Moon Phase Calculator
Find the Moon phase, illumination, and lunar age for any calendar date.
Pick a date to see the Moon phase.
The Moon cycles through eight phases — New, Waxing Crescent, First Quarter, Waxing Gibbous, Full, Waning Gibbous, Last Quarter, and Waning Crescent — over one synodic month of about 29.53 days. This tool finds the phase for any date from how far that date sits into the cycle, then reports the lit fraction.
How the phase is worked out
The Moon phase depends on the angle between the Sun, Earth, and Moon, which repeats every synodic month — the 29.530588853 days from one new moon to the next. If you know the date of a recent new moon, you can count forward in whole cycles and read off where the current date falls. The remainder, called the Moon age, runs from 0 days (new) up to about 29.53 days (back to new), passing full at roughly the halfway point.
To pin down a starting point, astronomers use a reference new moon at a known instant: 6 January 2000, 18:14 UTC, or Julian Date 2451550.1. Converting your chosen date to a Julian Date and subtracting this reference gives the days elapsed; the remainder over 29.53 days is the Moon age that sets the phase and illumination.
age is the Moon age in days (0 at new moon). The cosine term traces the lit fraction from 0 at new moon, to 1 at full moon, and back — expressed here as a value between 0 and 1.
Worked example
Take 25 January 2024. Its Julian Date at 00:00 UTC is 2460334.5, so the days since the reference new moon are 2460334.5 − 2451550.1 ≈ 8784.4. Dividing by 29.53 leaves a remainder of about 13.8 days — close to the halfway point — giving roughly 99% illumination, a Full Moon.
- 1 Convert the date to a Julian Date. Use the standard JDN algorithm at 00:00 UTC — for 25 Jan 2024 this is 2460334.5.
- 2 Subtract the reference new moon. 2460334.5 − 2451550.1 = 8784.4 days since 6 Jan 2000.
- 3 Take the remainder over the synodic month. 8784.4 mod 29.530588853 ≈ 13.8 days — the Moon age.
- 4 Read the phase and illumination. illumination = (1 − cos(2π × 13.8 ÷ 29.53)) ÷ 2 ≈ 0.99, and an age near 14.8 days means Full Moon.
The eight Moon phases
Approximate Moon age and illumination through one 29.53-day synodic month.
| Phase | Approx. age (days) | Illumination |
|---|---|---|
| New Moon | 0 | ≈ 0% |
| Waxing Crescent | ≈ 3.7 | ≈ 25% |
| First Quarter | ≈ 7.4 | ≈ 50% |
| Waxing Gibbous | ≈ 11.1 | ≈ 75% |
| Full Moon | ≈ 14.8 | ≈ 100% |
| Waning Gibbous | ≈ 18.5 | ≈ 75% |
| Last Quarter | ≈ 22.1 | ≈ 50% |
| Waning Crescent | ≈ 25.8 | ≈ 25% |
Why this is an approximation
This calculator assumes the Moon moves through its phases at a perfectly steady rate. In reality the Moon’s orbit is elliptical and tugged by the Sun, so the true time of new or full moon can drift by up to roughly a day from the average. Expect the phase name to be reliable and the illumination and Moon age to be accurate to about a day — good enough for planning, stargazing, or checking a date, but not a substitute for a full ephemeris when timing an eclipse to the minute.