Moon Phase Calculator

Background.

This calculator gives the Moon's phase, illumination and age for any UTC instant, and it does so from the true instants of the new and full moons rather than from a 29.5-day average. That difference is the reason the page exists.

Almost every moon phase calculator online works by dividing the time since some reference new moon by 29.53 days. The size of the error that introduces is documented by the same source that supplies the 29.53: NASA Goddard's own page on the Moon's orbit gives the mean synodic month as 29.53059 days and its actual range over five thousand years as 29.26574 to 29.84089 days, a spread of thirteen hours and forty-eight minutes. Lunations are simply not equal, because the Moon's orbit is eccentric and perturbed. Across 2026 alone the lunations computed here run from 29.2842 to 29.7560 days — over eleven hours of spread inside a single year. Dividing by the average therefore misplaces the new moon by up to about fourteen hours, which is enough to name the wrong phase near a quarter and enough to be a day out on when to look for a thin crescent.

What this page does instead is compute the true instants of the new moons on either side of your date, and of the next full moon, from a periodic series, and then report the length of the lunation you are actually in as an output. If you have ever wondered why a printed almanac and a phone widget disagree by half a day, that output is the answer.

The illumination is computed separately, from the Sun–Moon–Earth phase angle, and the phase name is derived from that illumination together with an exact waxing or waning flag. That pairing is deliberate. An earlier draft of this page named the phase from how far through the lunation the instant fell, and produced a visible contradiction: for 22 July 2026 it printed 'First Quarter' next to an illumination of 55.6 percent. Both numbers were right — the Moon does not move uniformly through a lunation, so a quarter of the way through and half lit are different instants — but the label was wrong. Naming from the illumination makes the label and the number agree by construction, and the case is now pinned by a regression test.

Accuracy is measured, not claimed. The series carried here is truncated at fifteen seconds of correction, and rather than assert that this is harmless, the test suite reproduces all twenty-five tabulated new and full moons of 2026 from Fred Espenak's Six Millennium Catalog of Phases of the Moon, which is computed from a full lunar theory. The worst disagreement across all twenty-five is one and a half minutes; most are under a minute. The illumination series is checked the same way: at every tabulated new moon the computed illumination is under 0.001 percent, and at every full moon over 99.999 percent. Since sixty-odd series coefficients cannot be individually verified by a reader, twenty-five independently published instants reproduced to under two minutes is the stronger claim and it is the one this page makes.

Conventions are declared. The instant you enter is UTC. The lunar series are computed in Dynamical Time, so the calculator converts using TT minus UTC equals 32.184 seconds plus the leap-second count, and that count is an editable input defaulting to 37 seconds — the value in force since 2017 and confirmed unchanged for the end of 2026 by IERS Bulletin C. Everything is geocentric: topocentric parallax moves the illuminated fraction by well under a tenth of a percent and the phase instants not at all. The phase angle is 180 degrees at new moon and zero at full moon, running opposite to the elongation, which is a classic sign trap. And the phase names themselves use display thresholds — within two percent of full illumination for new and full, within two percent of half illumination for the quarters, which works out at roughly a day and a third either side of new and full and about nine hours either side of a quarter. Those windows are a labelling convention rather than physics, and the page says so where the answer is rather than in a footnote.

What is moon phase calculator?

The Moon's phase is the fraction of its Earth-facing hemisphere that is sunlit, and it cycles through new, first quarter, full and last quarter over a synodic month. The synodic month is the interval from one new moon to the next: it averages 29.53059 days but is not constant, ranging from about 29.27 to 29.84 days because the Moon's orbit is elliptical and continually perturbed, chiefly by the Sun.

The Moon's 'age' is the time elapsed since the last new moon, usually quoted in days. The illuminated fraction is a different quantity that happens to correlate with it: it is set by the Sun–Moon–Earth angle, and because the Moon speeds up near perigee and slows near apogee, a given age does not always correspond to the same illumination.

Waxing means the illuminated fraction is increasing, from new moon to full moon, with the lit limb on the western side as seen from the northern hemisphere. Waning means it is decreasing, from full back to new. The eight conventional names divide that cycle at the new, quarter and full points.

How to use this calculator.

1. 01Enter the date and the time of day in UTC. Phases are geocentric instants, so the answer is the same everywhere on Earth — only your local clock reading differs.
2. 02Leave the leap-second offset at 37 for anything since 2017; set it to the value in force at the time for older dates.
3. 03Read the phase name and the illumination together — they are derived from the same quantity, so they always agree.
4. 04Read the moon age to know how far into the lunation you are.
5. 05Check this lunation's length. If it is not 29.53, that is not an error; it is why a mean-lunation calculator would have been hours out.
6. 06Use the days-to-next-full and days-to-next-new outputs for planning; both come from the same periodic series as the age.

The formula.

