The Moon Phase Calculator

The formula this calculator uses

age = (JDN - epoch) mod 29.530588853

JDN

Julian Day Number of the date at midnight

epoch

Julian Day Number of a reference new moon

age

Days elapsed since the most recent new moon

f

Phase fraction, from 0 at new moon to 0.5 at full moon

illumination

Fraction of the visible disc lit by the Sun

How to check the result by hand

1. 1

   Convert the date to a Julian Day Number

   The Julian Day Number is a single running count of days, which is what makes a repeating cycle easy to handle. The date 18 October 2026 has a Julian Day Number of 2461332. Using the local date rather than the date at Greenwich shifts the result slightly.

2. 2

   Subtract the reference new moon

   Take the Julian Day Number of a known new moon, such as 2451550.1 for 6 January 2000, away from the date in question. For 18 October 2026 that gives 9781.9 days since the reference new moon.

3. 3

   Reduce modulo the synodic month

   Divide by 29.530588853 and keep the remainder. 9781.9 days is 331 whole lunar months plus 7.2751 days, so the Moon is 7.2751 days old. The whole months are discarded because the cycle repeats.

4. 4

   Divide the age by the cycle length

   7.2751 divided by 29.530588853 is 0.2464, a phase fraction just short of the 0.25 that marks first quarter. The fraction, not the age, is what the phase names and the illumination are derived from.

5. 5

   Convert the fraction to an illuminated percentage

   Multiply the fraction by a full turn and take one minus the cosine of that angle, halved. A fraction of 0.2464 gives about 48.86 percent illuminated, which rounds to the familiar half-lit first quarter Moon.