Moon phase calculator
In the northern hemisphere a waxing moon is lit on the right and a waning one on the left. The mnemonic is that it fills and empties like the letters D, O, C. South of the equator everything is inverted, because you are effectively looking at the same moon upside down, which is why the mnemonic confuses so many people who learned it in one hemisphere and moved to the other.
Uses the mean synodic month from a fixed reference new moon, computed at 00:00 UTC on the date you choose. It is right to within a few hours; the exact minute of a new or full moon needs an ephemeris.
The moon returns to the same phase every 29.530589 days on average, the synodic month. Illumination follows the cosine of the phase angle, zero at new moon and 100% at full. This counts forward from the new moon of 6 January 2000 at 18:14 UTC.
How to find the moon phase
The whole calculation is one subtraction and one remainder. It counts the days from a reference new moon, 6 January 2000 at 18:14 UTC, divides by the mean synodic month of 29.530589 days, and reads the phase from where the remainder falls in the cycle. The illuminated fraction then comes from the cosine of that position, which is why the percentage climbs slowly near new and full and races through the quarters.
What the mean month costs you
Real lunations do not keep to the average. Individual lunations run from roughly 29.3 to 29.8 days, because the orbit is an ellipse and the Sun tugs at it differently depending on where the Earth is in its own year. A model built on the mean therefore drifts back and forth against the real sky by up to roughly half a day, never accumulating into a permanent error but never quite agreeing either.
On top of that, the phase here is evaluated at 00:00 UTC on the date you pick, so a moon that turns full late in your evening is already being reported for the following day if you are far enough east. For "is it waxing or waning" and "roughly how lit is it tonight", neither limitation matters. For the exact minute of an eclipse or a supermoon, it is the wrong tool, and an ephemeris is the right one.
One row needs a footnote. Lunations here are counted from that same January 2000 reference and the first of them reads 0, so it is an internal index rather than one of the numbering schemes an almanac uses.
Two different months, and why the phase follows the longer one
A circuit against the background stars takes 27.32 days, the sidereal month. Phases take 29.53. The extra two days exist because the Earth has moved about 27 degrees along its own orbit in the meantime, so the moon has to travel a little further to line up with the Sun again. Phases track the Sun and therefore the synodic month; the moon among the constellations tracks the sidereal one, and any calendar that tries to serve both ends up with the leap months that lunisolar calendars are built around.
What people use it for
- Checking the phase before a photography or camping plan
- Finding the next full moon
- Planning around dark skies for stargazing
- Looking up the phase on a historical date
- Settling which way round the crescent should face
Questions
29.530589 days on average, the synodic month. Individual cycles run anywhere from roughly 29.3 to 29.8 days.
The moon comes back to the same place among the stars in 27.32 days, but Earth has moved along its own orbit by then, so lining up with the Sun again takes about two days longer.
Growing towards full. Waning is shrinking back towards new. The panel names which one you are in.
Within a few hours of the real thing, and up to about half a day off at the extremes, since it uses the average cycle length rather than tracking the actual elliptical orbit.
In the northern hemisphere the right-hand limb when waxing and the left when waning. South of the equator it is reversed, because you are looking at the same moon the other way up.
Because it follows a cosine. The lit fraction is flattest at new and full and changes fastest through the quarters, so a moon looks full to the eye for two or three nights running.