Lunar Calendar Calculator
Show the Moon’s phase, illuminated percentage and age for any date, with the dates of the next full and new moons.
Updated Formula covered by automated tests
Pick any date and the calculator shows the Moon’s phase, the percentage of its disk that is lit, its approximate age in days since the last new moon, and the dates of the next full and new moons. Step through days with the arrows to watch a crescent fatten into a full moon over two weeks.
Night-sky photographers use the phase to choose dark nights for the Milky Way or a bright one for moonlit landscapes. Anglers and hunters plan around it, gardeners who follow lunar planting traditions check it, and many religious and cultural calendars (Ramadan, Passover, Easter, the Lunar New Year, Diwali) are tied to new or full moons.
The formula
- JD
- Julian Date, a continuous count of days used by astronomers (JD 2451545.0 is noon UTC on January 1, 2000)
- T
- Julian centuries since that epoch
- D, M, M′
- Mean elongation of the Moon from the Sun, mean anomaly of the Sun, and mean anomaly of the Moon, in degrees (reduced to 0 to 360)
- e
- Moon-Sun elongation: 0° is new moon, 90° first quarter, 180° full moon, 270° last quarter
- 29.530589
- Average length of a lunar cycle (synodic month) in days
The phase depends on the angle between the Moon and the Sun as seen from Earth. If both moved in perfect circles that angle would grow at a steady 12.19° per day, but the Moon’s elliptical orbit and the Sun’s pull make it speed up and slow down, so a real new moon can come up to about 14 hours earlier or later than the average cycle predicts. The sine terms are the largest of those corrections, taken from Jean Meeus’s Astronomical Algorithms, and bring the error down to roughly an hour or two.
The four principal phases are instants, not days. The calculator labels a date "Full Moon" (or new, first quarter, last quarter) only if that instant falls within that date in UTC; other dates get the in-between names such as waxing gibbous, judged at noon UTC. An earlier version of this page left out the Gregorian calendar correction when computing the Julian Date, which shifted every result by 13 days and could show a waning crescent on the night of a full moon.
Worked example
A photographer wants to confirm that March 3, 2026, the date of a total lunar eclipse, is a full moon, using the position at 12:00 UTC.
- 1 Julian Date of 2026-03-03 12:00 UTC is 2461103.0, so T = (2461103.0 − 2451545.0) ÷ 36525 = 9558 ÷ 36525 = 0.261684.
- 2 Mean angles, reduced to 0 to 360°: D = 177.03°, M = 57.90°, M′ = 90.17°.
- 3 Corrections: +6.289 × sin 90.17° = +6.289; −2.100 × sin 57.90° = −1.779; +1.274 × sin 263.89° = −1.267; the last three terms add −0.063.
- 4 Elongation: 177.03 + 6.289 − 1.779 − 1.267 − 0.063 = 180.21°, essentially opposite the Sun.
- 5 Illumination: (1 − cos 180.21°) ÷ 2 = 0.99999, shown as 100%; age ≈ 180.21 ÷ 360 × 29.53 = 14.8 days.
Result: The Moon is full on March 3, 2026 (the exact instant is about 11:38 UTC), 100% illuminated and about 14.8 days into its cycle.
Before you rely on the result
- Accuracy is about one to two hours in the timing of a phase, enough for the correct date in nearly all cases, but use an almanac such as the US Naval Observatory tables for eclipse timing or scientific work.
- The calculator does not give moonrise or moonset times, which depend on your latitude and longitude.
Frequently asked questions
Why is the full moon on a different date in my calendar app?
The calculator labels phases by the UTC date. A full moon at 02:00 UTC on the 15th happens at 10:00 p.m. on the 14th in New York, so a local calendar will list the 14th. Near midnight UTC the label can also be off by a day because of the small error in the formula.
Is the illumination percentage the same everywhere on Earth?
Essentially yes. Everyone sees the same fraction lit at the same moment. What changes with location is orientation: in the Southern Hemisphere the lit side of a waxing moon appears on the left rather than the right.
What is a blue moon?
In popular use it is the second full moon in one calendar month. In 2026 there are full moons on May 1 and May 31, so May 31 is a blue moon by that definition. An older definition calls it the third of four full moons in an astronomical season.
Why does a lunar cycle not line up with calendar months?
The average new-moon-to-new-moon period is about 29.53 days, shorter than every month except February. Twelve lunar cycles take about 354 days, 11 fewer than a solar year, which is why purely lunar calendars such as the Islamic calendar drift through the seasons.
Sources
- NASA Science: Moon Phases (science.nasa.gov)
- U.S. Naval Observatory: Phases of the Moon (aa.usno.navy.mil)