# Moon phase calculator

> The moon cycles through its phases every 29.5 days. Enter a date to see whether the moon is new, full, crescent, or gibbous — plus how much of its face is illuminated and when the.

Find the moon phase for any date — new moon, full moon, or anything in between. Shows phase name, illumination percentage, and the dates of the next new and full moons.

**Interactive version:** https://onlinecalculator.me/date-time/moon-phase/
**Category:** Date & Time

## Phase names

| Phase fraction | Name |
|----------------|------|
| 0 – 0.0625 | New Moon |
| 0.0625 – 0.1875 | Waxing Crescent |
| 0.1875 – 0.3125 | First Quarter |
| 0.3125 – 0.4375 | Waxing Gibbous |
| 0.4375 – 0.5625 | Full Moon |
| 0.5625 – 0.6875 | Waning Gibbous |
| 0.6875 – 0.8125 | Last Quarter |
| 0.8125 – 1 | Waning Crescent |

## Formula

```
daysSinceNewMoon = JD(date) − 2451550.259
phase = (daysSinceNewMoon mod 29.53058867) / 29.53058867
illumination = 0.5 × (1 − cos(2π × phase))
```

The reference JD 2451550.259 corresponds to the known new moon on January 6, 2000 at 18:14 UTC (source: US Naval Observatory).

## Worked example

**Date:** January 20, 2000 (Full Moon)

Days since Jan 6 new moon ≈ 14.77 → phase ≈ 0.5 → Full Moon, illumination ≈ 100%.

## Notes

- All calculations use Julian Day arithmetic — the same system used in professional astronomy.
- The next new/full moon dates are approximate (±1 day) due to the Moon's variable orbital speed.
- The phase shown is based on noon UTC for the chosen date.

## Frequently asked questions

### How is the moon phase calculated?

The calculator measures days elapsed since a known new moon (January 6, 2000 at 18:14 UTC) and divides by the synodic period of 29.53058867 days. The remainder, expressed as a fraction of the cycle, gives the current phase.

### What is the synodic period?

The synodic period is the time between two successive new moons as seen from Earth — 29.53058867 days on average. It differs from the sidereal period (27.32 days) because Earth also moves around the Sun during that time.

### How accurate is this calculator?

It is accurate to within a day for casual purposes. The synodic period varies slightly due to the Moon's elliptical orbit. For precise predictions, use an ephemeris.

### What does illumination mean?

Illumination is the fraction of the Moon's visible face that is lit by the Sun. At new moon it is 0%; at full moon it is 100%. The formula is 0.5 × (1 − cos(2π × phase)).

### How do I find the next full moon?

The "Next full moon" field shows the approximate date of the next full moon from your selected date. For the current date, leave the date picker on today.

## Sources

- [Lunar phase](https://en.wikipedia.org/wiki/Lunar_phase) — Wikipedia
- [Dates of Primary Phases of the Moon](https://aa.usno.navy.mil/data/MoonPhases) — U.S. Naval Observatory

## Related calculators

- [Julian date converter](https://onlinecalculator.me/date-time/julian-date/) — Convert Gregorian dates to Julian Day Numbers used in lunar calculations.
- [Sunrise and sunset calculator](https://onlinecalculator.me/date-time/sunrise-sunset/) — Find sunrise, sunset, and twilight times for any location and date.
- [Date difference calculator](https://onlinecalculator.me/date-time/date-difference/) — Find the exact number of days between two dates.
- [Countdown calculator](https://onlinecalculator.me/date-time/countdown/) — Count down to any future date or event.
- [Days until holiday](https://onlinecalculator.me/date-time/days-until-holiday/) — See how many days remain until every major holiday.

---

Part of [onlinecalculator.me](https://onlinecalculator.me/) — free calculators that run entirely in your browser.
Machine-readable index: https://onlinecalculator.me/llms.txt