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Astronomy · Solar System

Moon Phase Calculator

Find the Moon phase, illumination, and lunar age for any calendar date.

Moon phase

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.

illumination = (1 − cos(2π · age ÷ 29.53)) ÷ 2

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. 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. 2
    Subtract the reference new moon. 2460334.5 − 2451550.1 = 8784.4 days since 6 Jan 2000.
  3. 3
    Take the remainder over the synodic month. 8784.4 mod 29.530588853 ≈ 13.8 days — the Moon age.
  4. 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.

PhaseApprox. age (days)Illumination
New Moon0≈ 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.

What is a synodic month?
A synodic month is the average time from one new moon to the next — about 29.530588853 days. It is longer than the Moon’s orbital period around Earth (the sidereal month, ≈27.3 days) because Earth also moves along its orbit, so the Moon must travel a little further to line up with the Sun again.
How accurate is this moon phase calculator?
It uses the average synodic month, so the phase name is dependable and the Moon age and illumination are typically accurate to within about a day. It ignores orbital perturbations — the elliptical orbit and the Sun’s pull — that shift the true new or full moon by up to roughly a day from the mean.
What is the difference between a waxing and waning moon?
A waxing moon is growing brighter, from new toward full, with the lit side on the right as seen from the Northern Hemisphere. A waning moon is shrinking, from full back toward new, lit on the left. “Crescent” means less than half lit; “gibbous” means more than half.
What does the illumination percentage mean?
It is the fraction of the Moon’s visible disc that is sunlit — 0% at new moon, about 50% at the quarters, and 100% at full moon. It is computed as (1 − cos(2π × age ÷ 29.53)) ÷ 2, so it rises and falls smoothly through the cycle rather than in steps.
What is the Moon age?
The Moon age is the number of days since the last new moon, from 0 up to about 29.53. It is the remainder when the days since a reference new moon are divided by the synodic month, and it determines which of the eight phases the Moon is in.
Why use a Julian Date to work out the phase?
A Julian Date is a continuous day count that ignores calendar quirks like leap years and month lengths, so subtracting one date from another gives an exact number of days. That makes it the natural way to measure how many days have passed since the reference new moon.
Does the phase look the same from both hemispheres?
The phase and illumination are the same everywhere on Earth at a given instant, but the orientation flips: a waxing crescent lit on the right in the Northern Hemisphere appears lit on the left from the Southern Hemisphere, because you are effectively viewing it upside down.