The calculation has two independent halves. The first finds the instants of the new and full moons using the periodic series of Meeus's chapter 49: a mean term linear in the lunation index k, plus corrections driven by the Sun's mean anomaly, the Moon's mean anomaly, the Moon's argument of latitude and the node. The largest correction, −0.40720 sin M′ for a new moon, is worth almost ten hours on its own — that single term is most of the difference between this page and a mean-lunation calculator. Terms are carried down to 0.00017 days, fifteen seconds, plus the largest of the additional planetary arguments.

The second half computes the Sun–Moon–Earth phase angle from the mean elements of chapter 47 using the low-precision expression of chapter 48, and converts it to an illuminated fraction with k = (1 + cos i)/2. The phase name then follows from that fraction plus a waxing flag, where waxing simply means the instant precedes this lunation's computed full moon.

Work through the example. At 00:00 UTC on 22 July 2026 the preceding true new moon was 14 July at 09:44 UT, so the Moon's age is 7.5944430644 days. The next full moon is 7.6082555924 days away and the next new moon 21.7339179698 days away; adding the age to the wait gives 29.3283610342 days, which is this lunation's length and is fifteen minutes shy of the 29.53-day average. The phase angle is 83.528054988 degrees, so the illuminated fraction is (1 + cos 83.528°)/2 = 55.6358347928 percent, and since the instant precedes the full moon the phase is Waxing Gibbous.

HOW THE COEFFICIENTS ARE VERIFIED. Rather than ask a reader to trust sixty series coefficients, the test suite reproduces every new and full moon of 2026 tabulated in Espenak's Six Millennium Catalog — twenty-five independently computed instants from a full lunar theory. The worst disagreement is 1.525 minutes and most are under a minute; the test threshold is two minutes for every one. The illumination series is checked the same way, requiring under 0.5 percent illumination at each tabulated new moon (worst case observed 0.0004 percent) and over 99.5 percent at each full moon (worst case 99.9995 percent). A single mistyped coefficient breaks these immediately. Note honestly that Espenak's catalogue derives from a lunar theory in the same family, so this validates the truncation and the transcription rather than independently confirming the theory itself.

ROUNDING STAGE. Nothing is rounded part-way through. Working precision is 28 significant digits rather than the 40 used elsewhere on this site, because this module evaluates several dozen high-precision sine terms per call and 28 digits still leaves fifteen orders of headroom on a quantity that needs a resolution of 10⁻⁶ days. The single rounding is at the return boundary.

APPROXIMATION REGIME AND WHERE IT BREAKS. The series are fitted for roughly 1000 to 3000 CE. The Dynamical-Time conversion uses the leap-second count you enter, so for dates before 1972 the returned instants drift by the difference between the true value of ΔT and what you entered — tens of seconds a century back to 1900, minutes by 1600. The phase name and the illumination are unaffected at that level; only the quoted instants move.

INVALID DOMAIN. Gregorian dates only, with the correct leap rule, so 29 February 2026 is refused and 29 February 2028 accepted. Hours must be 0 to 23, minutes 0 to 59, and the leap-second offset 0 to 60 seconds.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Espenak, F. (NASA/GSFC), 'Eclipses and the Moon's Orbit' (last revised 2012 January 12). Verified by retrieval 2026-07-29 to state: mean synodic month 29.53059 days (29d 12h 44m 03s); the duration of the lunation varies over a range of 13h 48m 13s across 5000 years, with the shortest 29.26574 days and the longest 29.84089 days. This is the source of the variable-lunation argument on this page. Open access.
2. [2]Espenak, F., 'Six Millennium Catalog of Phases of the Moon' / 'Moon Phases: 2001 to 2100' (AstroPixels). Verified by retrieval 2026-07-29 for all twelve new moons and thirteen full moons of 2026 in Universal Time. This table is the empirical validation set: the module reproduces all twenty-five instants to within 1.525 minutes, and the test suite asserts under two minutes for every one. Computed from a full lunar theory in the same family as the series implemented here, so it validates the truncation and the transcription rather than independently confirming the theory. Open access.
3. [3]Meeus, J. (1998). Astronomical Algorithms, 2nd edition, Willmann-Bell: chapter 47 (position of the Moon, mean elements), chapter 48 (illuminated fraction of the Moon's disk, low-precision phase angle) and chapter 49 (phases of the Moon). Source of every series coefficient implemented. Print / bibliographic reference.
4. [4]IERS Bulletin C, International Earth Rotation and Reference Systems Service. Verified by retrieval 2026-07-29: the difference between UTC and TAI is −37 seconds 'from 2017 January 1, 0h UTC, until further notice', and no leap second will be introduced at the end of December 2026. Source of the default leap-second input used to convert Dynamical Time to UTC. Open access.
5. [5]Chapront-Touzé, M. & Chapront, J. (1983), 'The lunar ephemeris ELP 2000', Astronomy & Astrophysics 124:50–62, and the later ELP2000-85 revision. The lunar theory from which the condensed series used here derive. Peer-reviewed; bibliographic reference.