Moon Phase by Date Calculator
The moon repeats its cycle of phases roughly every 29.53 days, the mean synodic month, and you can estimate the phase on any date by counting forward from a known new moon. This calculator does exactly that: it measures the days from a reference new moon to your chosen date, finds the moon's age within the current cycle, names the nearest of the eight phases, and approximates the illuminated fraction of the disc. Because it uses the average cycle rather than the moon's varying true motion, treat the result as a close estimate; the U.S. Naval Observatory publishes the precise phase times.
Moon phase formula
days since = your date - reference new moon (2000-01-06 18:14 UTC)
cycle position = (days since / 29.53058867) mod 1
moon age = cycle position * 29.53058867
illuminated fraction = (1 - cos(2 * pi * cycle position)) / 2
The synodic month of 29.53058867 days is the mean new-moon-to-new-moon interval. The cycle position runs from 0 at new moon to 0.5 at full moon and back to 1. The illuminated fraction uses a cosine approximation of the phase angle.
Moon phase notes
- The eight phases run new, waxing crescent, first quarter, waxing gibbous, full, waning gibbous, last quarter, waning crescent.
- Waxing means growing; waning means shrinking.
- The estimate can be up to about a day off the true phase due to mean-cycle assumptions.
- The U.S. Naval Observatory publishes exact phase dates and times.
- Illuminated fraction is 0 percent at new moon and 100 percent at full moon.
Moon phase: frequently asked questions
How is the moon phase estimated?
The calculator counts the days from a known reference new moon to your date, then divides by the mean synodic month of 29.53 days. The fractional part gives the moon's age within its cycle, which maps to phases from new moon at 0 to full moon at about half the cycle and back.
What is the synodic month?
The synodic month is the average time from one new moon to the next, about 29.53 days. It is longer than the moon's orbital period because the Earth also moves around the Sun, so the moon must travel a little further each cycle to return to the same phase as seen from Earth.
How accurate is this estimate?
It uses the mean cycle, so it can differ from the true phase by up to roughly a day because the moon's actual motion varies. For exact phase times and dates, consult the U.S. Naval Observatory, which publishes precise lunar phase data. This tool is intended as a quick approximation.
What is the illuminated fraction?
The illuminated fraction is how much of the moon's disc appears lit, from 0 at new moon to 1 at full moon. The calculator approximates it from the phase angle using a simple cosine relationship, which is close to the true value for most purposes.
What are the eight named moon phases?
The cycle runs new moon, waxing crescent, first quarter, waxing gibbous, full moon, waning gibbous, last quarter, and waning crescent, then back to new. Waxing means the lit portion is growing; waning means it is shrinking. The calculator names the phase closest to your date.
Official sources
- U.S. Naval Observatory: Moon Phases.
- U.S. Naval Observatory: Astronomical Applications.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.