for true new and full moons (planetary terms omitted) and equation 48.4 for the phase angle and illuminated fraction. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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