Free Moon Phase Calculator
Estimate the Moon's illumination fraction and phase from the number of days since the last known new moon.
days
Illumination (%)
50.0 %
Phase (0-1 cycle)0.2499
Illumination (%) vs Days Since New Moon
Moon Phase Estimation
The synodic month (new moon to new moon) averages 29.53 days.
Illumination Formula
Illumination = (1 - cos(2π × d / 29.53)) / 2
where d = days since last new moon. This gives 0% at new moon, 50% at first/third quarter, and 100% at full moon.
Phase names: 0-1.85 days = New, 1.85-7.38 = Waxing Crescent, 7.38 = First Quarter, 7.38-14.76 = Waxing Gibbous, 14.76 = Full, etc.
Example Calculation
7.38 days after new moon (first quarter).
- 01Phase = 7.38 / 29.53 = 0.250 (25% of cycle)
- 02Illumination = (1 - cos(2π × 0.250)) / 2
- 03= (1 - cos(π/2)) / 2 = (1 - 0) / 2 = 50%
- 04First quarter: half the disc is lit.