doomath Calculator
Moon Phase & Lunar Cycle Calculator
Determine current moon phase, illumination percentage, age in synodic cycle, distance to Earth, and next full moon timing.
InputsChange a value to recalculate instantly
ResultUpdates as you type
PHYSICAL SIMULATOR
Lunar Phase & Orbital Mechanics Simulator
LIVE ENGINE 60FPS
Lunar Cycle & Illumination Phase
Real-time simulation of lunar illumination percentage, synodic age, and Earth-Moon orbital distance.
MOON
FORMULA & STEPSMoon Phase & Lunar Cycle Calculator — Mathematical Derivation & Steps
2 StepsSequential Calculation Breakdown
1
Phase Angle & Illumination Calculation
The fraction of the Moon disk illuminated by direct sunlight.
2
Orbital Distance & Apparent Diameter
Apparent visual angular diameter in minutes of arc.
λ DooMathWork with this calculation
Local · deterministic · optionalQuick mathNatural-language-style shortcuts for deterministic arithmetic.
Calculator guide
How to use the Moon Phase & Lunar Cycle Calculator
Determine current moon phase, illumination percentage, age in synodic cycle, distance to Earth, and next full moon timing.
01Set inputsChoose values, units and assumptions.
02Apply the modelMoon Age: A = (JD - 2451549.5) mod 29.53059; Illumination: k = (1 + cos(ψ)) ÷ 2
03Read the resultCheck the output against the assumptions before using it.
What this calculator does
Computes the moon synodic phase angle and fractional illumination from the astronomical Julian day. Calculates lunar distance between perigee and apogee.
Formula & method
Moon Age: A = (JD - 2451549.5) mod 29.53059; Illumination: k = (1 + cos(ψ)) ÷ 2
Assumptions & notes
- The mean synodic lunar month is 29.530589 days.
- Libration allows approximately 59% of the lunar surface to be visible from Earth over time.
- Tidal forces follow an inverse-cube relationship with lunar distance.