Work out lunar calendar date instantly with clear inputs, formula shown and shareable results.
Moon age is the time since a known new moon epoch reduced modulo the synodic month of 29.530588853 days, and illumination follows as one minus the cosine of that phase angle, halved. The mean synodic month is accurate to within a few hours over decades, though the true new moon can differ by up to about half a day because the Moon's orbit is elliptical.
Moon age
age = (Julian day - 2451550.09766) mod 29.530588853
Illumination
illuminated fraction = (1 - cos(2 pi x age / synodic month)) / 2
age = (Julian day - 2451550.09766) mod 29.530588853. Moon age is the time since a known new moon epoch reduced modulo the synodic month of 29.530588853 days, and illumination follows as one minus the cosine of that phase angle, halved.
The mean synodic month is accurate to within a few hours over decades, though the true new moon can differ by up to about half a day because the Moon's orbit is elliptical.
Enter date, hour of day in utc. The defaults shown are a realistic worked example — swap in your own figures to get a result you can use.