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Moon phase calculator

The moon cycles through its phases every 29.5 days. Enter a date to see whether the moon is new, full, crescent, or gibbous — plus how much of its face is illuminated and when the.

About this calculator

Phase names

Phase fractionName
0 – 0.0625New Moon
0.0625 – 0.1875Waxing Crescent
0.1875 – 0.3125First Quarter
0.3125 – 0.4375Waxing Gibbous
0.4375 – 0.5625Full Moon
0.5625 – 0.6875Waning Gibbous
0.6875 – 0.8125Last Quarter
0.8125 – 1Waning Crescent

Formula

daysSinceNewMoon = JD(date) − 2451550.259
phase = (daysSinceNewMoon mod 29.53058867) / 29.53058867
illumination = 0.5 × (1 − cos(2π × phase))

The reference JD 2451550.259 corresponds to the known new moon on January 6, 2000 at 18:14 UTC (source: US Naval Observatory).

Worked example

Date: January 20, 2000 (Full Moon)

Days since Jan 6 new moon ≈ 14.77 → phase ≈ 0.5 → Full Moon, illumination ≈ 100%.

Notes

  • All calculations use Julian Day arithmetic — the same system used in professional astronomy.
  • The next new/full moon dates are approximate (±1 day) due to the Moon’s variable orbital speed.
  • The phase shown is based on noon UTC for the chosen date.

Frequently asked

How is the moon phase calculated?
The calculator measures days elapsed since a known new moon (January 6, 2000 at 18:14 UTC) and divides by the synodic period of 29.53058867 days. The remainder, expressed as a fraction of the cycle, gives the current phase.
What is the synodic period?
The synodic period is the time between two successive new moons as seen from Earth — 29.53058867 days on average. It differs from the sidereal period (27.32 days) because Earth also moves around the Sun during that time.
How accurate is this calculator?
It is accurate to within a day for casual purposes. The synodic period varies slightly due to the Moon's elliptical orbit. For precise predictions, use an ephemeris.
What does illumination mean?
Illumination is the fraction of the Moon's visible face that is lit by the Sun. At new moon it is 0%; at full moon it is 100%. The formula is 0.5 × (1 − cos(2π × phase)).
How do I find the next full moon?
The "Next full moon" field shows the approximate date of the next full moon from your selected date. For the current date, leave the date picker on today.