Moon Phase Calculator
The Moon cycles through its phases in a synodic month of about 29.53 days, from new moon to new moon. Counting the days since a known new moon and dividing by that cycle length tells you exactly where in the cycle any date falls, and from there the lunar age, the phase name, and the percent of the disc that is lit all follow. Enter a date and this calculator returns the Moon's age in days, its illumination, the current phase, and the days until the next new moon.
Moon phase formula
Synodic month = 29.530588853 days
Reference new moon = 2000-01-06 18:14 UTC
Days since reference = (date - reference) in days
Phase fraction = (days since / synodic month) mod 1
Lunar age = phase fraction * synodic month
Illumination = (1 - cos(2 pi * phase fraction)) / 2
The phase fraction runs from 0 (new) through 0.5 (full) back to 1 (new). The illumination follows a cosine of the phase angle.
Lunar context
- The synodic month (new moon to new moon) averages about 29.53 days.
- Illumination is 0 percent at new moon, 50 percent at the quarters, and 100 percent at full moon.
- Waxing phases grow toward full; waning phases shrink toward new.
- This mean-cycle method is accurate to within a few hours, ideal for everyday planning.
- For precise eclipse or moonrise times, consult the U.S. Naval Observatory almanac.
Moon phase calculator: frequently asked questions
How does the moon phase calculator work?
It measures how many days have passed since a known new moon, then divides by the length of one lunar cycle (the synodic month of about 29.53 days) to find where in the cycle the date falls. The fractional position gives the phase, the age in days, and the percent of the disc that is lit.
What is the synodic month?
The synodic month is the average time from one new moon to the next, about 29.530589 days. It is longer than the Moon's orbit around Earth because the Earth also moves around the Sun during that time, so the Moon must travel a little further to line up again. This calculator uses the synodic month as its cycle length.
How accurate is this estimate?
This uses a mean synodic month from a fixed reference new moon, which is accurate to within a few hours for the phase and is excellent for everyday use. The true Moon speeds up and slows down slightly in its elliptical orbit, so for precise eclipse or rise-time work, consult an astronomical almanac.
What do the phase names mean?
New moon is fully dark, first quarter is half-lit and waxing, full moon is fully lit, and last quarter is half-lit and waning. The crescent and gibbous phases fall between these. Waxing means the lit portion is growing toward full; waning means it is shrinking toward new.
How is percent illumination calculated?
The fraction of the Moon's visible disc that is lit follows a smooth cosine relationship with its phase: illumination equals one minus the cosine of the phase angle, all divided by two. It is 0 percent at new moon, 50 percent at the quarters, and 100 percent at full moon.
Official sources
- U.S. Naval Observatory: Phases of the Moon.
- NASA: Moon phases and the lunar cycle.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.