# Moon phase calculator

> Moon phase for any date and time: the phase name, percentage illuminated and moon age in days, with the dates of the next new and full moons.

Interactive version: https://www.calcopenly.com/earth/moon-phase-calculator
Subject: Weather, earth and fun calculators

The Moon's phase follows from two things: the time since the last true new moon (its age) and the phase angle between the Sun and Earth as seen from the Moon, which sets the lit fraction k = (1 + cos i)/2. New, quarter and full moon instants come from Jean Meeus's lunar series, which reproduce all 50 US Naval Observatory phase times for 2026 to within 0.8 minutes.

Observers, photographers and anglers use it to plan around dark skies or a full moon. At 12:00 UT on 15 January 2026 the Moon was a waning crescent, 10% lit and 26.43 days old, with the next new moon 3.33 days away.

A phase name covers 12 hours either side of the exact instant, so a calendar that labels whole days can differ by one day. Times are shown in the zone you pick, and the Southern Hemisphere option mirrors which side of the disk is lit.

## Inputs

- **Date**
- **Time**
- **Time zone** (options: This device's time zone, UTC, Honolulu, Anchorage, Los Angeles, Denver, Phoenix, Chicago, Mexico City, New York, Toronto, Bogotá, Halifax, St John's, Santiago, São Paulo, Buenos Aires, Reykjavík, London, Dublin, Lisbon, Lagos, Casablanca, Paris, Berlin, Madrid, Rome, Amsterdam, Stockholm, Oslo, Johannesburg, Cairo, Athens, Helsinki, Kyiv, Istanbul, Nairobi, Moscow, Riyadh, Tehran, Dubai, Karachi, India (Kolkata), Kathmandu, Dhaka, Bangkok, Jakarta, Singapore, China (Shanghai), Hong Kong, Manila, Perth, Seoul, Tokyo, Adelaide, Brisbane, Sydney, Auckland, Chatham Islands, Kiritimati)
- **Seen from** (options: Northern hemisphere, Southern hemisphere)

## Results

- Phase — main result
- Illuminated
- Age (days since new moon) (days)
- Waxing or waning
- Days to next new moon (days)
- Days to next full moon (days)
- Next new moon
- Next full moon

## Formula

$$
k = \frac{1 + \cos i}{2},\quad i \approx 180^\circ - D - 6.289^\circ \sin M' + 2.100^\circ \sin M - \dots
$$

## Worked examples

### Full moon of the 3 March 2026 lunar eclipse

- Date: 2026-03-03
- Time: 12:00
- Time zone: UTC
- **Phase: Full moon**
- **Illuminated: 100.0%**
- **Age (days since new moon): 14.00 days**
- Checked against: USNO API: full moon 2026-03-03 11:38 UT, 100% illuminated at noon; previous new moon 2026-02-17 12:01 UT → age 13.999 days (Python datetime)

### Waning crescent in mid-January 2026

- Date: 2026-01-15
- Time: 12:00
- Time zone: UTC
- **Phase: Waning crescent**
- **Illuminated: 10.0%**
- **Age (days since new moon): 26.43 days**
- **Days to next new moon: 3.33 days**
- **Days to next full moon: 17.42 days**
- Checked against: USNO API: 10% illuminated at 12:00 UT; new moons 2025-12-20 01:43 and 2026-01-18 19:52 UT, full moon 2026-02-01 22:09 UT (differences by Python datetime)

### Hours before the 12 August 2026 solar eclipse (new moon)

- Date: 2026-08-12
- Time: 12:00
- Time zone: UTC
- **Phase: New moon**
- **Illuminated: 0.0%**
- **Age (days since new moon): 29.10 days**
- Checked against: USNO API: new moon 2026-08-12 17:37 UT, 0% illuminated; previous new moon 2026-07-14 09:43 UT → age 29.095 days

### Just after first quarter

- Date: 2026-01-26
- Time: 12:00
- Time zone: UTC
- **Phase: First quarter**
- **Illuminated: 54.0%**
- **Age (days since new moon): 7.67 days**
- Checked against: USNO API: first quarter 2026-01-26 04:47 UT (7.2 h earlier), 54% illuminated at noon; new moon 2026-01-18 19:52 UT → age 7.672 days

### Precise age check (tight tolerance)

- Date: 2026-01-15
- Time: 12:00
- Time zone: UTC
- **Age (days since new moon): 26.43 days**
- **Days to next new moon: 3.33 days**
- Checked against: Python datetime from USNO times: 2026-01-15 12:00 − 2025-12-20 01:43 = 26.4285 d; to 2026-01-18 19:52 = 3.3278 d (USNO times are rounded to the minute)

## Questions

### How long is a lunar cycle?

The mean synodic month, from one new moon to the next, is 29.530589 days, about 29 days 12 hours 44 minutes. Single lunations vary because the Moon's orbit is elliptical: the same Meeus series used here gives lengths between 29.27 and 29.83 days for every lunation from 1900 to 2100.

### Why do moon calendars give different dates for the full moon?

The full moon is a single instant, so its calendar date depends on the time zone. The full moon of December 2026 is at 01:28 UT on 24 December (USNO), which is still 23 December at 20:28 in New York. Enter your own time zone to see the date and time that apply where you are.

### What is a blue moon?

The common definition is the second full moon in one calendar month, which happens because the 29.5-day lunar cycle is shorter than most months. 31 May 2026 was one: USNO lists full moons at 17:23 UT on 1 May and 08:45 UT on 31 May. The older almanac definition is the third of four full moons in an astronomical season.

### Is the Moon waxing or waning?

It is waxing from new moon to full moon, when the lit fraction grows each night, and waning from full back to new. Each half lasts about 14.8 days on average. In the Northern Hemisphere a waxing moon is lit on the right; south of the equator the picture is mirrored, so it is lit on the left.

### How much of the Moon is lit at first quarter?

About 50%. The name refers to the Moon having travelled a quarter of its orbit since new moon, not to the lit area. The lit fraction passes 50% within hours of first and last quarter: at 12:00 UT on 26 January 2026, 7.2 hours after first quarter, it was 54% (USNO).

### How accurate is the moon phase calculator?

Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 5 worked examples whose answers come from independent sources; for example, “Full moon of the 3 March 2026 lunar eclipse” is checked against USNO API: full moon 2026-03-03 11:38 UT, 100% illuminated at noon; previous new moon 2026-02-17 12:01 UT → age 13.999 days (Python datetime).

### Where does the method come from?

J. Meeus, Astronomical Algorithms, 2nd ed. (1998), ch. 48 (illuminated fraction) and ch. 49 (phases of the Moon); US Naval Observatory — Phases of the Moon (cross-check).

## Sources

- J. Meeus, Astronomical Algorithms, 2nd ed. (1998), ch. 48 (illuminated fraction) and ch. 49 (phases of the Moon)
- [US Naval Observatory — Phases of the Moon (cross-check)](https://aa.usno.navy.mil/data/MoonPhases)