Moon Phase Calculator
Find the Moon's phase, illumination and age for any date, plus the dates of the next new and full moons.
How to use this calculator
- 1Enter any date — past or future.
- 2Read the phase and illumination percentage for that date.
- 3Use the next new and full moon dates for rough planning; for anything precise, check an ephemeris.
How the calculation works
fraction = ((date − reference new moon) ÷ 29.530588853) mod 1 illumination = (1 − cos(2π × fraction)) ÷ 2- reference new moon
- 6 January 2000, 18:14 UTC — a known new moon used as the epoch
- 29.530588853
- Mean synodic month in days: the average time from one new moon to the next
- fraction
- Position through the cycle, 0 at new moon and 0.5 at full moon
Illumination is not linear in the Moon's age. The terminator — the day/night boundary — is a half-ellipse projected onto a sphere, so the lit fraction follows a cosine curve. This is why the Moon appears to brighten slowly near new, quickly around the quarters, and slowly again near full.
The synodic month (new moon to new moon, 29.53 days) is longer than the sidereal month (one orbit relative to the stars, 27.32 days). The difference exists because the Earth moves along its own orbit while the Moon circles it, so the Moon must travel a little further to return to the same alignment with the Sun.
This uses the mean synodic month. Real intervals vary by up to about half a day either side because the Moon's orbit is elliptical and perturbed by the Sun's gravity.
Worked example
The reference new moon itself
- 1.The reference epoch is a known new moon at 18:14 UTC on 6 January 2000.
- 2.Calculating at 00:00 UTC on that date puts us 18.233 hours *before* the exact new moon, which is 0.7597 days.
- 3.As a fraction of the 29.530589-day cycle that is 0.02573 short of a complete cycle, so the fraction wraps to 0.97427.
- 4.Illumination = (1 − cos(2π × 0.97427)) ÷ 2 = 0.0065, or about 0.65% — a very thin waning crescent, hours before it becomes new.
Result: Waning crescent, 0.65% illuminated, 28.77 days old
Why the Moon has phases at all
Half the Moon is always lit by the Sun. What changes is how much of that lit half faces Earth, and that depends entirely on where the Moon sits in its orbit relative to the Sun and us. At new moon the Moon lies roughly between Earth and the Sun, so the lit hemisphere faces away and we see nothing. At full moon the Earth sits between the two, so the whole lit hemisphere faces us.
The common belief that phases are caused by Earth's shadow falling on the Moon is wrong — that is a lunar eclipse, which is a rare event lasting hours, not the monthly cycle. Phases are simply a matter of viewing geometry.
Two different "months"
The Moon completes one orbit relative to the background stars in 27.32 days — the sidereal month. But the phase cycle takes 29.53 days, the synodic month. The gap exists because Earth does not stand still: in the time the Moon completes an orbit, Earth has moved about 27 degrees along its own path around the Sun, so the Moon must travel roughly two extra days' worth of orbit to line up with the Sun again.
The synodic month is the one that matters for phases, calendars and everyday observation, which is why it is the figure this calculator uses. It is also the origin of the word "month" itself, and the basis of every lunar and lunisolar calendar.
Why the cycle is not exactly 29.53 days each time
The 29.530589-day figure is a long-run mean, not a constant. The Moon's orbit is an ellipse, so it moves faster when closer to Earth and slower when further away, and the Sun's gravity perturbs the orbit further. Individual synodic months therefore range from roughly 29.27 to 29.83 days — a spread of more than half a day.
- Good enough for — knowing tonight's phase, planning around a full moon, understanding roughly when the next new moon falls, or teaching the cycle.
- Not good enough for — eclipse prediction, precise tide calculation, religious calendar determination, or astrophotography planning — all of which need a proper ephemeris that models the actual perturbed orbit.
Hemispheres, and which side is lit
A waxing crescent seen from London appears lit on the right; the identical Moon seen from Sydney at the same moment appears lit on the left. Nothing about the Moon has changed — southern-hemisphere observers are simply looking at it from an inverted orientation. This is why "the lit side points to where the Sun is" is a more reliable rule than memorising left or right, and why lunar diagrams drawn for one hemisphere confuse readers in the other.
The old mnemonic that a crescent shaped like a "D" is growing and one shaped like a "C" is shrinking holds only in the northern hemisphere. South of the equator it is exactly backwards.
What this assumes, and where it stops
Assumptions
- Phases are computed at 00:00 UTC on the date entered. A phase near a boundary can therefore appear to shift by a day depending on your time zone.
- The mean synodic month is used rather than a full orbital model.
Limitations
- Accurate to roughly half a day for the timing of new and full moons, because real lunar cycles vary between about 29.27 and 29.83 days. Use a published ephemeris where exact timing matters.
- Does not predict eclipses, which require the Moon to be near a node of its orbit as well as at the right phase.
- Illumination is the geometric lit fraction of the disc, not apparent brightness — a full moon is far more than twice as bright as a half moon, because of how the lunar surface scatters light back toward the Sun.
Common questions
Why is the Moon sometimes visible during the day?
Because its position in the sky depends on its phase, not on daylight. A first-quarter Moon rises around noon and sets around midnight, so it spends the entire afternoon above the horizon. Only the full moon is reliably a night-time object, since being opposite the Sun means it rises as the Sun sets.
How accurate are the next new and full moon dates?
Within roughly half a day. The calculation uses the mean synodic month, while actual cycles vary from about 29.27 to 29.83 days because the Moon's orbit is elliptical and perturbed by the Sun. For planning that is plenty; for eclipses or precise observation, use a proper ephemeris.
What is a blue moon?
Most commonly, the second full moon in a single calendar month. Because the 29.53-day cycle is slightly shorter than most months, this happens roughly every two and a half years. An older definition — the third full moon in a season containing four — is the original usage, and the two do not coincide.
Formula and content last reviewed on .
Results are estimates for information only, not professional advice.
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