Moon Phase Calculator
Calculate the moon phase and illumination for any date.
Last updated · View algorithm, constants and default inputs (JSON)
About this calculator
Select a calendar date to get an approximate phase and illumination from a fixed synodic-month model. Actual appearance depends on location, time and viewing conditions; this is not a live sky prediction.
Worked example
calculated with the default values below
Date 2026-10-31 Moon phase Waning Gibbous · Phase (0 = new moon) 5 · Illuminated 71 % · Moon age 20.12 days · Days to next full moon 24.18 days
General background references
Disclaimer
These calculators give general date results. Public holidays, working-day conventions and time-zone rules are set locally and change, so confirm against the official calendar for anything legally or contractually binding.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
a = ((d − d₀) ÷ 24 h) mod S; k = (1 − cos(2π a ÷ S)) ÷ 2; S = 29.530588853
- a
- moon age, days since new moon
- d
- query date (12:00 UTC)
- d₀
- new moon 2000-01-06 18:14 UTC
- k
- illuminated fraction
- S
- synodic month, days
Uses UTC date fields and a fixed reference new moon with a mean synodic month of 29.530588853 days. The result is an approximate phase estimate, not an astronomical ephemeris; years 1–99 are validated as written.
Frequently asked questions
Why does my moon age reset every 29.53 days instead of thirty?
The tool measures days since the reference new moon of 6 January 2000, 18:14 UTC, then takes the remainder modulo the synodic month of 29.530588853 days, not 30. So the Moon age wraps just before 29.53 days and the Illuminated percentage follows 1 minus cosine of 2 pi times fraction over 2, hitting 100 percent at full moon and 0 at new. The Days to next full moon counts forward from the current age to the 0.5 point of the cycle.