The moon, drawn by mathematics
The moon visual above is not an image — it is rendered live from the Moon's real position, computed from orbital mechanics the moment this page loads. The illuminated fraction, the shape of the terminator, the phase name: all derived from the same almanac equations observatories use. Select any date in the next week and watch the phase evolve.
Moonrise and moonset for New York
Because the Moon's orbit is tilted about 5 degrees from Earth's orbit, its rise and set times shift by roughly 50 minutes each day — the reason a full moon rises right at sunset while a crescent may not rise until after midnight. Times above are for New York in standard time.
Beyond the moon: the Sun and meteors
This site also computes sunrise and sunset and golden hour for photographers, and the annual meteor shower calendar for skywatchers.
A phase is an angle, not a shape
The moon is a sphere lit from one side. What changes night to night is not the moon but your viewing geometry: the angle between the sun, the moon and you. "Phase" is a shorthand for that angle, and every answer on this page comes from two numbers — the age of the moon in days and the fraction of the disc that is illuminated.
age = days since the last new moon · illuminated fraction = (1 − cos(2π · age / 29.530588)) / 2
Two useful checks fall straight out of that expression. At age 0 and age 29.53 the fraction is 0 — new moon. At age 14.77 the fraction is 1.000, fully illuminated, which is full moon. And it is symmetric: a moon 4 days old and a moon 25.5 days old look identical in shape but mirror-imaged.
| Phase | Typical age (days) | Illumination | Where it sits in the sky |
|---|---|---|---|
| New moon | 0 | 0% | Rises and sets with the sun |
| Waxing crescent | 3.7 | about 12% | Low in the west after sunset |
| First quarter | 7.4 | 50% | Overhead at sunset, sets near midnight |
| Waxing gibbous | 11.1 | about 88% | High in the south-east in the evening |
| Full moon | 14.77 | 100% | Rises as the sun sets |
| Waning gibbous | 18.5 | about 88% | Rises late, still up in the morning |
| Last quarter | 22.1 | 50% | Overhead at sunrise |
| Waning crescent | 25.8 | about 12% | Visible in the east before dawn |
The eight phases divide the 29.53-day cycle into eight equal spans of 3.69 days. That is why a phase name is only ever an approximation of a date — "first quarter" labels a window of about three and a half days, not an instant.
Why moonrise moves about 50 minutes later every day
The moon takes 27.32 days to orbit the Earth once against the fixed stars, but the Earth keeps turning inside that orbit. By the time the moon returns to the same celestial position, the Earth has rotated about 13.2° further — and 13.2° of rotation takes about 53 minutes. The moon therefore rises later relative to the sun almost every day.
average daily lag = 1440 min / 29.53 days ≈ 49 minutes
The lag is an average, not a rule. It swings between roughly 20 and 80 minutes across the month and across the year, because the moon's orbit is inclined 5.1° to the ecliptic and is elliptical. Around the equinoxes at mid-latitudes the lag can flatten almost to nothing, which is why some months produce a run of moonrises within a few minutes of each other.
| If the moon rose at | Tomorrow it rises near | Phase you are likely to see |
|---|---|---|
| Sunset (with the sun) | About 50 min after sunset | Full moon |
| Midnight | About 50 min later | Last quarter approaching |
| Sunrise (with the sun) | About 50 min after sunrise | New moon |
| Noon | About 50 min later | First quarter approaching |
That table also gives you the fastest way to estimate the phase without any tool: compare the moonrise time with sunrise and sunset. A moon that rises at sunset is full. A moon that rises at noon is near first quarter. A moon that rises at sunrise is new.
Synodic and sidereal months are not the same thing
Two month lengths appear in moon calculations and mixing them up produces wrong phases.
| Month | Length | What it measures | Used for |
|---|---|---|---|
| Synodic month | 29.530588 days | New moon to new moon | Phases, ages, illumination |
| Sidereal month | 27.321662 days | Orbit measured against the fixed stars | Lunar position in the sky |
| Anomalistic month | 27.554550 days | Perigee to perigee | Supermoons, distance, apparent size |
| Draconic month | 27.212221 days | Node to node | Eclipse prediction |
The 2.21-day gap between synodic and sidereal is not an error — it is the Earth's own motion. While the moon completes one orbit, the Earth has moved about 1/13 of its way around the sun, so the moon needs roughly two extra days to line up with the sun again and return to new.
Three worked examples
Example 1 — what does the moon look like 10 days after a new moon? Illuminated fraction = (1 − cos(2π × 10 / 29.530588)) / 2 = (1 − cos(121.9°)) / 2 = (1 + 0.5296) / 2 = 76.5%. That is a waxing gibbous moon, between first quarter (7.4 days) and full (14.77 days).
Example 2 — how many days until the next first quarter? First quarter sits at one quarter of the cycle: 29.530588 / 4 = 7.38 days after new. Full moon is at half the cycle, 14.77 days, and last quarter at 22.15 days. Each is a fixed fraction, so once you know the age you know the countdown.
Example 3 — the moon rose at 21:40 tonight. Roughly when did it rise yesterday? Subtract the average lag: 21:40 − 49 min = 20:51. Remember this is an approximation with a real spread of 20–80 minutes, so treat it as a planning hint rather than a schedule.
The moon is not the only thing that moves in the sky
Phases are the most-searched lunar fact, but the same solar geometry drives the sun's own page and the twilight bands that decide when the sky is dark enough to see anything at all.
- Sunrise and sunset follow the hour angle equation and depend on your latitude and the date, not on the moon.
- Twilight depth sets how far into the skylight the moon has to compete. A first-quarter moon in astronomical twilight is visible; the same moon in full daylight is not.
- Meteor showers are read against the moon: a full moon removes most of the meteors you would otherwise see, which is why shower-planning guides always quote the lunar phase for the peak night.
Getting closer to tonight’s Moon
The phase decides what is actually visible along the terminator tonight. These are the items that turn the live visual on this page into something you can see for yourself.
- 10x50 binoculars — The quickest way to confirm the phase you are reading. Along the terminator the relief is obvious, even hand-held.
- Refractor telescope — For the craters and mare the binocular only hints at. A modest refractor is enough for a first close look at the Moon.
- Moon filter — Past first quarter the Moon is bright in any scope; a moon filter makes the surface comfortable to study.
- Planisphere — Shows where the Moon sits tonight among the stars, which the phase on its own does not tell you.
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Sources and standards
Where these figures come from
Every formula on this page is implemented from the published reference material below. Where a value depends on a regional code, the calculator lets you override it rather than assuming one jurisdiction.
- NASA Science — Moon — lunar phases, libration and the orbital mechanics behind the phase fraction.
- NASA Science — Moon phases — the synodic month and the eight named phases used here.
- NOAA Global Monitoring Laboratory — solar and local time calculations used for rise and set.
Figures, formulas and reference tables last verified: 24 September 2026