Moon Phase Calculator
Enter any date to estimate the moon phase, the percentage of the disk that is lit, the lunar age in days, and when the next new and full moons fall.
Waxing Gibbous
91%
litIlluminated
91%
Dark
9%
- 1
Julian Day (JD)
2,461,218.5Continuous day count from the Julian epoch used in astronomy. - 2
Days since reference new moon
2,461,218.5 − 2451550.1 = 9,668.4 - 3
Lunar age (days into cycle)
11.9(daysSinceNew mod 29.531 + 29.531) mod 29.531, keeping the value positive. - 4
Phase fraction (0 = new, 0.5 = full)
11.9 ÷ 29.531 = 0.4029 - 5
Illumination fraction
(1 − cos(2π × 0.4029)) ÷ 2 = 0.9097 - 6
Illumination %
0.9097 × 100 = 91
How does this calculator work?
Convert your date to a Julian Day, subtract a reference new moon, and take the remainder over the 29.53-day synodic month. That gives the lunar age and phase fraction; illumination is (1 − cos(2π · fraction)) / 2. The result shows the phase name, lit percentage, age in days, and the next new and full moons.
Formula
How this is calculated
The calculator first converts your calendar date (YYYY-MM-DD) into a Julian Day number (JD), a continuous day count used in astronomy. It then measures how many days have passed since a known reference new moon at JD 2451550.1 (6 January 2000).
Dividing that elapsed time by the mean synodic month of 29.53059 days and taking the remainder gives the phase fraction, from 0 (new moon) through 0.5 (full moon) back toward 1 (next new moon). The lit fraction of the disk is computed as (1 − cos(2π · fraction)) / 2, which peaks at 100% at full moon and drops to 0% at new moon. The phase name comes from rounding the fraction into one of eight octants: New, Waxing Crescent, First Quarter, Waxing Gibbous, Full, Waning Gibbous, Last Quarter and Waning Crescent.
This is a mean (average) model: it ignores the Moon’s elliptical orbit and observer location, so dates of new and full moons can differ from precise ephemerides by up to about a day, and illumination by a few percent. All dates are treated as midnight Universal Time.
Frequently asked questions
It uses the mean synodic month and a single reference new moon, so the phase and illumination are approximate. Predicted new and full moon dates are typically within about a day of precise astronomical tables.
Lunar age is the number of days elapsed since the most recent new moon. It ranges from 0 to about 29.5 days, reaching roughly 14.8 days at full moon.
This model assumes a constant 29.53059-day cycle and midnight Universal Time. Real lunar motion varies because of the Moon’s elliptical orbit, and your local time zone can shift the apparent date.
Also known as
TG we-Calculate Editorial Team. (2026). Moon Phase Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/moon-phase
TG we-Calculate Editorial Team. "Moon Phase Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/moon-phase.
TG we-Calculate Editorial Team, "Moon Phase Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/moon-phase
@misc{wecalculate_moon_phase, title = {Moon Phase Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/moon-phase}}, year = {2026}, note = {TG we-Calculate} }
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